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sm_N completely factorized smallest Sm with unknown factors Sm with unknown factors Sm is prime (smallest one > Sm344869 ref. E. Weisstein)!

Prefatory Notes & Sources

In the table below you'll find all the prime factors of the concatenation
of numbers from 1 up to n.
These numbers are called  Smarandache Concatenated Numbers.

The first one with an unknown prime factor is when n = 124.
If there is a breaktrough in partially or completely factorising Sm124, please let me know,
so that I can update the list.

For the factorization I also followed the sources from
Micha Fleuren, Smarandache factors
Hans Havermann, Factorization of Smarandache Concatenated Numbers, Sm-n (n < 84)

Other subject related sources on the web

Smarandache factors by Micha Fleuren
Primes by Listing by Carlos Rivera
Consecutive Number Sequences by Eric W. Weisstein
Smarandache Sequences by Eric W. Weisstein
Smarandache Prime by Eric W. Weisstein
List of factors of the Reversed Smarandache Concatenated Numbers by Patrick De Geest

Book sources

“Some Notions and Questions in Number Theory”, by C.Dumitrescu and V.Seleacu, Glendale, AZ:Erhus University Press, 1994.
(communicated to me by Marin Petrescu (email) from Bucharest)

“CRC Concise Encyclopedia of Mathematics”, by Eric W. Weisstein, CRC Press, Boca Raton, Florida, 1998.
(communicated to me by M.L. Perez (email))

OEIS entries (some sequences for illustration purpose)

A007908 - Concatenation of the numbers from 1 to n.
A019519 - Concatenate odd numbers.
A046460 - Number of prime factors of concatenation of numbers from 1 up to n, with multiplicity.
A046461 - Numbers n such that concatenation of numbers from 1 to n is a semiprime.
A046462 - Concatenation of numbers from 1 to a(n) has exactly 3 prime factors, with multiplicity.
A046463 - Concatenation of numbers from 1 to a(n) has exactly 4 prime factors, with multiplicity.
A046464 - Concatenation of numbers from 1 to a(n) has exactly 5 prime factors, with multiplicity.
A046465 - Concatenation of numbers from 1 to a(n) has exactly 6 prime factors, with multiplicity.
A046466 - Concatenation of numbers from 1 to a(n) has exactly 7 prime factors, with multiplicity.
A046467 - Concatenation of numbers from 1 to a(n) has exactly 8 prime factors, with multiplicity.
A046468 - Concatenation of numbers from 1 to a(n) has exactly 9 prime factors, with multiplicity.
A048342 - Numbers n such that the concatenation of the numbers 1, 2, ..., n is a product of distinct primes.
A050675 - Numbers n such that concatenation of numbers from 1 to n is nonsquarefree.
A050676 - Let b(n) = number of prime factors (with multiplicity) of concatenation of numbers from 1 to n; sequence gives smallest number m with b(m) = n.
A053067 - (n) is the concatenation of next n numbers (omit leading 0's).
A066811 - Numbers k such that the concatenation of odd numbers from 1 to k is a prime.
A089987 - Primes in the concatenation of consecutive numbers beginning with 2.
A105311 - a(n) = n concatenations of numbers from 1 to n, concatenated.
A241569 - Primes of the form: (concatenation of first n positive integers) + 1.
A241570 - Primes of the form: (concatenation of first n positive integers) – 1.
A259937 - Concatenation of the numbers from 1 to n with numbers from n down to 1.
A262299 - Let S(n) denote the sequence formed by concatenating the decimal numbers 1,2,3,..., omitting n; a(n) is the smallest prime in S(n), or -1 if no term in S(n) is prime.
A262300 - Let S(n,k) denote the number formed by concatenating the decimal numbers 1,2,3,...,k, but omitting n; a(n) is the smallest k for which S(n,k) is prime, or -1 if no term in S(n,*) is prime.
A262571 - Concatenation of the numbers from 2 to n.
A262577 - Concatenation of the numbers from 1 to n but omitting 7.
A279610 - a(n) = concatenate n consecutive integers, starting with the last number of the previous batch.

PrimeForm or PFGW

To calculate the length of a Smarandache number in PrimeForm you just enter at the prompt
pfgw64 -od -f0 -q"len(Sm(119))"
For the reversed Smarandache number you type
pfgw64 -od -f0 -q"len(Smr(119))"

Some Factorization Websites

Messages

[ April 25, 2015 ]
Stephen Tucker's (email) search for prime Smarandache numbers !

Dear Patrick,
I have found your list of Smaradache factors and noticed that no prime Smarandache number
has been found yet. Well, I decided to try looking for one.
Using Dario Alpern's ECM Factorizing applet, (and software I wrote myself to generate the numbers),
I have discovered that there are no prime Smarandache numbers less than Sm2659.
When I tried using Dario's applet to factorize Sm2659 (which, by the way, has no factors less than
or equal to 39989) the applet's attempt to start the Prime Check routine stalled.
I tried using it to check Sm2713, but the same thing happened again.
Dario's website does stipulate a maximum length of input number of 10000 digits. However, Sm2659
is "only" 9529 digits long, so perhaps his stated limit of 10000 is rounded up.
After a brief search on the web, I haven't discovered anything about prime Smaradanche numbers.
I wonder if it could be that a Smaradanche number cannot be prime.

Hope this is of interest.

Yours,
Stephen Tucker (UK).

Eric Weisstein [ http://mathworld.wolfram.com/ConsecutiveNumberSequences.html ]
wrote he extended the search up to 38712 terms which is
quite ahead of your Sm2659. He did find a probable prime for
the reversed case though (Rsm37765).

Note Primeform with the program PFGW64.EXE has a built-in command
Sm(x) and Smr(x) to search for (probable) primes directly.
I did a run up to Sm(10000) and found indeed none. For larger
values one needs a faster computer than I have at the moment.
So there is still opportunity to detect the first PRP Sm !

[ May 20, 2008 ]
Greg Childers (email) factorized Sm99 ! [ go to entry ]

Hi Patrick,

I finally got around to factoring Sm99 by SNFS. As for Sm94, I used
the GGNFS lattice siever and msieve for the postprocessing. The factors are

P65: 37726668883887938032416757819314355053940153680075342644295667759

P107: 14627910783072606795565990651314126145674770336615677946549896262532933945988541999815567058347827465728809

Greg

[ December 9, 2007 ]
Greg Childers (email) factorized Sm94 ! [ go to entry ]

Hi Patrick,

Here are the factors of Sm94. This was completed using SNFS.
GGNFS was used for the sieving and msieve for the post-processing.

p79: 1825097233762709447432521941926649289213154260264910537140594516431173070300371

p82: 2674525573684858697560701870658348933916102325593721165422426453989766526938215889

Greg

[ June 8, 2006 ]
Sean A. Irvine (email)

Excellent work! (reg. Sm98 by Ph. Strohl)

Sm94 is still struggling. My yield has dropped below 1 and I've sieved
to special-q 70M already, but still don't have enough relations.

S.

[ June 6, 2006 ]
Philippe Strohl (email)

Hi Patrick !
I have factorized the remaining part of the 98th Smarandache
concatenated number. It was a 126 digits composite.
I have obtained it with ggnfs (a wonderful program : I have done it with
a common laptop computer with "only" 512 megs of ram and a 1.4 GHz
celeron M in two weeks).

the results :
N = 709891330215674922888729762564179876071621230485156504316706784486089628388958197669654729613064737223993515869067455247541707
( 126 digits)
Divisors found:
r1=3588472635471667861938967869443938442910813342994227048889 (pp58)
r2=197825482406769698151783117995020967519766027202915861687264259155363 (pp69)
Version: GGNFS-0.77.1-20060513-pentium-m
(prp verified prime with apr-cl)

Thanks for your site and for keeping tracks of our work.
Best regards.

Philippe Strohl

[ September 11, 2005 ]
Sean A. Irvine (email)

The next two have finished:

Sm87 C145 =
(p51) * (p95)
by SNFS, 14 days
Sm88 C153 =
(p42) * (p51) * (p61)
by GNFS, 8 hours

Sm90 looks like it will have to be SNFS since ECM has failed
to find a factor.

Regards,
Sean.

[ August 29, 2005 ]
Philippe Strohl (email)

Hi Patrick !
Thanks for accepting my "colouring" idea ! I am very pleased !

I should report you this 39 digits factor for Sm98 (Partial factorization):

Sm98* 2.3^2.23.37.199
p16: 1495444452918817(MF)
c165: 270825497607069872452415496119443135107702791840293286471110488510
4768274391266695197120574357173627794391936143016235446328574795690351940341420
23605896434694145167

Line=16/32 Curves=47/1000 B1=1000000 factors=0
C165 Using B1=1000000, B2=839549780, polynomial Dickson(6), sigma=594918519
Step 1 took 28422ms
Step 2 took 18926ms
********** Factor found in step 2: 381502754125464943168932369122248696781
Found probable prime factor of 39 digits:
381502754125464943168932369122248696781

Composite cofactor
709891330215674922888729762564179876071621230485156504316706784486089628388958197669654729613064737223993515869067455247541707
has 126 digits

Thanks again.
Best regards.
Philippe Strohl

[ August 29, 2005 ]
Sean A. Irvine (email)

Here is the last part of Sm86:

10828687641092318839822035841363590407263202742239027773 (p56) *
1089075252400674157091531724111232381528208779232955680665273 (p61)
by GNFS, 2 days.

As before I'm now working on Sm87.

Sean.

[ August 28, 2005 ]
Sean A. Irvine (email) latest results.

Here are my latest results. Like I mentioned earlier
I expect to complete Sm86 today as well:

Sm83 C134
21875480270521598141087357354188092945840550359281483 (p53) *
3966169790267211790412249283896602109358687165012835285295541472324348526743126307 (p82)
by SNFS, 8 days

Sm85 C158 =
120549814855596987772827562271063563633851059 (p45) *
Using B1=11000000, sigma=1708124291
2112809210944968177871685727287164545437750155430310661 (p55) *
197843626412162026434764405036310959588059884460495810550047 (p60)
by GNFS, 1 day

Sm86 C154 =
718252229986396496762902999331863301257 (p39) * C116
Using B1=11000000, sigma=3414478964
C116 by GNFS nearly done

Sm87 C145 Sieving by SNFS started 2005-08-29.

Others with B1=1e6 (I have now completed 1000 curves with B1=1e6
on all Sm(n), n <= 200)

Sm114 8678622406220213516465050301044327
Sm159 45941358846148651407783221723920871719
Sm171 40202471819457246557501649563881337
Sm193 5167315927941164272437909427556797

Sean.

It seems that a fierce competition is going on. But to avoid
duplicate work and loose valuable cpu time I advice strongly
to make arrangements among yourselves!

[ August 28, 2005 ]
Philippe Strohl (email)

..., for example : the smallest unfactored Sm number is sm83
(unfactored) but I have factored last year Sm85 (involving a p45 found by
ecm) and Sm86 (with a p39 and a ggnfs on the remaining c115)... This
represents quite a large amount of cpu work. Sm84 factorization is still
known on M Fleuren page...

[ August 3, 2005 ]
Sean A. Irvine (email) completely factorized Sm78 ! [ go to entry ]

Sm78 C139 =
205155431830422787082756234197593935249202704547671264423 (p57) *
17403902113720391120287411398887911225298966708915583006414519403038472992542973083 (p83)
by GNFS (General Number Field Sieve), 9 days

Here is a bunch more factors for higher values which I have not seen
previously reported. All these were found with ECM B1=1e6.

