World!Of Numbers | |||
Smoothly Undulating Palindromic Primes (SUPP's) | |||
1 2 3 4 5 6 Near Smoothly Undulating Primes NSUP's (with 6-digit undulators) Near Smoothly Undulating Primes NSUP's (with 22-digit undulators) Palindromic Wing Primes Plateau & Depres. Primes Palindromic Merlon Primes Home Primes Circular Primes SUPP-sorted |
101 | 121 | 131 | 141 | 151 | 161 |
---|---|---|---|---|---|
171 | 181 | 191 | 313 | 323 | 343 |
353 | 373 | 383 | 717 | 727 | 737 |
747 | 757 | 787 | 797 | 919 | 929 |
949 | 959 | 979 | 989 |
Smoothly Undulating Palindromic Primes (or SUPP's for short)
are numbers that are primes, palindromic in base 10, and the digits alternate,
but why smooth one might ask !
The smoothness was added to make a difference with the normal
undulating numbers. The description for normal undulating numbers
is that the next digits alternately go up and down (or down and up)
but the absolute difference values between two adjacent digits may differ.
(e.g. 906343609)
In a smoothly undulating number the absolute difference values
between two adjacent digits are always equal, therefore only two distinct
digits can appear in the number.
(e.g. 74747474747474747)
SUPP's sorted by length |
---|
[ October 21, 2004 ]
Some nontrivial combinations can never produce primes...
By Julien Peter Benney (email)
Thus in both last cases only for w of the form 3n+2
is there any chance of a prime !
[ February 9, 2001 ]
Jeff Heleen wrote :
" As far as I could see you didn't have a section on your site for these numbers.
While I'm sure someone somewhere must have done this before, I have done it also.
Within the limitations of the program I believe these are ALL the smoothly undulating
palindromic prime numbers with two distinct digits each, smaller than 843 digits long.
I used a modified APRT-CLE program in UBASIC to automate and perform the search
on a Pentium_II 300 MHz laptop."
That is indeed a very nice and interesting compilation, thanks Jeff. Great job!
At the same time it is a topic that might attract other dedicated number crunchers.
Perhaps you know a source where larger SUPP's are displayed.
Those are welcome as well! Send them in and I'll add them to the table.
[ February 12, 2001 ]
Jeff Heleen wrote :
" I have found the following website:
http://www.utm.edu/research/primes/lists/top_ten/topten.pdf
where, if you will look on page 43 (of 93) you will see the top ten
SUPP's as of February 24, 2001. The smallest two on this list are the same as my
highest two. It doesn't say whether these are ALL there are up to the
highest one shown. However, I suspect not, as they all start and end with
the digit 1. So perhaps there are more to discover in this range."
[ February 14, 2001 ]
Message from Carlos Rivera
Carlos argues 'As a matter of fact the real SUPP 'sThere are several extra terms :
(37)k3, is prime for k=424 & 946
(75)k7, is prime for k=539 & 707
(79)k7, is prime for k=838
(92)k9, is prime for k=428
(95)k9, is prime for k=647(please verify them) In the meanwhile I used PRIMEFORM to get the next pseudoprime
following my record from 1997:
(12)k1, is pseudoprime for k=3904 (7809 digits) far beyond the current
possibilities of rigorous primality testing of the speediest code (TITANIX)
[ April 2001 ]
Start of above date I noticed a new entry in G. L. Honaker, Jr.'s Prime Curios!
website of Landon Curt Noll. A beautiful SUPP, proved prime with special
hardware a few years ago (?), was introduced there, which immediately shattered
Carlos Rivera's previous record !
This SUPP has a length of 2883 digits 3(73)1441
See Prime Curios! 37373...37373
You can contact L. C. Noll through his home page at http://www.isthe.com/chongo/
The following link includes many details about Landon's proof of the SUPP and why his proof got lost : Yahoo Message 1942 - Is (37*10^288373)/99 prime? References: |
[ May 6, 2001 ]
Enters Hans Rosenthal with new and more impressive data !
