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 = 118.
If there is a breaktrough in partially or completely factorising Sm118, 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
Factorization using the Elliptic Curve Method
GGNFS - A Number Field Sieve implementation
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).
Answer
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...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...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 * c169 [ Length = 261 ] |
3 *
7 *
37 *
413923 *
1565875469 *
5500432543504219 *
12347002211187670552593982429 *
2829927788416784955921382453753 *
1275508792274091607610942667677615438914771991780366753136716508498221303922106124824943698365001188759373368412203569594335316126100490059526352131895389719438604325459
| p29 and p31 found by Sean A. Irvine on 3 August 2005 (see Messages)
| |
| 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 * c486 [ Length = 489 ] |
| 151 *
817594629808689612020938531072988227312931306509472273068500240886353669817446658706943675837916255335480701725935520838189913044418362499839521713894581644932838992642323968834103291257609934444384788768907987464292113311994119954398113351
768994166358418027305457782292232636616755835312139961159841967802245961199616842014206265875153305630140080484464603683159987809007689815650093809047464689862054113723001153477987928332312451531007835656855537663497941656895312537709901961
570849
|
| 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.
|
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Patrick De Geest - Belgium 
- Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com