Sm89 496118159817126721484175235476073
Sm89 26459905787227421825352754831024262009257.P64
Sm92 46731404628893905607210235741707
Sm93 19544056951015647623992763251

Sm95 244987542265129586458446183157595351.P141
Sm100 970447246795177523033247400823.P118
Sm106 95383501607400293616004374931
Sm106 54259599094002572583355411045946413
Sm108 132761751746390611923240080737166083.P161
Sm109 9943216978062352390003139833531
Sm114 2042059881000388200555074336219
Sm116 9787002048140152171263515060558503699.P198
Sm121 105299178204417486675841093021769.P214
Sm123 12347002211187670552593982429
Sm123 2829927788416784955921382453753
Sm125 295999706346724665505289
Sm137 144065103514544138702103468451
Sm148 8817212782626223819399721069204897.P254
Sm152 4103096315830350734534473515557
Sm152 12805089500421274253268517941967
Sm152 17815076027044127272632744936161.P205
Sm154 32063206397901252963254536935569
Sm159 11855111297257593607972759339201
Sm160 64603936118676024484144135734907
Sm162 22260247937572504750086047
Sm164 1039418554780603268384723777072953
Sm165 13183356310254866666237435750357.P328
Sm176 1011379313630785579015894871
Sm183 553245689211853052761209813199
Sm184 677008100402429325901609057.P342
Sm187 1080829169904060835770214147747.P411
Sm193 419908232491384495189
Sm195 165897663095213559529993681.P412
Sm198 14158849264684185910199571953

Further, after studying Backstrom's work on Rsm76 I am now able to generate
SNFS polynomials for all the remaining Sm numbers below 100. It would have
been much faster to do Sm78 by SNFS, but I had already started it before
working out how to apply SNFS to the number. It should be possible to complete
all values up to Sm(100) by SNFS, although a few will be quite difficult runs.

The next smallest unfactored number of this form is now Sm83 [ C134 ].

Sean.

[ November 18, 2004 ]
Sean A. Irvine (email) completely factorized Sm75 ! [ go to entry ]

It took him 13 days, by using GNFS.
Well done, congratulations for factoring Sm75(c133) into this p47 * p87 :
38824496309870038690197243565592769246963314017 (p47) *
219358378032318168161320006998916878634145966511629131235131312083699783021949850982403 (p87)

Next challenge is this composite factor of 139 digits of Sm78 :
3570505053674714753162296261527331568459971771942/
9181309659088118527251315326728064046015264067596/
03889145976969679985423963150530264526109

[ March 23, 2004 ]
Philippe Strohl (email) completely factorized Sm73 ! [ go to entry ]

Hello Patrick !

This mail to inform you that the factorization of the 73th concatenated smarandache number is now complete
with the discovery of a p46 by GMP-ECM...

Sm73 = 37907.p46.p87
p46: 1612352371081094864112011094480307952600705089
p87: 201992666185187831800817490810938117880341395186600971262233773863756955874363353778851
...
Sm74 factorization is known and the next composite to challenge is Sm75
with no factors expected below 35 digits...

Sm74 = 2.3.7.1788313.21565573.p20.p25.p31.p49
p20: 99014155049267797799
p25: 1634187291640507800518363(PZ)
p31: 1981231397449722872290863561307
p49: 2377534541508613492655260491688014802698908815817

Sm75* 3.5^2.193283.c133
c133:
851647853845481367839983983361331811035304896846801931077529055832/
3936344974946612980172082837107906069172212808249295700548030242851