Here is a probable prime of length 10419 for your SUPP page:Hans added that many more of the _abababa_ type will follow within not too long.
3(13)5209 = 310*(10104181)/99+3
I don't know whether this one has been discovered by someone
else before (if you know of this, please send me a note).
[ June 26, 2001 ]
Carlos Rivera writes the following interesting observations.
1) Any smooth undulating palindrome number composed of two distinct digits
can be expressed in any one of the two forms:a(ba)n = (ab)na 2) (ab)na = (ab)nx10+a
3) (ab)n = (ab)xR(2n)/R(2)
4) R(k) = (10k 1)/(101)5) Consequently a(ba)n = (ab)na = (ab)x((102n1)/99)x10+a
6) But:
(ab)x((102n1)/99)x10+a = [(ab)x102n+1 (ab)x10 + 99a]/99 = [(ab)x102n+1 (ab)x10 + 100a a]/99 = [(ab)x102n+1 (ba)]/99 7) a(ba)n = (ab)na = (ab)x((102n1)/99)x10+a = [(ab)x102n+1 (ba)]/99
8) The form a(ba)n = [(ab)x102n+1 (ba)]/99 is the one used by you in your
But the second form (ab)na = (ab)x((102n1)/99)x10+a is a kind of more suitable
page and formally is correct.
one form for primality test purposes, especially if:
° a = 1 &
° [(102n 1)/99] can be factorized until certain extent in order to use classical
theorems like the Pocklington one.
Thanks Carlos for the interesting observations on the formula formats for the SUPP's.
Before Hans Rosenthal entered the stage I used the format you promote in entry 7
(highlighted in yellow).
But Hans convinced me to use to other one for the following reasons.
First the format [(ab)*102n+1(ba)]/99 displays the exact digitlength
of the SUPP namely via the exponent (2n+1).
Secondly the (ab) and (ba) coefficients indicate straight away how the SUPP starts and ends !
[ September 4, 2001 ]
Hans Rosenthal broke Landon Curt Noll's old record
by prime proving the following SUPP of 3015 digits !
3(23)1507 = (32*10301523)/99
[ October 19, 2001 ]
Hans Rosenthal sent in a list of five new records.
The largest one he prime proved is the following SUPP of 4859 digits !
" All Primo certificates have been validated with Cert_Val. The proof of the above
largest known SUPP (second largest known ECPP prime) took exactly 11 weeks
on an Athlon 1.4 GHz, the full validation of this certificate took 20 and a half hours
on the same PC.
I believe that from now on it's a real challenge (also for myself) to complete/enlarge
the SUPP table."
[ October 27, 2002 ]
Hans Rosenthal sent a new SUPP record of 4885 digits !
( Announced at Walter Schneider's site at Undulants )
The proof was done using Marcel Martin's Primo and took 2008 hours and 57 minutes
on a AMD Athlon 1.33 GHz. The Primo certificate was then validated with Cert_Val which took
on the same PC an additional 25 hours and 11 minutes.
See also the Top 20 ECPP records at http://www.ellipsa.eu/public/primo/top20.html
[ December 10, 2002 ]
Hans Rosenthal informs :
[ December 22, 2002 ]
David Broadhurst announced via a message (http://groups.yahoo.com/group/primeform/message/2937) in the
User group for the PrimeForm program that
the following SUPP is prime !
[ December 23, 2002 ]
Reaction from Hans Rosenthal ¬
" Yes, David informed me, nice result, such a proof won't happen every day.
Jim Fougeron double-checked the primality of 1(71)_2442 = (17*10^488571)/99
by use of BLS (he only took about 24 hours for that). Both, David and Jim were pretty
lucky with finding enough factors in N1 for their proofs. However, this can only
work for the SUPP's that start/end in 1 -- it will never work for the others.
I am really glad that I am no longer the only one to contribute new results to the
SUPP page. You should update it and also announce the new record on your main page."