The List of Sm Factors

 1 Sm1 = p1 [ Length = 1 ] unity 1
 12 Sm2 = (p1)^2 * p1 [ Length = 2 ] 2^2 * 3
 123 Sm3 = p1 * p2 [ Length = 3 ] semiprime 3 * 41
 1234 Sm4 = p1 * p3 [ Length = 4 ] semiprime 2 * 617
 12345 Sm5 = p1 * p1 * p3 [ Length = 5 ] 3 * 5 * 823
 123456 Sm6 = (p1)^6 * p1 * p3 [ Length = 6 ] 2^6 * 3 * 643
 1234567 Sm7 = p3 * p4 [ Length = 7 ] semiprime 127 * 9721
 12345678 Sm8 = p1 * (p1)^2 * p2 * p5 [ Length = 8 ] 2 * 3^2 * 47 * 14593
 123456789 Sm9 = (p1)^2 * p4 * p4 [ Length = 9 ] 3^2 * 3607 * 3803
 12345678910 Sm10 = p1 * p1 * p10 [ Length = 11 ] 2 * 5 * 1234567891
 1234567891011 Sm11 = p1 * p1 * p2 * p2 * p3 * p6 [ Length = 13 ] 3 * 7 * 13 * 67 * 107 * 630803
 1234567...12 Sm12 = (p1)^3 * p1 * p4 * p10 [ Length = 15 ] 2^3 * 3 * 2437 * 2110805449
 1234567...13 Sm13 = p3 * p6 * p9 [ Length = 17 ] 113 * 125693 * 869211457
 1234567...14 Sm14 = p1 * p1 * p18 [ Length = 19 ] 2 * 3 * 205761315168520219
 1234567...15 Sm15 = p1 * p1 * p19 [ Length = 21 ] 3 * 5 * 8230452606740808761
 1234567...16 Sm16 = (p1)^2 * p10 * p13 [ Length = 23 ] 2^2 * 2507191691 * 1231026625769
 1234567...17 Sm17 = (p1)^2 * p2 * p4 * p18 [ Length = 25 ] 3^2 * 47 * 4993 * 584538396786764503
 1234567...18 Sm18 = p1 * (p1)^2 * p2 * p5 * p18 [ Length = 27 ] 2 * 3^2 * 97 * 88241 * 801309546900123763
 1234567...19 Sm19 = p2 * p2 * p2 * p3 * p4 * p18 [ Length = 29 ] 13 * 43 * 79 * 281 * 1193 * 833929457045867563
 1234567...20 Sm20 = (p1)^5 * p1 * p1 * p6 * p7 * p16 [ Length = 31 ] 2^5 * 3 * 5 * 323339 * 3347983 * 2375923237887317
 1234567...21 Sm21 = p1 * p2 * p2 * p2 * p3 * p3 * p6 * p18 [ Length = 33 ] 3 * 17 * 37 * 43 * 103 * 131 * 140453 * 802851238177109689
 1234567...22 Sm22 = p1 * p1 * p4 * p4 * p5 * p22 [ Length = 35 ] 2 * 7 * 1427 * 3169 * 85829 * 2271991367799686681549
 1234567...23 Sm23 = p1 * p2 * p3 * p32 [ Length = 37 ] 3 * 41 * 769 * 13052194181136110820214375991629
 1234567...24 Sm24 = (p1)^2 * p1 * p1 * p18 * p19 [ Length = 39 ] 2^2 * 3 * 7 * 978770977394515241 * 1501601205715706321
 1234567...25 Sm25 = (p1)^2 * p5 * p11 * p25 [ Length = 41 ] 5^2 * 15461 * 31309647077 * 1020138683879280489689401
 1234567...26 Sm26 = p1 * (p1)^4 * p5 * p7 * p12 * p18 [ Length = 43 ] 2 * 3^4 * 21347 * 2345807 * 982658598563 * 154870313069150249
 1234567...27 Sm27 = (p1)^3 * (p2)^2 * p4 * p5 * p32 [ Length = 45 ] 3^3 * 19^2 * 4547 * 68891 * 40434918154163992944412000742833
 1234567...28 Sm28 = (p1)^3 * p2 * p3 * p15 * p27 [ Length = 47 ] 2^3 * 47 * 409 * 416603295903037 * 192699737522238137890605091
 1234567...29 Sm29 = p1 * p3 * p20 * p26 [ Length = 49 ] 3 * 859 * 24526282862310130729 * 19532994432886141889218213
 1234567...30 Sm30 = p1 * p1 * p1 * p2 * p8 * p18 * p23 [ Length = 51 ] 2 * 3 * 5 * 13 * 49269439 * 370677592383442753 * 17333107067824345178861
 1234567...31 Sm31 = p2 * p10 * p42 [ Length = 53 ] 29 * 2597152967 * 163915283880121143989433769727058554332117
 1234567...32 Sm32 = (p1)^2 * p1 * p1 * p23 * p30 [ Length = 55 ] 2^2 * 3 * 7 * 45068391478912519182079 * 326109637274901966196516045637
 1234567...33 Sm33 = p1 * p2 * p3 * p4 * p18 * p31 [ Length = 57 ] 3 * 23 * 269 * 7547 * 116620853190351161 * 7557237004029029700530634132859
 1234567...34 Sm34 = p1 * p58 [ Length = 59 ] semiprime 2 * 6172839455055606570758085909601061116212631364146515661667
 1234567...35 Sm35 = (p1)^2 * p1 * p3 * p3 * p8 * p10 * p37 [ Length = 61 ] 3^2 * 5 * 139 * 151 * 64279903 * 4462548227 * 4556722495899317991381926119681186927
 1234567...36 Sm36 = (p1)^4 * (p1)^2 * p3 * p3 * p56 [ Length = 63 ] 2^4 * 3^2 * 103 * 211 * 39448709943503776711542648338171477043440283875433388943
 1234567...37 Sm37 = p2 * p5 * p7 * p52 [ Length = 65 ] 71 * 12379 * 4616929 * 3042410911077206144807069396988766146557218727107817
 1234567...38 Sm38 = p1 * p1 * p23 * p43 [ Length = 67 ] 2 * 3 * 86893956354189878775643 * 2367958875411463048104007458352976869124861
 1234567...39 Sm39 = p1 * p2 * p3 * p4 * p25 * p36 [ Length = 69 ] 3 * 67 * 311 * 1039 * 6216157781332031799688469 * 305788363093026251381516836994235539
 1234567...40 Sm40 = (p1)^2 * p1 * p4 * p5 * p6 * p10 * p20 * p26 [ Length = 71 ] 2^2 * 5 * 3169 * 60757 * 579779 * 4362289433 * 79501124416220680469 * 15944694111943672435829023
 1234567...41 Sm41 = p1 * p3 * p6 * p8 * p56 [ Length = 73 ] 3 * 487 * 493127 * 32002651 * 53545135784961981058419604998638516483529257158438201753
 1234567...42 Sm42 = p1 * p1 * p3 * p3 * p11 * p25 * p34 [ Length = 75 ] 2 * 3 * 127 * 421 * 22555732187 * 4562371492227327125110177 * 3739644646350764691998599898592229
 1234567...43 Sm43 = p1 * p2 * p3 * p72 [ Length = 77 ] 7 * 17 * 449 * 231058353953907153927797941629430896528705484237484443924582239474910453
 1234567...44 Sm44 = (p1)^3 * (p1)^2 * p26 * p52 [ Length = 79 ] 2^3 * 3^2 * 12797571009458074720816277 * 1339846151380678925030581935625950075102697197563351
 1234567...45 Sm45 = (p1)^2 * p1 * p1 * p2 * p3 * p4 * p13 * p18 * p41 [ Length = 81 ] 3^2 * 5 * 7 * 41 * 727 * 1291 * 2634831682519 * 379655178169650473 * 10181639342830457495311038751840866580037
 1234567...46 Sm46 = p1 * p2 * p3 * p9 * p18 * p25 * p28 [ Length = 83 ] 2 * 31 * 103 * 270408101 * 374332796208406291 * 3890951821355123413169209 * 4908543378923330485082351119
 1234567...47 Sm47 = p1 * p4 * p6 * p22 * p53 [ Length = 85 ] 3 * 4813 * 679751 * 4626659581180187993501 * 27186948196033729596487563460186407241534572026740723
 1234567...48 Sm48 = (p1)^2 * p1 * p3 * p4 * p7 * p29 * p46 [ Length = 87 ] 2^2 * 3 * 179 * 1493 * 1894439 * 15771940624188426710323588657 * 1288413105003100659990273192963354903752853409
 1234567...49 Sm49 = p2 * p3 * p7 * p10 * p23 * p47 [ Length = 89 ] 23 * 109 * 3251653 * 2191196713 * 53481597817014258108937 * 12923219128084505550382930974691083231834648599
 1234567...50 Sm50 = p1 * p1 * (p1)^2 * p2 * p3 * p5 * p18 * p20 * p44 [ Length = 91 ] 2 * 3 * 5^2 * 13 * 211 * 20479 * 160189818494829241 * 46218039785302111919 * 19789860528346995527543912534464764790909391
 1234567...51 Sm51 = p1 * p20 * p73 [ Length = 93 ] 3 * 17708093685609923339 * 2323923950500978408934946776574079545611397611995364705071565292612305003
 1234567...52 Sm52 = (p1)^7 * p17 * p76 [ Length = 95 ] 2^7 * 43090793230759613 * 2238311464092386636761884511894978048448617178182150344531477542781856216843
 1234567...53 Sm53 = (p1)^3 * (p1)^3 * p18 * p76 [ Length = 97 ] 3^3 * 7^3 * 127534541853151177 * 1045271879581348729278017817925065799872257805888381045072615907010178634849
 1234567...54 Sm54 = p1 * (p1)^6 * p2 * p3 * p4 * p5 * p11 * p22 * p51 [ Length = 99 ] 2 * 3^6 * 79 * 389 * 3167 * 13309 * 69526661707 * 8786705495566261913717 * 107006417566370797549761092803112128112769421435739
 1234567...55 Sm55 = p1 * p9 * p15 * p22 * p55 [ Length = 101 ] 5 * 768643901 * 641559846437453 * 1187847380143694126117 * 4215236719202000513320239996510510828557825033460062191
 1234567...56 Sm56 = (p1)^2 * p1 * p25 * p77 [ Length = 103 ] 2^2 * 3 * 4324751743617631024407823 * 23788800764365032854813369830458732886158417401021113465643479155975828316681
 1234567...57 Sm57 = p1 * p2 * p8 * p13 * p37 * p47 [ Length = 105 ] 3 * 17 * 36769067 * 2205251248721 * 2128126623795388466914401931224151279 * 14028351843196901173601082244449305344230057319
 1234567...58 Sm58 = p1 * p2 * p31 * p75 [ Length = 107 ] 2 * 13 * 1448595612076564044790098185437 * 327789067063631145720134335581588856152921479945230066396717484857630796759
 1234567...59 Sm59 = p1 * p18 * p36 * p55 [ Length = 109 ] 3 * 340038104073949513 * 324621819487091567830636828971096713 * 3728107520554143574058126525447653708074390492098041537
 1234567...60 Sm60 = (p1)^3 * p1 * p1 * p2 * p3 * p104 [ Length = 111 ] 2^3 * 3 * 5 * 97 * 157 * 67555753880267981819314968257940564232852139165917171861439543181780049107204700168947673874146559500327
 1234567...61 Sm61 = p8 * p14 * p92 [ Length = 113 ] 10386763 * 35280457769357 * 33689963756771087787406890988794422071942750389483226687410462898596940470571223420915460371
 1234567...62 Sm62 = p1 * (p1)^2 * p4 * p6 * p7 * p34 * p64 [ Length = 115 ] 2 * 3^2 * 1709 * 329167 * 1830733 * 9703956232921821226401223348541281 * 6862941251271421600892952202464376235224342144596167046191804311
 1234567...63 Sm63 = (p1)^2 * p11 * p43 * p63 [ Length = 117 ] 3^2 * 17028095263 * 2435984189933032657913735712547671618367909 * 330698276590517405413770500371046766676563523569978590938716221
 1234567...64 Sm64 = (p1)^2 * p1 * p2 * p2 * p3 * p6 * p19 * p29 * p60 [ Length = 119 ] 2^2 * 7 * 17 * 19 * 197 * 522673 * 1072389445090071307 * 20203723083803464811983788589 * 611891180337745942599768541236768900814521123060392220304537
 1234567...65 Sm65 = p1 * p1 * p2 * p5 * p43 * p70 [ Length = 121 ] 3 * 5 * 31 * 83719 * 8018741962917674781000851595476715337223177 * 3954865825608609239925917139441010044747553878722812487568124023324127
 1234567...66 Sm66 = p1 * p1 * p1 * p5 * p6 * p36 * p36 * p39 [ Length = 123 ] 2 * 3 * 7 * 20143 * 971077 * 319873117219722504963051951872747251 * 927600480728565729398211282118577179 * 506464674142683362314480915373647544917
 1234567...67 Sm67 = p3 * p18 * p105 [ Length = 125 ] 397 * 183783139772372071 * 169207186381096030569641287629182352063847752831832860300985727686482291228260812667458777140342739211041
 1234567...68 Sm68 = (p1)^4 * p1 * p2 * p9 * p10 * p50 * p56 [ Length = 127 ] 2^4 * 3 * 23 * 764558869 * 1811890921 * 16210201583355429120740178111425145802012035286597 * 49798299077316075944525952275152868666920234906076151289
 1234567...69 Sm69 = p1 * p2 * p2 * p22 * p24 * p32 * p49 [ Length = 129 ] 3 * 13 * 23 * 8684576204660284317187 * 281259608597535749175083 * 15490495288652004091050327089107 * 3637485176043309178386946614318767365372143115591
 1234567...70 Sm70 = p1 * p1 * p7 * p24 * p41 * p60 [ Length = 131 ] 2 * 5 * 2411111 * 109315518091391293936799 * 11555516101313335177332236222295571524323 * 405346669169620786437208619979711016226055320437594464205451
 1234567...71 Sm71 = (p1)^2 * p2 * p4 * p31 * p95 [ Length = 133 ] 3^2 * 83 * 2281 * 7484379467407391660418419352839 * 96808455591058960266687738381050176698103277406505724847082994829643349780363432993640165860627
 1234567...72 Sm72 = (p1)^2 * (p1)^2 * p4 * p27 * p103 [ Length = 135 ] 2^2 * 3^2 * 5119 * 596176870295201674946617769 * 1123704769960650101739921630151581054522510738566183226239911321871780637830758881774623162921434662407
 1234567...73 Sm73 = p5 * p46 * p87 [ Length = 137 ] (by Philippe Strohl ) 37907 * 1612352371081094864112011094480307952600705089 * 201992666185187831800817490810938117880341395186600971262233773863756955874363353778851 Factor p46 Sm73 by GMP-ECM Sm73 = 37907.p46.p87 None of these factors could have been found by P-1 or P+1 with B1<10^14 and I was lucky enough to catch the p46 with a ECM B1 of 10^6. The group order of the curve is very smooth (B1=620227 and B2=1473569 are enough). 325683354264679693500307906698027336176043019186246110832678756888/ 805244789707561834881407263896785700945962383243895973215176272739 (132 digits) Using B1=2000000, B2=5000000, polynomial x^6, sigma=2799427343 Step 1 took 181065ms ********** Factor found in step 1: 1612352371081094864112011094480307952600705089 Found probable prime factor of 46 digits: 1612352371081094864112011094480307952600705089 Probable prime cofactor 201992666185187831800817490810938117880341395186600971262233773863756955874363353778851 has 87 digits (both proven prime by S. Tomabechi APR-CL part of p_1 program)
 1234567...74 Sm74 = p1 * p1 * p1 * p7 * p8 * p20 * p25 * p31 * p49 [ Length = 139 ] 2 * 3 * 7 * 1788313 * 21565573 * 99014155049267797799 * 1634187291640507800518363 * 1981231397449722872290863561307 * 2377534541508613492655260491688014802698908815817
 1234567...75 Sm75 = p1 * (p1)^2 * p6 * p47 * p87 [ Length = 141 ] (by Sean A. Irvine ) 3 * 5^2 * 193283 * 38824496309870038690197243565592769246963314017 * 219358378032318168161320006998916878634145966511629131235131312083699783021949850982403
 1234567...76 Sm76 = (p1)^3 * p18 * p27 * p97 [ Length = 143 ] 2^3 * 828699354354766183 * 213643895352490047310058981 * 8716407028594814374740596028898426313034395366012872513707917231855753694435270081076237925828389
 1234567...77 Sm77 = p1 * p24 * p24 * p39 * p58 [ Length = 145 ] 3 * 383481022289718079599637 * 874911832937988998935021 * 164811751226239402858361187055939797929 * 7442132227048590901854639419294226672231934035068486536423
 1234567...78 Sm78 = p1 * p1 * p2 * p6 * p57 * p83 [ Length = 147 ] (by Sean A. Irvine ) 2 * 3 * 31 * 185897 * 205155431830422787082756234197593935249202704547671264423 * 17403902113720391120287411398887911225298966708915583006414519403038472992542973083
 1234567...79 Sm79 = p2 * p3 * p20 * p24 * p29 * p74 [ Length = 149 ] 73 * 137 * 22683534613064519783 * 132316335833889742191773 * 35488612864124533038957177977 * 11589330059060921218833486882285427414280233987959540582909167514265308253
 1234567...80 Sm80 = (p1)^2 * (p1)^3 * p1 * p3 * p8 * p25 * p115 [ Length = 151 ] 2^2 * 3^3 * 5 * 101 * 10263751 * 1295331340195453366408489 * 1702600917839548328745392482587491026230318172323434581398602992701169952537157469971305061091390839579932352102383
 1234567...81 Sm81 = (p1)^3 * p3 * p30 * p119 [ Length = 153 ] 3^3 * 509 * 152873624211113444108313548197 * 58762581888644185603361112342786137599799640821735382180404307223995625796855706598141292123658134092320545833186103011
 1234567...82 Sm82 = p1 * p2 * p4 * p5 * p35 * p42 * p70 [ Length = 155 ] 2 * 29 * 4703 * 10091 * 12295349967251726424104854676730107 * 334523571229968373890203385137399026475051 * 1090461105551993653223776199179348475393504023636425991597284018461539
 1234567...83 Sm83 = p1 * p2 * p3 * p18 * p53 * p82 [ Length = 157 ] (by Sean A. Irvine ) 3 * 53 * 503 * 177918442980303859 * 21875480270521598141087357354188092945840550359281483 * 3966169790267211790412249283896602109358687165012835285295541472324348526743126307 by SNFS, 8 days
 1234567...84 Sm84 = (p1)^5 * p1 * p157 [ Length = 159 ] 2^5 * 3 * 1286008219803251368907934564500221065877631534197190762847328503894160459817025473591130156786722443288099853756419412985069550726116382682039247695813352379
 1234567...85 Sm85 = p1 * (p1)^2 * p45 * p55 * p60 [ Length = 161 ] (by Sean A. Irvine ) 5 * 7^2 * 120549814855596987772827562271063563633851059 * 2112809210944968177871685727287164545437750155430310661 * 197843626412162026434764405036310959588059884460495810550047 Sm85 C158 = 120549814855596987772827562271063563633851059 (p45) * Using B1=11000000, sigma=1708124291 2112809210944968177871685727287164545437750155430310661 (p55) * 197843626412162026434764405036310959588059884460495810550047 (p60) by GNFS, 1 day
 1234567...86 Sm86 = p1 * p1 * p2 * p7 * p39 * p56 * p61 [ Length = 163 ] (by Sean A. Irvine ) 2 * 3 * 23 * 1056149 * 718252229986396496762902999331863301257 * 10828687641092318839822035841363590407263202742239027773 * 1089075252400674157091531724111232381528208779232955680665273 Sm86 C154 = 718252229986396496762902999331863301257 (p39) * C116 Using B1=11000000, sigma=3414478964 10828687641092318839822035841363590407263202742239027773 (p56) * 1089075252400674157091531724111232381528208779232955680665273 (p61) by GNFS, 2 days.
 1234567...87 Sm87 = p1 * p1 * p9 * p10 * p51 * p95 [ Length = 165 ] (by Sean A. Irvine ) 3 * 7 * 231330259 * 4275444601 * 101784611215757903569658774280830604745279416597473 * 58398250025786270255235847423735930777973447337337804788906368149837276410666257137526766841721 Sm87 C145 = (p51) * (p95) by SNFS, 14 days.
 1234567...88 Sm88 = (p1)^2 * p14 * p42 * p51 * p61 [ Length = 167 ] (by Sean A. Irvine ) 2^2 * 12414068351873 * 462668377429470430246269302055630668010673 * 144494999796935291164027251780366969508458166480331 * 3718931833006826909360514481439595803175244655637881136348103 Sm88 C153= 462668377429470430246269302055630668010673 (p42) B1=11000000, sigma=1512552247 144494999796935291164027251780366969508458166480331 (p51) * 3718931833006826909360514481439595803175244655637881136348103 (p61) by GNFS, 8 hours
 1234567...89 Sm89 = (p1)^2 * p2 * p2 * p2 * p9 * p18 * p33 * p41 * p64 [ Length = 169 ] (by Sean A. Irvine ) 3^2 * 13 * 31 * 97 * 163060459 * 789841356493369879 * 496118159817126721484175235476073 * 26459905787227421825352754831024262009257 * 2075552579046417801880667285191357553672027185826871770761977511
 1234567...90 Sm90 = p1 * (p1)^2 * p1 * p4 * p6 * p7 * p67 * p87 [ Length = 171 ] (by Sean A. Irvine ) 2 * 3^2 * 5 * 1987 * 179827 * 2166457 * 5469640487155071172064105436159054827205011884517193846381587779057 * 323974513721871489318385733207245357406204798917206286895918649972193592038458818136011 Sm90 C154= (p67) * (p87) by SNFS, 32 days Submitted on Monday October 24, 2005 22:51
 1234567...91 Sm91 = p2 * p3 * p16 * p24 * p55 * p75 [ Length = 173 ] (by Sean A. Irvine ) 37 * 607 * 5713601747802353 * 100397446615566314002487 * 3581874457050057021838729610409482762969149632972915379 * 267535593139950330755907265689770024664090795106497661308268157342396003221 Sm91 C129= (p55) * (p75) by GNFS, 4 days Submitted on Monday October 24, 2005 22:51
 1234567...92 Sm92 = (p1)^3 * p1 * p5 * p32 * p65 * p72 [ Length = 175 ] (by Sean A. Irvine ) 2^3 * 3 * 75503 * 46731404628893905607210235741707 * 17357685121487530272314084020479969142526171001787819150223751641 * 839921864959969600234341350615454280584339900783049158479018433912354703 p32 by Sean A. Irvine Sm92 C137= (p65) * (p72) by GNFS, 9 days Submitted on Sunday January 22, 2006 21:28
 1234567...93 Sm93 = p1 * p2 * p4 * p10 * p29 * p52 * p82 [ Length = 177 ] (by Sean A. Irvine ) 3 * 73 * 1051 * 3298142203 * 19544056951015647623992763251 * 4886013639051371332965225321191263200785903705285317 * 1703057751798522700187996077196637285517155003415445664199429017748369723643706497 p29 by Sean A. Irvine Sm93 C133= (p52) * (p82) by GNFS, 5 days Submitted on Monday February 20, 2006 23:01
 1234567...94 Sm94 = p1 * p8 * p11 * p79 * p82 [ Length = 179 ] (by Greg Childers ) 2 * 12871181 * 98250285823 * 1825097233762709447432521941926649289213154260264910537140594516431173070300371 * 2674525573684858697560701870658348933916102325593721165422426453989766526938215889 Summary for Sm94(c160) = p79 * p82 The factorization was completed using SNFS. GGNFS was used for the sieving and msieve for the post-processing. Submitted on Sun, 9 Dec 2007 11:27
 1234567...95 Sm95 = p1 * p1 * p1 * p3 * p36 * p141 [ Length = 181 ] (by Sean A. Irvine ) 3 * 5 * 7 * 401 * 244987542265129586458446183157595351 * 119684333324585760380296925278736677052991667067598465535119086641122308977254652550763964697554302296677991161440001789403458655109609795769
 1234567...96 Sm96 = (p1)^2 * p1 * p2 * p5 * p175 [ Length = 183 ] 2^2 * 3 * 23 * 60331 * 7414218343605898007054904008539678229463872328651811494111562828507144051357405695052612835346584059319708614758837877621899193657692066488505067022654601125869790297498349041
 1234567...97 Sm97 = p2 * p183 [ Length = 185 ] semiprime 13 * 949667608470093318578167063015547864032712517561002409487257972106456954941803426651911500396348881197366045850894335742820591305439790288275136759985244833729682214530699379184227669
 1234567...98 Sm98 = p1 * (p1)^2 * p2 * p2 * p3 * p16 * p39 * p58 * p69 [ Length = 187 ] (by Philippe Strohl ) 2 * 3^2 * 23 * 37 * 199 * 1495444452918817 * 381502754125464943168932369122248696781 * 3588472635471667861938967869443938442910813342994227048889 * 197825482406769698151783117995020967519766027202915861687264259155363
 1234567...99 Sm99 = (p1)^2 * p5 * p12 * p65 * p107 [ Length = 189 ] (by Greg Childers ) 3^2 * 31601 * 786576340181 * 37726668883887938032416757819314355053940153680075342644295667759 * 14627910783072606795565990651314126145674770336615677946549896262532933945988541999815567058347827465728809 Summary for Sm99(c177) = p65 * p107 I finally got around to factoring Sm99 by SNFS. As for Sm94, I used the GGNFS lattice siever and msieve for the postprocessing. Submitted on Tue, 20 May 2008 4:35
 1234567...100 Sm100 = (p1)^2 * (p1)^2 * (p1)^3 * p4 * p7 * p10 * p20 * p30 * p118 [ Length = 192 ] (by Sean A. Irvine ) 2^2 * 5^2 * 7^3 * 8171 * 1065829 * 2824782749 * 20317177407273276661 * 970447246795177523033247400823 * 7420578382899399028284464392651452937744039836185355778662961413780805734369643748805299589898776112804950234221784569
 1234567...101 Sm101 = p1 * p4 * p21 * p61 * p109 [ Length = 195 ] (by Bob Backstrom ) 3 * 8377 * 799917088062980754649 * 1399463086740105394672913130945493026937913499238148790743003 * 4388325012701307167526588635576876644759452668196597056747408345988387366211263062577487913664612635611915493 Summary for Sm101(c169) = p61 * p109 Hello Patrick, Here's another wanted number for your tables: Sm(101) = 3 * 8377 * 799917088062980754649 * C169 Tue Jun 5 01:18:11 2012 prp61 factor: 1399463086740105394672913130945493026937913499238148790743003 Tue Jun 5 01:18:11 2012 prp109 factor: 4388325012701307167526588635576876644759452668196597056747408345988387366211263062577487913664612635611915493 Tue Jun 5 01:18:11 2012 elapsed time 04:27:08 (Just the elapsed time for ONE sqrt - it only took one, luckily). The whole number took many weeks on various machines. The relations were slow coming because the Snfs coefficients were pretty dreadful as you can see from the Msieve log below. Mon Jun 4 20:51:03 2012 Msieve v. 1.44 Mon Jun 4 20:51:03 2012 random seeds: 4714fab8 a98d82fd Mon Jun 4 20:51:03 2012 factoring 6141298867893783540378996188437492127764003798590081909642744192552148805391571094462286943973793319/ 310495244779697771718230720369645297842348701438176773337763517045479 (169 digits) Mon Jun 4 20:51:04 2012 no P-1/P+1/ECM available, skipping Mon Jun 4 20:51:04 2012 commencing number field sieve (169-digit input) Mon Jun 4 20:51:04 2012 R0: -10000000000000000000000000000000000000 Mon Jun 4 20:51:04 2012 R1: 1 Mon Jun 4 20:51:04 2012 A0: -8919910099 Mon Jun 4 20:51:04 2012 A1: 0 Mon Jun 4 20:51:04 2012 A2: 0 Mon Jun 4 20:51:04 2012 A3: 0 Mon Jun 4 20:51:04 2012 A4: 0 Mon Jun 4 20:51:04 2012 A5: 12099999899800 Mon Jun 4 20:51:04 2012 skew 1.00, size 3.077673e-16, alpha -0.346420, combined = 6.775396e-13 Kind regards, --Bob. Submitted on Mon, 4 June 2012 18:44
 1234567...102 Sm103 = p1 * p1 * p2 * p2 * p4 * p5 * p5 * p10 * p172 [ Length = 198 ] 2 * 3 * 19 * 89 * 3607 * 15887 * 32993 * 2865523753 * 2245981950884772863770930273540385579914865629636627917458256811732689892492870743326877749976350147897124023992523914020180640624011740696205659507665744332920411510673767
 1234567...103 Sm103 = p3 * p4 * p16 * p71 * p110 [ Length = 201 ] (by Sean A. Irvine ) 131 * 1231 * 1713675826579469 * 16908963624339537484508436321314327604030763349996047014668841426185197 * 26420435289199660352290245657167852985476641946070651819895933156168339498719086012326404560442282402403559611 Summary for Sm103(c180) = p71 * p110 The factorization of the C180 after removal of the small factors was completed by SNFS using yafu. The entire factorization took 6 months of otherwise idle time on a single 12-core machine. Regards, Sean A. Irvine Submitted on Mon, 15 February 2016 10:46
 1234567...104 Sm104 = (p1)^6 * p1 * p2 * p3 * p20 * p69 * p109 [ Length = 204 ] (by Sean A. Irvine ) 2^6 * 3 * 59 * 773 * 19601852982312892289 * 117416055745722199032551613030131955173140365000320768767578421207867 * 6125726861692155074440026231293274444423805613657273299528150618521012506340221515290231138888396870065232607 Summary for Sm104(c177) = p69 * p109 I completed the factorization of the remaining C177 of Sm104 by GNFS after 6 months of sieving and 17 days linear algebra. The entire computation was done with yafu running on a single 3.4 GHz i7-2600 machine. Regards, Sean A. Irvine Submitted on Sat, 21 March 2020 2:18
 1234567...105 Sm105 = p1 * p1 * p3 * p13 * p44 * p146 [ length = 207 ] (by Sean A. Irvine ) 3 * 5 * 193 * 6942508281251 * 90853974148830729568788807471204169448373857 * 67609243102773972838875424854217967300371972209133190536893586620791162850744838052281507779485845273498264830080938632761526794830712920440816557 Hi Patrick, It has been a long time between drinks, but I finally factored another of these numbers Sm105(c190) Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=982310399 Step 1 took 63945ms Step 2 took 30405ms ********** Factor found in step 2: 90853974148830729568788807471204169448373857 Found probable prime factor of 44 digits: 90853974148830729568788807471204169448373857 Probable prime cofactor 67609243102773972838... ...94830712920440816557 has 146 digits Sean. Submitted on Wed, 22 Dec 2010 19:43