[ July 13, 2003 ]
Hans Rosenthal announced via a message in
Number Theory List (NMBRTHRY@LISTSERV.NODAK.EDU)
that the following SUPP is proven prime !
3(23)3479 = (32*10695923)/99He thereby also established a new Primo ECPP world record
" I would like to inform you that I have certified the primality of
(32*10^695923)/99, a smoothly undulating palindromic prime (SUPP) [1]
having 6959 decimal digits, with the program Primo [2], Marcel Martin's
implementation of the elliptic curve primality proving (ECPP) algorithm.The Primo certificate of primality is available at
http://www.ellipsa.eu/public/primo/files/ecpp6959.zip (4457 KB)The certification of this ordinary prime was started on 21 January 2002
with Primo 1.1.0 (tests 1 to 47) and completed on 7 July 2003 with
Primo 2.0.0 (tests 48 to 953) on an AMD Athlon 1.4 GHz. There was one
relevant interruption of the certification process from 29 March 2003,
6:47, until 3 April 2003, 22:45. So the total running time amounts to
approximately 527 days.I thank Marcel Martin for his help and advice, and most of all, for
making the ECPP algorithm available to the world of PC users in the
most comfortable form I can imagine: his marvellous Primo.Hans Rosenthal "
[1] http://www.worldofnumbers.com/undulat.htm#
[2] http://www.ellipsa.eu/public/primo/top20.html
SUPP (Smoothly Undulating Prime Palindromes) reference files | |||
1(01)w = (10*10n1)/99 | Factorization of Repunits (M. Kamada) with even exponents n divided by 11. | ||
1(21)w = (12*10n21)/99 | Factorization of 133...331 (M. Kamada) with odd exponents n divided by 11. | ||
1(31)w = (13*10n31)/99 | Factorization of 144...441 (M. Kamada) with odd exponents n divided by 11. | ||
1(41)w = (14*10n41)/99 | Factorization of 155...551 (M. Kamada) with odd exponents n divided by 11. | ||
1(51)w = (15*10n51)/99 | Factorization of 166...661 (M. Kamada) with odd exponents n divided by 11. | ||
1(61)w = (16*10n61)/99 | Factorization of 177...771 (M. Kamada) with odd exponents n divided by 11. | ||
1(71)w = (17*10n71)/99 | Factorization of 188...881 (M. Kamada) with odd exponents n divided by 11. | ||
1(81)w = (18*10n81)/99 | Factorization of 199...991 (M. Kamada) with odd exponents n divided by 11. | ||
1(91)w = (19*10n91)/99 | facsupp191.htm (maintained by Patrick De Geest). | aba(1,9,n)=191...191 (n=1 to 100) (Hisanori Mishima) | Free to factor 7 remaining |
3(13)w = (31*10n13)/99 | Factorization of 344...443 (M. Kamada) with odd exponents n divided by 11. | ||
3(23)w = (32*10n23)/99 | Factorization of 355...553 (M. Kamada) with odd exponents n divided by 11. | ||
3(43)w = (34*10n43)/99 | Factorization of 377...773 (M. Kamada) with odd exponents n divided by 11. | ||
3(53)w = (35*10n53)/99 | Factorization of 388...883 (M. Kamada) with odd exponents n divided by 11. | ||
3(73)w = (37*10n73)/99 | facsupp373.htm (maintained by Patrick De Geest). | aba(3,7,n)=373...373 (n=1 to 100) (Hisanori Mishima) | Free to factor 7 remaining |
3(83)w = (38*10n83)/99 | facsupp383.htm (maintained by Patrick De Geest). | aba(3,8,n)=383...383 (n=1 to 100) (Hisanori Mishima) | Free to factor 6 remaining |