 1234567...106 Sm106 = p1 * p2 * p3 * p3 * p29 * p35 * p69 * p71 [ Length = 210 ] (by Sean A. Irvine ) 2 * 11 * 127 * 827 * 95383501607400293616004374931 * 54259599094002572583355411045946413 * 375159085605310877928459072269605386653376782374874196433925741599663 * 27518056325201854933261643718251313697576510084474601978478694683051383 by GNFS, 7 days Finally did another of these numbers, sorry but it is not the most wanted Sm101. Submitted on Wed, 29 Apr 2009 17:50
 1234567...107 Sm107 = (p1)^3 * p12 * p199 [ Length = 213 ] 3^3 * 536288185369 * 8526150295974562563911703097396807303361305853752080385827103422281006173895434732314352853475423512542010066856002013066381244223149688686332747287256098942256562363655334309484941298623600483738889
 1234567...108 Sm108 = (p1)^2 * (p1)^3 * p18 * p36 * p161 [ Length = 216 ] (by Sean A. Irvine ) 2^2 * 3^3 * 128451681010379681 * 132761751746390611923240080737166083 * 67031425578179280405553486489006742336953759049830840809351016348413007664845819742768984976575205426833399525010462614317613333284615639359796130220299502987337
 1234567...109 Sm109 = p1 * p4 * p8 * p20 * p31 * p67 * p90 [ Length = 219 ] (by Unknown ) 7 * 1559 * 78176687 * 73024355266099724939 * 9943216978062352390003139833531 * 1330054388136326845371542874560114721263427298182714056642677810603 * 149840603084337475988993463236995110967352586095183241932010459722363567237123276130962657 p31 by Sean A. Irvine
 1234567...110 Sm110 = p1 * p1 * p1 * p4 * p20 * p197 [ Length = 222 ] 2 * 3 * 5 * 4517 * 18443752916913621413 * 49396290575478070579962193789705514377113696579391181438562209557211046308140914955475375292377669698324210580411428837724109733589770430705239901861854012027457023299672370583841892589110518827197
 1234567...111 Sm111 = p1 * p3 * p3 * p6 * p6 * p9 * p10 * p12 * p13 * p17 * p19 * p23 * p109 [ Length = 225 ] 3 * 293 * 431 * 230273 * 209071 * 241423723 * 3182306131 * 171974155987 * 1532064083461 * 59183601887848987 * 8526805649394145853 * 27151072184008709784271 * 2440480034289871822370862693886835126099170952229129167119083277062899175394632300484951689048576681026896223
 1234567...112 Sm112 = (p1)^3 * p5 * p6 * p9 * p17 * p23 * p169 [ Length = 228 ] 2^3 * 16619 * 449797 * 894009023 * 74225338554790133 * 10021106769497255963093 * 3104515050823723908076909137590343647825269545315652029790926783188211767084523827184031625338265911008653113512314794480936566758254656863951748098953803988065923879729
 1234567...113 Sm113 = p1 * p2 * p2 * p4 * p7 * p8 * p18 * p37 * p75 * p83 [ Length = 231 ] (by Sean A. Irvine ) 3 * 11 * 13 * 5653 * 1016453 * 16784357 * 116507891014281007 * 6844495453726387858061775603297883751 * 274083639473114418810098845553160469060803472020901711735885001850493035179 * 13652330611204925298260606291932608056492271043478425764831204949788104223444207523 Summary for Sm113(c157) = p75 * p83 " The entire computation of Sm104(C157) was done with yafu running on a single 3.4 GHz i7-2600 machine ". Further, I also factored the remaining C157 composite of Sm113 by GNFS in 1 month using a similar machine. I believe Sm114 is next smallest unfactored number of this form. Regards, Sean A. Irvine Submitted on Sat, 21 March 2020 2:18
 1234567...114 Sm114 = p1 * p1 * p1 * p6 * p31 * p34 * p47 * p53 * p63 [ Length = 234 ] (by Sean A. Irvine ) 2 * 3 * 7 * 178333 * 2042059881000388200555074336219 * 8678622406220213516465050301044327 * 24075568431816864297632248860777423507383641907 * 62041046777207692242447572091924037212783315235431589 * 622671572255303237737485133617360962819046403525686867675770351 Summary for Sm114(c162) = p47 * p53 * p63 "The third to last factor (47 digits) was found by ECM with b1=11e7, leaving an easy C116 by GNFS to finish it off." Submitted on Wed, 29 April 2020 6:05
 1234567...115 Sm115 = p1 * p3 * p3 * p3 * p5 * p8 * p18 * p50 * p152 [ Length = 237 ] (by Sean A. Irvine ) 5 * 17 * 19 * 41 * 36607 * 71518987 * 283858194594979819 * 35876849722942437286649396513492746925705038271531 * 69929007238910189440896360020171554156771275344878594027300265571638084469443386117564529410882181001246595145982221865975563979407080860715180311683161 Summary for Sm115(c202) = p50 * p152 GMP-ECM 6.4 [configured with GMP 6.0.0, --enable-asm-redc] [ECM] Input number is 2508832483 ... 6758389491 (202 digits) Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=1588162844 Step 1 took 1113195ms Step 2 took 257537ms ********** Factor found in step 2: 35876849722942437286649396513492746925705038271531 Found probable prime factor of 50 digits: 35876849722942437286649396513492746925705038271531 Probable prime cofactor 6992900723 ... 0311683161 has 152 digits Submitted on Sun, 8 November 2020 22:46
 1234567...116 Sm116 = (p1)^2 * (p1)^2 * p4 * p37 * p198 [ Length = 240 ] (by Sean A. Irvine ) 2^2 * 3^2 * 2239 * 9787002048140152171263515060558503699 * 156497968367245515655059056455089617073959013222149265770586804523805308165572520510050272136981198250507087284878063256342705928229557508508670247743582143974583381133763456377474127925121483818271
 1234567...117 Sm117 = (p1)^2 * p5 * p12 * p20 * p35 * p42 * p130 [ Length = 243 ] (by Sean A. Irvine ) 3^2 * 31883 * 333699561211 * 28437086452217952631 * 29899433706805424728763564400367447 * 319505907958401958357051507462193336760619 * 4746032403816815975214853624607036716257319634142438753425546024369121494473738828190063585349428105104156771415393005556040837247 p35 by Philippe Strohl Summary for p35 of Sm117 Philippe Strohl found a new factor of Sm117 (but the cofactor is still composite) : Input number is (above) c206 Using B1=50000000, B2=288591693406, polynomial Dickson(12), sigma=759744520 dF=65536, k=6, d=690690, d2=17, i0=56 Expected number of curves to find a factor of n digits: 20 25 30 35 40 45 50 55 60 65 2 5 14 51 223 1139 6555 42004 296146 2292504 Step 1 took 1567405ms Step 2 took 365869ms ********** Factor found in step 2: 29899433706805424728763564400367447 Found probable prime factor of 35 digits: 29899433706805424728763564400367447 Composite cofactor 1516385392381488800257172455421115218103131389426237636403907504872104848630821256747576627427151045/ 955402969807173970504574397911322632329216437824800943241454211577975893 has 172 digits Submitted on Friday 22/08/2008 14:59 Summary for Sm117(c172) = p42 * p130 Unexpectedly, the next one came out rather quick, here is the rest of Sm117: Run 657 out of 4590: Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3332531727 Step 1 took 35672ms Step 2 took 13620ms ********** Factor found in step 2: 319505907958401958357051507462193336760619 Found probable prime factor of 42 digits: 319505907958401958357051507462193336760619 Probable prime cofactor 4746032403 ... 6040837247 has 130 digits Sean. Submitted on Mon, 9 November 2020 10:42
 1234567...118 Sm118 = p1 * p2 * p11 * p20 * p40 * p59 * p115 [ Length = 246 ] (by Sean A. Irvine ) 2 * 83 * 33352084523 * 20481677004050305811 * 5747203274595182101743782698650656863747 * 38736194414035077015862227517019570665653714001970285448031 * 4890405641955581530316483984640301950064909595593296445634478042384514510212369135301909949580873481446130666608313 p40 submitted to factordb.com on 4 November 2018 (communicated by Alex Latham on Oct 17, 2022) Sean A. Irvine finished running GNFS on the c174 for Sm118, after ca. four months of running time. Submitted on Mon, 4 November 2023 9:13
 1234567...119 Sm119 = p1 * p2 * p3 * p3 * p4 * p39 * p201 [ Length = 249 ] 3 * 59 * 101 * 139 * 2801 * 165365274022584034353506983708790719561 * 107262549014827605108170553542444185119309836220993508589614438998203997313532847379414499036635601582268738238072638661210529907049649737748338042860755091137808486160371905612311536822281399382425993 Summary for Sm119(c239) = p39 * p201 Submitted to factordb.com on 20 August 2021 (communicated by Alex Latham on Oct 17, 2022)
 1234567...120 Sm120 = (p1)^4 * p1 * p1 * p2 * p8 * p40 * p57 * p145 [ Length = 252 ] (by Sean A. Irvine ) 2^4 * 3 * 5 * 13 * 16693063 * 1024001412736320019392148995069160443859 * 279576210246975591413879862591888691573777646278467665473 * 8279871212684048932811865452420379047357376308108739348862728517513525996252897386381120699815551355652654310647683079460112202910478437779699811 p40 submitted to factordb.com on 23 August 2021 (communicated by Alex Latham on Oct 17, 2022) Sean A. Irvine has completed the factorization of the remaining c202 for Sm120 with ECM: Using B1=110000000, B2=776278396540, polynomial Dickson(30), sigma=1:1717354337 Step 1 took 224646ms Step 2 took 75326ms ********** Factor found in step 2: 279576210246975591413879862591888691573777646278467665473 Found prime factor of 57 digits: 279576210246975591413879862591888691573777646278467665473 Prime cofactor 8279871212684048932811865452420379047357376308108739348862728517513525996252897386381120699815551355652654310647683079460112202910478437779699811 has 145 digits Submitted on Thu, 10 August 2023 21:29
 1234567...121 Sm121 = p9 * p33 * p214 [ Length = 255 ] (by Sean A. Irvine ) 278240783 * 105299178204417486675841093021769 * 4213754301973277818574830150933029703205115128282586723382785882706969263182976786615125991432774212665571280081392800541558354419799245310412621791925662551088708112110138158616156416375634374522084788731721938623
 1234567...122 Sm122 = p1 * p1 * p2 * p9 * p14 * p233 [ Length = 258 ] 2 * 3 * 23 * 618029123 * 31949422933783 * 45306856641154521457766703270320242968763335849955546717684945081881187367338244144043437588658869218015907458822474001579325203473863284859671581548238274058627446886736975249452833365841005182926249382278321304570156703240708360441
 1234567...123 Sm123 = p1 * p1 * p2 * p6 * p10 * p16 * p29 * p31 * p66 * p103 [ Length = 261 ] (by Mehrshad Alipour ) 3 * 7 * 37 * 413923 * 1565875469 * 5500432543504219 * 12347002211187670552593982429 * 2829927788416784955921382453753 * 490603365766589761252788965584567538918689227625761502090641756359 * 2599877785756834172022406612564836069586385438389342330277037342180578839138482051324007676975879994901 p29 and p31 found by Sean A. Irvine on 3 August 2005 (see Messages) Summary for Sm123[c169] = p66 * p103 The factorization was submitted to factordb.com on 5 May 2024 by Mehrshad Alipour from Iran. Mehrshad used the application cado-nfs to factorize c169 on a core i3-12100 machine starting with 16GB of ram. That seemed not enough, so he upgraded to 64GB, only to find out that 32GB was enough.
 1234567...124 Sm124 = (p1)^2 * p6 * p16 * p47 * c195 [ Length = 264 ] 3 * 7 * 37 * 413923 * 1565875469 * 5500432543504219 * 12347002211187670552593982429 * 2829927788416784955921382453753 * 588877553843538799713765306327801633937621519940786897171404658557267917294998835137411559467118303182766629323132762988786937564320755535254244869454947966182720042357960885486699110417389933289 p47 submitted to factordb.com on 23 August 2021 (communicated by Alex Latham on Oct 17, 2022)
 1234567...125 Sm125 = (p1)^2 * (p1)^3 * p4 * p13 * p24 * c224 [ Length = 267 ] 3^2 * 5^3 * 4019 * 7715697265127 * 295999706346724665505289 * 11955782051578068870996715574113327579491930757843833929238411263341491346956518715403679155140414913709005653897587053549582183867657144773717207515691678321060898354418349891914476834296835485120424057740487394866072756061 p24 by Sean A. Irvine
 1234567...126 Sm126 = p1 * (p1)^2 * p2 * p3 * p5 * p20 * p241 [ Length = 270 ] 2 * 3^2 * 29 * 103 * 70271 * 11513388742821485203 * 2838101657660281121635838482974785973172167634896902551225760546451986983167250817906190353710808248210766825163587350127671515116185896138062902354614719664032678541176075402608400798508031875431084629720784104890703458832231455912845908997
 1234567...127 Sm127 = p2 * p3 * p4 * p20 * c245 [ Length = 273 ] 53 * 269 * 4547 * 56560310643009044407 * 336705404741718452285011996925008237983156298846751623241302417011439351512564751598258632876057850530172766665240704250459291142219371648485922051590024341491094563539601763084457941803051106303965794068147883280296718180327425940329546813
 1234567...128 Sm128 = (p1)^3 * p1 * p1 * p2 * p2 * p6 * p22 * p37 * c206 [ Length = 276 ] 2^3 * 3 * 7 * 11 * 59 * 215329 * 8154316249498591416487 * 6532897159547245195514315108364288167 * 98710898075961375591497576343869714560966518634525903244905883607415709511772198694915446957053353657200532766380047193644750347571820095362243784257001037933159988823119601450482070667441278561741520802319 p37 submitted to factordb.com on 23 August 2021 (communicated by Alex Latham on Oct 17, 2022)
 1234567...129 Sm129 = p1 * p2 * c277 [ Length = 279 ] 3 * 19 * 216590858072126546342388979284247758463601100496368970584813221708490182706025342920611394827237464132732606948449585344853819069661706556975031190873827769096243312085948981217455433298068596668600180884394922994926507210721249321252833537 0475756475791598633739019739054861897
 1234567...130 Sm130 = p1 * p1 * p12 * c269 [ Length = 282 ] 2 * 5 * 166817332889 * 740071711752279910983019901841593591648354166865247904157453792498389691374311212656163491454209390262070838164677567905044297208414725870301513275011714771337094973862269224701377289863230095375764361913248848544286050290270877878944285487 88712386545342905816900184217
 1234567...131 Sm131 = p1 * p2 * p2 * p4 * p11 * p12 * c256 [ Length = 285 ] 3 * 19 * 83 * 1693 * 23210501651 * 575587270441 * 115374375622583204904626854763579378161681853367824843538204694489322440978846825705379514910738068110360614417250486541312628796378285948125088504493116857699550355498755996568827733438394219834563218985157890363976341096338717600242843577 5463258992823927
 1234567...132 Sm132 = (p1)^2 * p1 * p2 * p13 * p40 * c233 [ Length = 288 ] 2^2 * 3 * 79 * 2312656324607 * 2540283627438011189845145124230082384829 * 22167327235734680246954535484159674257350229311619825971454555872005134356413350091925458264983364766604313638095683747947702394137604469363279931375761072570287699886944053701726478970874854873078943899736212491323470043614941916953 p40 submitted to factordb.com on 23 August 2021 (communicated by Alex Latham on Oct 17, 2022)
 1234567...133 Sm133 = p19 * c272 [ Length = 291 ] 8223519074965787731 * 150126470159158411307354179427311909786914154368133057691312700814270531804867102727595499538987896919299489741052249203939541976424727007104548147059468454650509456337270881012305602988590501033242133410293709190605598108732774128883869352 34108358887029883282968579008743
 1234567...134 Sm134 = p1 * (p1)^3 * p2 * p4 * p16 * p28 * c243 [ Length = 294 ] 2 * 3^3 * 73 * 6173 * 5527048386371021 * 1417349652747970442615118133 * 647637238580596134413990886300825671550680475409685218179098924618498914927104640633532943345067820744812553228940215778123341572783466566042033295998510679182938541016629300843037698433762972565398466495051910740988433510616905148611907123 793
 1234567...135 Sm135 = (p1)^3 * p1 * p2 * p2 * p3 * p10 * p12 * p15 * c254 [ Length = 297 ] 3^3 * 5 * 11 * 37 * 647 * 1480867981 * 174496625453 * 151994480112757 * 884201662685354854162961490943984946862561136365041850271367084854547849535258115659320127178312884999919228692361705210800628973255564980721192533025579132697820992767814246183252506853608646901744760779307509528964724222125808559518799337 30483300768869
 1234567...136 Sm136 = (p1)^5 * p4 * p4 * p13 * p26 * c253 [ Length = 300 ] 2^5 * 1259 * 4111 * 9485286634381 * 10151962417972135624157641 * 774089776410313692582963143248216990889359543901305539550575594212990653019739428528811986910012321273856511600990265329693201025273620175861191305564980593289797791957528815550315936969244873277097479121470596925993041811253406967627659675 8353772948387
 1234567...137 Sm137 = p1 * (p1)^2 * p13 * p30 * c258 [ Length = 303 ] 3 * 7^2 * 7459866979837 * 144065103514544138702103468451 * 781461818612935912244179550077619047624409137230897390960927211720319424489482120677056304543119202666345117064993923187797034738474116872610069940024770710458555402525815906735118829990247455514063749506571518448384576137944429510953795847 353376929543475333 p30 by Sean A. Irvine
 1234567...138 Sm138 = p1 * p1 * p3 * p5 * p6 * p15 * c277 [ Length = 306 ] 2 * 3 * 181 * 78311 * 914569 * 413202386279227 * 384134297539886771745157582011666871416171008362507862601104573416627494921896979465320508666644777197086681865142822466426671043899514977282744754378183884195577205642799029159495681020641145782569215536253978369362749427322571742832444712 7238477150642009708211085821751772731
 1234567...139 Sm139 = p2 * p11 * p12 * p12 * p22 * p37 * p215 [ Length = 309 ] 13 * 62814588973 * 115754581759 * 964458587927 * 9196988352200440482601 * 2662520919727992778114192625316520801 * 55303251118984373249719165791340201877773320666711687179919506291237507133144359434557545077885351236962474986502203967588520562972438544696550056777370734171639162749148850530316319312049593515270674597150927754227 p37 submitted to factordb.com on 20 August 2021 (communicated by Alex Latham on Oct 17, 2022)
 1234567...140 Sm140 = (p1)^2 * p1 * p1 * p2 * p3 * p4 * p5 * p11 * p18 * p23 * c248 [ Length = 312 ] 2^2 * 3 * 5 * 23 * 761 * 1873 * 12841 * 34690415939 * 226556543956403897 * 10856300652094466205709 * 572857536199494174553472060884991021196252030246440267253089355048901533389268822589986492945490993840333040443467034288047970883561484316580158280419398112514033176528197798372329409768901398456695157755890812961156323240437923070144890424 36853463
 1234567...141 Sm140 = p1 * p6 * p309 [ Length = 315 ] 3 * 107171 * 383986927748215877476685913764050667700070066476099918925031138317391222570889654429987263505753591785270225342727241656065779205528774069713410589301464725796029049802001534289280983910134582741917443786425762277444797286924983167443043099 710176941896971886434216112960058001166765048791598268608535695720357
 1234567...142 Sm142 = p1 * p1 * p4 * p5 * p5 * p22 * c282 [ Length = 318 ] 2 * 7 * 4523 * 14303 * 76079 * 2244048237264532856611 * 798428869689961124854550782227208206273280990815818701909134575585798799012842305146271145428913184008743313408308740113445618126241703975768157709038561029940687370106599765807432072305730054753607196825725385032893725258315522226903933141 997489082505346965529222057364249227244973
 1234567...143 Sm143 = (p1)^2 * p3 * c317 [ Length = 321 ] 3^2 * 859 * 159690582202964857605952293612755429212589092333372543310494808399740530516665949378797691180345821440509100970917428077307821588031525983023887956018732154164867013179395834036928724589185228432417673139445228440186404229868208657501119022 27023427644563591013209691518060681429198050851394791635640426482749856440453
 1234567...144 Sm144 = (p1)^2 * (p1)^2 * p4 * p13 * p14 * p21 * p271 [ Length = 324 ] 2^3 * 3^2 * 6361 * 6585181700551 * 81557411089043 * 165684233831183308123 * 302931689993912862383229276114787027281405114796886618094086589746232331834212621096315668911107376877078295312200829930661169651615343618354721976565378756498778447770707406136218366476787471181094421056805395804695142359050642416127994721 1076715922035883967781648857763
 1234567...145 Sm145 = p1 * p8 * c318 [ Length = 327 ] 5 * 96151639 * 256796015928781268960296596071589008117173389593349133098695356350273767340428685702899968354206327269486453497930001269279823445770222881953718498335908404816393588234082872563305128849439789791003153059315205447736796478552200473907917713 429966844600789638381773450842844453497314031500041583555608734112455722447211
 1234567...146 Sm146 = p1 * p1 * p2 * p2 * p12 * p19 * c296 [ Length = 330 ] 2 * 3 * 13 * 83 * 720716898227 * 1122016187632880261 * 235818816245539713600331981587715785788524823275091489592452248030557841504828966423942497595543800995982128928947575522035526321290583995004579719700822772682600721229040541590622379858203374604761120936537888169703192813046776187209261825 37034382300824024667214545220707793570241011633788755207
 1234567...147 Sm147 = p1 * p5 * p22 * p31 * c276 [ Length = 333 ] 3 * 59113 * 1833894252004152212837 * 1519080701040059055565669511153 * 249893860720970494660634402277189581860549347857029659352882266281982140619591595175164744201005542378361314264168974568464619893796710116738490423551159286776817143982445018286530486370621230721463856257491419478839889336250857686273580085 622742942302372787167916598094915093
 1234567...148 Sm148 = (p1)^2 * p3 * p5 * p5 * p6 * p6 * p13 * p13 * p34 * p254 [ Length = 336 ] (by Sean A. Irvine ) 2^2 * 197 * 11927 * 17377 * 273131 * 623321 * 3417425341307 * 4614988413949 * 8817212782626223819399721069204897 * 319300070156852478246718889830464122077571283705311623132323743476820895657676871869020093470476964497764322177957871760330493034912815489120806404979668011225719250826344570989463507211375055519415190119868082433415218699761826055025612259 15860092642869
 1234567...149 Sm149 = p1 * p3 * p3 * p4 * c331 [ Length = 339 ] 3 * 103 * 131 * 1399 * 218005518831775286892220693280915331832422938462254589272983429390587747715450661786063453849101531242812611967783476299771065065722131756483034494660680361931168552313336782900304233819135050234312766352918628069165010454614977978087165160 9522750606874407386894407750358278911837926871675466385373538882923085051171657273064013869
 1234567...150 Sm150 = p1 * p1 * (p1)^2 * p2 * p2 * p16 * p26 * c296 [ Length = 342 ] 2 * 3 * 5^2 * 11 * 23 * 2315007810082921 * 92477662071402284092009799 * 151954615147351455095110171852352613079653903481393655907561645565943483369431384166253265727397630989754924090769984676181814684321838064669502503815963810062634297111660745087962800954144852613451217337413083025689750684296077069060732783 30637748385315835235144059764059612685623536281382927503
 1234567...151 Sm151 = p1 * p2 * p4 * p4 * c335 [ Length = 345 ] 7 * 53 * 1801 * 3323 * 556028450455378906419549862887664624216859834610752656822523083975961916967920924042850190210814971110936378324496736009717140694715000056821531441497934729954707133637288052170296970957404914191065131035752999884986622675900738108656350421 57728347098279107910029663171640821794586869438170757815204918091255373015675237077975233874447
 1234567...152 Sm152 = (p1)^4 * (p1)^2 * p3 * p5 * p20 * p22 * p31 * p32 * p32 * p205 [ Length = 348 ] (by Sean A. Irvine ) 2^4 * 3^2 * 131 * 10613 * 29354379044409991753 * 2587833772662908004979 * 4103096315830350734534473515557 * 12805089500421274253268517941967 * 17815076027044127272632744936161 * 8672648427724666836335878649605123533671234498113722493001839423884394310675246313883662523667972796225220735409952709165862130017818166129799353719223483490503275166918260572071118186769070106198500506817
 1234567...153 Sm153 = (p1)^2 * p2 * p4 * p7 * p7 * p9 * c322 [ Length = 351 ] 3^2 * 29 * 7237 * 6987053 * 8237263 * 389365981 * 291662721014734703170595264452931192413345222129502917962456593142482468756674368499704879388193619235970327807465985644040573575289839791982794486031875237070876729415843686066457407897951275102408749386102467915352964244073766628873594128 1200381311694470835474221652767087655442802101924633966639113856928724902506353031
 1234567...154 Sm154 = p1 * p2 * p2 * p2 * p18 * p21 * p32 * c279 [ Length = 354 ] 2 * 17 * 19 * 43 * 444802312089588077 * 855286987917657769927 * 32063206397901252963254536935569 * 364357868151023104065690014392869296210548056261116243234467027829933297505578352030641966675499413252868435017382566068584271649811907764798030137051147261948778664806775328763343536767857383585802163855622996879404308912106199251738632133 631036988979348920693263712626113446243 p32 by Sean A. Irvine
 1234567...155 Sm155 = p1 * p1 * p9 * p24 * p323 [ Length = 357 ] 3 * 5 * 665009999 * 223237752082537677918401 * 554405975361398849086315094251866436826149186233995916322648863211855040945417732420881665849442175218073101972058302322367513350203978349990409656089950991903311063087768208087655812903149437572283142094574622685970434438853115676471655863 94732777654606357440424620177768705937886072566917369570519043697226934404184296523
 1234567...156 Sm156 = (p1)^2 * p1 * p1 * p4 * c354 [ Length = 360 ] 2^2 * 3 * 7 * 3307 * 444428085810445848687350490993207850318417740445700725853325328573730341636191791815155784452623419858516516050427893381163609910101130133323857685710260444601129954818030005953999441948173067595080072228120387155341876215355278532960801460 527877802929288241835947287593874206694062130589273597618097747700185537680325079356002225247844216273385287172787
 1234567...157 Sm157 = p2 * p2 * p6 * p8 * p12 * p18 * c318 [ Length = 363 ] 11 * 53 * 492601 * 43169527 * 645865664923 * 125176035875938771 * 123171562836153566068957324589265381565397200006993644472677662947419327821108690678960820685810830317459667900820066018147149358545252745157761989566806866502588364923606853126753693645014338621771464893122776977411815508084552766667202431 657516180225309291242630464351473412595422593795161392959158351372056609357669
 1234567...158 Sm158 = p1 * p1 * p2 * p2 * p8 * p21 * c334 [ Length = 366 ] 2 * 3 * 17 * 29 * 53854663 * 164031369541076815133 * 472461673917671792105317513599604927664704742613889071872507044016561219352623852114255155374993904236374485314532495024374124185919007147881270097540813614075468629948463178857820486606814500407661441815131112776560582298359589940029000432 2478992176999471111543050860603885776920143088996841845389885280574199247401746496842934843519
 1234567...159 Sm159 = p1 * p2 * p3 * p10 * p25 * p32 * p38 * c261 [ Length = 369 ] 3 * 71 * 647 * 3175105177 * 1957802969152764074566129 * 11855111297257593607972759339201 * 45941358846148651407783221723920871719 * 264602852938896854658792238839624264257227720584770327380191939141444501695531301016572569666318193692536121526266335701564755783626175997269133907697855056392892412943072813878004724885082914162981075053940022130859199511425477323866542802 507239213817360628747 p32 by Sean A. Irvine p38 submitted to factordb.com before November 4, 2018.
 1234567...160 Sm160 = (p1)^3 * p1 * p2 * p6 * p6 * p8 * p27 * p32 * c292 [ Length = 372 ] 2^3 * 5 * 37 * 130547 * 859933 * 21274133 * 122800249349203273846720291 * 64603936118676024484144135734907 * 440262457055513843388420187113234615175539026557285007915212958926035750460796131607770797636416464742586933863254729469894378005856037206329537366657963179350321131804864209307357231697508442628918674169893694027939483607973600783194622060 8343717739966765078765180632177404530263379499117877 p32 by Sean A. Irvine
 1234567...161 Sm161 = (p1)^4 * p2 * p3 * p8 * p360 [ Length = 375 ] 3^4 * 59 * 491 * 81705851 * 643936877262798276809635056823437176599393889312742534497858808401753128376387988973593769339663303074973747362480368159636806324001422178459069558417749689063473399179492414686898291521605975723614710064627963449867860721592074010892366031 555385848957957814583492377279631045136591702621255249517529486990821313347343984837578614067656268464133530164155430699
 1234567...162 Sm162 = p1 * (p1)^5 * p4 * p21 * p26 * c325 [ Length = 378 ] 2 * 3^5 * 2999 * 393803780657062026421 * 22260247937572504750086047 * 966256356744337186813716438702029991240981869552730990577342121545852624144032531193978476954880363092560643243407536698394784819429029461996401613001373819470855425200715281560745361889795571079780911200452959631077051186405319582536638396 2910424248139920421207225113340568687828821563236607127519116419856244591389453966259 p26 by Sean A. Irvine
 1234567...163 Sm163 = p4 * p11 * p12 * p25 * c330 [ Length = 381 ] 2381 * 72549525869 * 666733067809 * 1550529016982764630292633 * 691335900725482080926917327062976539204766778306445304306865702181369731538361534632243829486752179341455231055622553838521294888867369456421187293017360639461294096828185536793711361401395360250892938068201952066269448631904818275686743871 673666548396517255969560532102847984782998980743506213320593123686023459761093650116039411
 1234567...164 Sm164 = (p1)^2 * p1 * p34 * c349 [ Length = 384 ] 2^2 * 3 * 1039418554780603268384723777072953 * 989790466132055809201598724528734111805917730992528043185856800614231631401248702785939536339220094829967353922370866655803401211500643473347187680255000891403779620475087779288754227270393067481010476919021853118379746985450814950701004194 4117175183407038587950993904880534631736688265614558444741381814088317864257796204987978223422894902225701349
 1234567...165 Sm165 = p1 * p1 * p1 * p2 * p2 * p9 * p15 * p32 * p328 [ Length = 387 ] (by Sean A. Irvine ) 3 * 5 * 7 * 13 * 31 * 247007767 * 490242053931613 * 13183356310254866666237435750357 * 182756768194173135612106227451977729186376097283472414010936473228314943112176399502623782011430368154965927915015628712360221995550660112984516422314017356319293007617461998788639226078300814391329518357914807533066417404260975659341568447 5050607014396967804555792833912178431145501933981844058731687369979309788684753888188553
 1234567...166 Sm166 = p1 * p2 * p23 * p365 [ Length = 390 ] 2 * 89 * 55566524959746113370037 * 124819298554773166559157445477277487337716282207978059721756572699958798452384754690990740475025356570275858324048001456345375082508297216418812977378322921989705015381981809816775570071353103697462706966273542556642092741015816112733351258 37066891409220213283241287036537487578933027111131002578906570041512881790750932046472049727896182641483362152927269462128531
 1234567...167 Sm167 = p1 * p4 * c389 [ Length = 393 ] 3 * 3313 * 124214497536082233036685499740437893474446752473015709058601002489022441032734123618823317286975907591968594386373139799342667139256638230682933674210767510197060758515938141959905017587180903613142270956942455083115111288973852614059880386 47461326000615869013293502880181821926665673722923144595546447040762565664668693343811766389691935722924957455795769710851912482056561139165224284653
 1234567...168 Sm168 = (p1)^7 * p1 * p6 * p387 [ Length = 396 ] 2^7 * 3 * 532709 * 603522851971363056053086471460131641232657761647161378373243414272220133232696215753408594930216329782348267889419651716542028915466222028367855478231713927777146934588265861839504136032656803583107087547373357350061730026927186252221522034 647424957857508362343485359766694504572433323177563554355036283969742099565724747353391785680734331649209278234155881952734543699242149766194876903
 1234567...169 Sm169 = p4 * p4 * c391 [ Length = 399 ] 2671 * 5233 * 883263643892205631751053960627718889951063140418964557379349826171107084818870406662757686146253651753824642928318090545296605153834836402567839816180241326158045115505793334927457936604253756247536481748391708689613677721946954532875920095 2363987856642075831087791515606873790614577543967629193555322863446875428408828712591881457523661625113668037849121621767252771800775094534287680080983
 1234567...170 Sm170 = p1 * (p1)^2 * p1 * p1 * p3 * p14 * c382 [ Length = 402 ] 2 * 3^2 * 5 * 7 * 701 * 73406007054077 * 380824437250218390642711000487470435317764078406179828054713887071775626262999569231657076078241421333054393670747570497329417165047159309022971579965927198131584925118926270860822627577291033932783028680258488377265216404001474676750503257 1048077343859148582844187613558824620925360746281373753641688512508403218287638916088620430386196058562666232177613198392916656646285297946067
 1234567...171 Sm171 = (p1)^2 * p4 * p19 * p35 * c347 [ Length = 405 ] 3^2 * 1237 * 6017588157881558471 * 40202471819457246557501649563881337 * 458381995434290276780026329457306309599832028089258909410723788009960543250019282795503968692995316177770560873868121654523993391631745124897309167031353187113136545060015834532727481853999734192184998020873255164455971921071976556049381548 15818418717934999045768636798768946312086623752717198318776203091444825110534298458738806616172143489508281 p35 submitted to factordb.com before November 4, 2018.
 1234567...172 Sm172 = (p1)^2 * p2 * p2 * p2 * c403 [ Length = 408 ] 2^2 * 11 * 13 * 37 * 583333911836666657603296721754022029504123168035013765041313250679641864214866969687906327024784325059807153471065316795344343553709944894517897272718209357327814628090110183774095619825643073620781057947954574310660126205401210135674329597 9829810958236681256998871911081417885519284215277505865391047870824945196614162877723735879188629235973877913114446945575371298391616006528216035020136418832412123
 1234567...173 Sm173 = p1 * p2 * p2 * p3 * p3 * p5 * p6 * c394 [ Length = 411 ] 3 * 17 * 53 * 101 * 153 * 11633 * 228673 * 112598438975384525795964952885713259316211807910146645468747235898340487605112996572313156396766077274355481456687685221720825807277812290919651748036025735617949705610114846641136657569251387708677478676902379802127424944542569035138705831 3245695892072630734928512398207585925730787826881050308184073006444853981896559973362071401130738487216683572137650869945082064111147965975618965556509621
 1234567...174 Sm174 = p1 * p1 * p2 * p3 * p7 * p22 * c381 [ Length = 414 ] 2 * 3 * 59 * 277 * 2522957 * 2928995151034569627547 * 170374049139074441955313533775194677405516436467843998391485343636738238949897611127630276666084204263154157569961673514019928732374837739342927715427878760888271460044186277683456132497810905350981546058356886019041125140515640638391238808 226984114355571708402014421989338985125561710342164665525596506429137345160304355731323542384937336885717105617685802906878356788482538517857
 1234567...175 Sm175 = (p1)^2 * p13 * c403 [ Length = 417 ] 5^2 * 2606426254567 * 189465232534072586430380437789305348621796984271461517764260313855410550439352656919592639943033811757687341257059150269560693765167920068477356749478808018707499792145974637281654226531167550908668989738930517712034538498675230549495379945 9789327486993728002787191548702358765087457496689540698887725334144913559171630312205829806249803247209927637936591025274501863974764846584005786565989449914377201
 1234567...176 Sm176 = (p1)^3 * p1 * p2 * p4 * p19 * p28 * c369 [ Length = 420 ] 2^3 * 3 * 19 * 1051 * 1031835687651103571 * 1011379313630785579015894871 * 246844132111589264774295918561288270010049003962486940960336738030267353753979092662351186496489931394287619228294826123320508008970637308623684665406250162349206113529819143311090877209337095517735125522715128522115121903624007157453687783 101184451167113574192627797148134289718072501213867999851602987775540007552311248123583917134628838942206588694961343202339141031 p28 by Sean A. Irvine
 1234567...177 Sm177 = p1 * p3 * p6 * p7 * p11 * p16 * c382 [ Length = 423 ] 3 * 109 * 153277 * 6690569 * 32545700623 * 2984807754776597 * 378980783869354890538816255367593075202190045751217621297869071239780345755165921020779119695885741103236195862450588874903945027110841023437085828489552963316325430858011521085926022200058916224740198499989255463685262286855781435939999629 3440402766775517800195161154573193192674724474116122408730657141905650547933629847903241569132651991594329540743608706808592370391581652873217
 1234567...178 Sm178 = p1 * p13 * p17 * p397 [ Length = 426 ] 2 * 3144036216187 * 11409535046513339 * 172079642495898962119712019149827088042504874761467313828842743572736517221186780659959064616853777634881618576072376718877160473546754450767450623088053060230669445261102516543716228829003436778158472775178297406525014801821796893544680462 3840678229929925088293377235585961990200769128189780441052457501524916828668303939775759676867206470259475035320103878284258922951791050919791562775748396373
 1234567...179 Sm179 = (p1)^2 * p1 * p2 * p3 * c423 [ Length = 429 ] 3^2 * 7 * 11 * 359 * 496234888081419573430933763388043677218876497899529771384129943983565878210816664314246705219828023794079216199464858077659511428278699198413774750280689217623343212824588580970668069392287780716444601623497634953225486500947043507555117896 502301644057451241918284014543071495412260813998051080382560733230189439726119705387118885420653607906165322758641549422426244776295229100247055373336095407594328365920137202406782417
 1234567...180 Sm180 = (p1)^2 * (p1)^2 * p1 * p2 * p2 * p4 * c422 [ Length = 432 ] 2^2 * 3^2 * 5 * 43 * 89 * 7121 * 251676707884849271586469056114820416546044067619470872986836265328749404061380097363600377035468650171374739637213703309931350792802397006101444991714006354871395194208756754923804081397036986631962231024133786310814737893930745210617347374 29298710344943971920271451361862065999766413463881704853828383639087131780406100968444205259151769448075494634988840205559689627122832587374251926808211805277247445155500228085691053
 1234567...181 Sm181 = p2 * p3 * p5 * p20 * c406 [ Length = 435 ] 31 * 197 * 70999 * 46096011552749697739 * 617691287803957604354670479035303436880525007901231281260320058331189159370022184962600350466073568809354923730624285711086006496664449256635895885709227919057044800688848598345369015933183832367829892805340292153317586510051350836417671167 4914719627912121673905385266220378636560543997233035910127660226891146647601065876808661674207986783379855958430566520723383976510786416744649673628932518018146086203
 1234567...182 Sm182 = p1 * p1 * p9 * c429 [ Length = 438 ] 2 * 3 * 123529391 * 166568711707256954764125349181099233736545374429596695781955697185510834074073979507096270786177186711861937861433402579966680250353230697240529285318128363995116875854792753051443977112430811575174180078468270636240877970640352995175206409 133189092788615682728660805273630694265477990756241881112509406955816612287222322046614728510437581004711599570062581511684073845443741619572900084383112744627673494550746461861825494871067
 1234567...183 Sm183 = p1 * p2 * p3 * p4 * p16 * p30 * c387 [ Length = 441 ] 3 * 29 * 661 * 1723 * 3346484052265661 * 553245689211853052761209813199 * 672980049261465141250864434641248049265730497041894387954853629835936315929533090803537084165515844522331841746663644293981888933067135811782184635548156762607364535885873075659189283632774785514756517177185728297187493432197212026342257143 091828814145190188574510919071309948539948109458202665604654469473601291989153661303806239391458358553404937934740227612677288883152389890090656077 p30 by Sean A. Irvine
 1234567...184 Sm184 = (p1)^4 * p1 * p2 * p3 * p4 * p4 * p11 * p17 * p18 * p19 * p27 * p342 [ Length = 444 ] (by Sean A. Irvine ) 2^4 * 7 * 59 * 191 * 1093 * 1223 * 22521973429 * 15219125459582087 * 158906425126963139 * 2513521443592870099 * 677008100402429325901609057 * 789497757457178155644478620259361413972150672081760436601552877576067637316044253034501948330770097859300923037781520324045517956750901709230536602932308434986143596639398443656273661658327853053173654182408958317242742517820581180854453052 925226658686768857580470091786086406610221754789129568203967384451608838167466879488313009807568569387
 1234567...185 Sm185 = p1 * p1 * p8 * p13 * p16 * c409 [ Length = 447 ] 3 * 5 * 94050577 * 4716042857821 * 3479131875325867 * 533351621984799969936162186866536516006398881165823993170915822324876528786193287723556035078086620884250934345842619491164243631630538572043211588172677044714775014150341345114863817926212892445158466139180663177538853890760364020235455026 7055385512856136507169703764079837433961386165083423151309476147627120057361209514039199017910453864732979322936673594217273723951595676820310077891234934325129397084761
 1234567...186 Sm186 = p1 * p1 * p4 * p21 * c425 [ Length = 450 ] 2 * 3 * 1201 * 574850252802945786301 * 298034124502074098101512668464482822908652542523273666028642684799238307322893078046907367202677614585558168699238971552745323664916104115985286964344522797611683828395310392532725464757984814175216673122414542074002937385454614948581222778 50919142186997475255773656256280391374441743491630892145619591257066811851741551542931599908954597575263175781858127461677445180342984555398523710492210530628444970003774434465773425031
 1234567...187 Sm187 = p3 * p9 * p31 * p411 [ Length = 453 ] (by Sean A. Irvine ) 349 * 506442073 * 1080829169904060835770214147747 * 646253213525936563202131494265843172809473362059914914173432708236767129869232028235090059727829636553795408840233127105558561773084467674051729709389777726767967802284317022428165091134213394445922362621714833233212554723714564174418111669 498936207951085298551799080803363445759267522417246541605647908977558423780331081208797817453303153554382680801195027077476809337778612645835221413891384933392084296657173
 1234567...188 Sm188 = (p1)^2 * (p1)^3 * c454 [ Length = 456 ] 2^2 * 3^3 * 114311841760289010569594183511130761411345025261972512253095867012814263094846708763656013936597550514497764778348392265339515620099234016181266461850075767023017303600917517864768145351758426019538984355652876025100101027880659363994551033 4417760362223343723362260417834510445640093806779010501251260529056843890195760584668010612473593973612510668084760695890344057029260751501510779307094140446010834918260862723844223862760918335010946140594307279511
 1234567...189 Sm189 = (p1)^3 * p2 * p7 * p10 * p10 * p21 * c410 [ Length = 459 ] 3^3 * 47 * 1515169 * 1550882611 * 1687056803 * 348528133548561476953 * 704118583577713797078398658908003728031900843914139757832144494986126668190798285697306191950099948172947632501506555031819766524522062844214386799757731790508877127338472304589241744718275536202751889039042846243680487678897872217017430439 38470123426043480817060031301133574570669933659146087080803463673846761765910881774365387978938262570593602449691692182700835337880269663784311472845785615307729864408601
 1234567...190 Sm190 = p1 * p1 * p3 * p23 * p435 [ Length = 462 ] 2 * 5 * 379 * 46645758388308293907739 * 698334678474731226954203275220474188515870231140888920157380649749714630298163563890827583156235678406707150178926396065948318381061042152090125065337104586954721906199767370480826970612106279221187509703470514016996510705114927761279158607 800399519570000171100337592081033222510846868634882798195310888649733519205868329146977603967516107577069874382756235348861655882370697739050483812729273344054763850637031321826560460734714491999
 1234567...191 Sm191 = p1 * p2 * p4 * p12 * p20 * c429 [ Length = 465 ] 3 * 13 * 5233 * 164130096629 * 13806214882775315521 * 266954214755806657783701473423485306938586062152607230052449979307325098257844629398194502635217917183182456273211216589853660356013322815793868770779953106120974798634815554092236537707402522742879243077382958327250723822564495930060837219 212743505119724423551387065633644991659252906850494873872085078946628642639294098329676357613123018172729123754334696906839700381847620698611068998052896832110315326273646505224537230670277
 1234567...192 Sm192 = (p1)^3 * p1 * p2 * p2 * c463 [ Length = 468 ] 2^3 * 3 * 29 * 41 * 432635229538520225032105824894944008705679237745059970680346006356319750989747846456225452241117726926190026495010736075717258444446217891350461798423331330196449004376895568033184738505393538341400697729552516495332594302323773875505029142 5466712893191797102716713103662991594096233919685069180513601665900586632364106502107693655282735812662992435981011885203152444601912011570057617226176309509713000111163904337509678202207007996256734762552046053658122693797
 1234567...193 Sm193 = p1 * p3 * p21 * p34 * c413 [ Length = 471 ] 7 * 419 * 419908232491384495189 * 5167315927941164272437909427556797 * 193991861438045294821418450482650835660608257847821702146502144717802684594876936255773787056318051381050263479767775186432726591977610274337692484275307556553233826842084153123151807857847749384786686767720441103069833962919524328197485152 10580721834447837028893276821143281090740143743099155351539413451083784961116254139247226012173583232566807527811327799722658362449748160624188756424757266299475543413844637 p21 by Sean A. Irvine p34 submitted to factordb.com before November 4, 2018.
 1234567...194 Sm194 = p1 * p1 * p2 * p2 * p3 * p8 * p14 * p16 * p19 * p20 * p21 * c373 [ Length = 474 ] 2 * 3 * 11 * 31 * 491 * 34188439 * 28739332991401 * 8203347603076921 * 1507421050431503839 * 22805873052490568609 * 168560953170124281211 * 263113134601433623506159251836470173818986318512714282934667360849921456133025826609027503552759240462919825207117836542620114188164780004461180452534576258311952733761630533028031272510138063018967189109162016573497133785379924297757292881 5960842229564148775574083899493815573787731753297181371675911056346444880131615129945020771988104129908002462227413731373835543197531
 1234567...195 Sm195 = p1 * p1 * p3 * p8 * p9 * p9 * p10 * p27 * p412 [ Length = 477 ] (by Sean A. Irvine ) 3 * 5 * 397 * 21728563 * 300856949 * 554551531 * 8174619091 * 165897663095213559529993681 * 421689179216004490268670579952138892539073288812243260875778257072007240866587533894580959087348349946204992973367677957665918840799383893405121462889149077964908152057144546772492950163139967315190731294500128685930803732434591580562083296 7849640928461423485497035455345542521700809846462266645935693244989301840859149448482745301257117142121991254187915811979621816086743861383233522991211424294391495728519167
 1234567...196 Sm196 = (p1)^2 * p2 * p2 * p2 * p10 * p464 [ Length = 480 ] 2^2 * 17 * 73 * 79 * 3834513037 * 821005175270568520408869433983216434183114591112676333745917354072569340548280754450517350676544898072821012903517554104139527969078949989299158584226264083288003675945748232271428765749277016711848572198548409604596374222112190891021649595 27873452634755168414750187208738721246827545799527258680876722972354788603612965854168365101059553630090692414068147728426416538096588069005207407056015550690564626039305537870197599450267926525787128394411912946409886699293
 1234567...197 Sm197 = (p1)^2 * p2 * p4 * p16 * c461 [ Length = 483 ] 3^2 * 37 * 6277 * 1368971104990459 * 431443900763626419637033585824555393600876092546075819339404222959249147825370084733652776320031918376058550371663755075056369556138150692154781392442924982822285263343203764600469394128581001243598705961766402429514750746361475735661791263 22884259594122545071451008793369483883440188589800418022199814209811781249776856825241223978909027822664031031884374456913126173644842841830316461498361487023246089650234667575493207727752598714881267791711099478763328863
 1234567...198 Sm198 = p1 * (p1)^2 * (p1)^2 * p2 * p29 * c453 [ Length = 486 ] 2 * 3^2 * 7^2 * 13 * 14158849264684185910199571953 * 760457735226784091294840569472145458786991928653508380971124951232445893341537228151786198097262922242993596257343257051703400175843430154722557677920874807863425475530765933204100503499768839606352399220179853720663569342290259555641027439 442943927504266724069376833160154122078614671268885319775025357850108512766756965068892272622194031924162199016275425966326165256651539551252483744445116646306879821859693369143742705388846172736661389828863605451 p29 by Sean A. Irvine
 1234567...199 Sm199 = p3 * p40 * c447 [ Length = 489 ] 151 * 4386264746954920374371567783174533011041 * 186398832942377429555452591563659684079765413854705864389921306888940333599059950208095535457614760128484399860037234160159192138094596242158068501774151388710210214383896282853147811799121298207590151664740033924177695648716063172173047017 911236453764993676049937409317754141571971633527089317399808119795275812472976282683848508770324255997254085144740663777094736682347251770666070758468752527785127982889419135231259082990979165068726974180289 p40 by Kevin Zhou The following factor of Sm199 was found on 2024/05/25: Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1:1648768524 Step 1 took 115453ms ********** Factor found in step 1: 4386264746954920374371567783174533011041 P = 2, Q = 3 (0.21%) p40 submitted to factordb.com on May 26, 2024.
 1234567...200 Sm200 = (p1)^5 * p1 * (p1)^2 * c488 [ Length = 492 ] 2^5 * 3 * 5^2 * 514403287921300547563173825800088426351052613678876305138931401557664183926810189436452062714688977315239941502567765194027820290446553072815699078325340951603577866204128830391456654082912917087925429600437942112950454625462967137975479650 487992163000504675513017188025529700538042213050554725563067238075579750588092263100604775613117288125629800638142313150654825663167338175679850688192363200704875713217388225729900738242413250754925763267438275779950788292463300804975813317 48832583 Source Smarandache Factors and Reverse Factors by Fleuren, Micha (page 18 of 35) dd. November 12, 1998.