7(17)w = (71*10n17)/99 | Factorization of 788...887 (M. Kamada) with odd exponents n divided by 11. | ||
7(27)w = (72*10n27)/99 | Factorization of 799...997 (M. Kamada) with odd exponents n divided by 11. | ||
7(37)w = (73*10n37)/99 | facsupp737.htm (maintained by Patrick De Geest). | aba(7,3,n)=737...737 (n=1 to 100) (Hisanori Mishima) | Free to factor 7 remaining |
7(47)w = (74*10n47)/99 | facsupp747.htm (maintained by Patrick De Geest). | aba(7,4,n)=747...747 (n=1 to 100) (Hisanori Mishima) | Free to factor 11 remaining |
7(57)w = (75*10n57)/99 | facsupp757.htm (maintained by Patrick De Geest). | aba(7,5,n)=757...757 (n=1 to 100) (Hisanori Mishima) | All factored (n ⩽ 100) |
7(87)w = (78*10n87)/99 | facsupp787.htm (maintained by Patrick De Geest). | aba(7,8,n)=787...787 (n=1 to 100) (Hisanori Mishima) | Free to factor 9 remaining |
7(97)w = (79*10n97)/99 | facsupp797.htm (maintained by Patrick De Geest). | aba(7,9,n)=797...797 (n=1 to 100) (Hisanori Mishima) | Free to factor 8 remaining |
9(19)w = (91*10n19)/99 | facsupp919.htm (maintained by Patrick De Geest). | aba(9,1,n)=919...919 (n=1 to 100) (Hisanori Mishima) | Free to factor 7 remaining |
9(29)w = (92*10n29)/99 | facsupp929.htm (maintained by Patrick De Geest). | aba(9,2,n)=929...929 (n=1 to 100) (Hisanori Mishima) | Free to factor 5 remaining |
9(49)w = (94*10n49)/99 | facsupp949.htm (maintained by Patrick De Geest). | aba(9,4,n)=949...949 (n=1 to 100) (Hisanori Mishima) | Free to factor 8 remaining |
9(59)w = (95*10n59)/99 | facsupp959.htm (maintained by Patrick De Geest). | aba(9,5,n)=959...959 (n=1 to 100) (Hisanori Mishima) | Free to factor 6 remaining |
9(79)w = (97*10n79)/99 | facsupp979.htm (maintained by Patrick De Geest). | aba(9,7,n)=979...979 (n=1 to 100) (Hisanori Mishima) | Free to factor 5 remaining |
9(89)w = (98*10n89)/99 | facsupp989.htm (maintained by Patrick De Geest). | aba(9,8,n)=989...989 (n=1 to 100) (Hisanori Mishima) | Free to factor 7 remaining |
|
|
Following condition must be imposed that gcd(A,B) = 1 (in Factorization of ABA...ABA), i.e. A and B are coprime, since if A and B have a common factor > 1, then we can divide this factor from the number,
e.g. factor 69696...69696 is equivalent to factor 23232...23232.
The reference table for Smoothly Undulating Palindromic Primes | |||||
This collection is complete for probable primes up to 100,000 (ref. RC) digits and for proven primes up to 6343 digits. | CR = Carlos Rivera | ||||
SUPP | Formula Accolades = prime exp Blue exp = # of digits | Who | When | Status | Program Output Logs |
¬ | | ||||
---|---|---|---|---|---|
1(01)1 | (10*10{3}01)/99 IMPORTANT NOTE |
JH | Feb 09 2001 | PRIME | View |
A062209 ¬ A056803 ¬ | | ||||
1(21)3 | (12*10{7}21)/99 | JH | Feb 09 2001 | PRIME | View |
1(21)5 | (12*10{11}21)/99 | JH | Feb 09 2001 | PRIME | View |
1(21)21 | (12*10{43}21)/99 | JH | Feb 09 2001 | PRIME | View |
1(21)69 | (12*10{139}21)/99 | JH | Feb 09 2001 | PRIME | View |
1(21)313 | (12*1062721)/99 | JH | Feb 09 2001 | PRIME | View |
1(21)699 | (12*10{1399}21)/99 | HR | Jun 17 2001 | PRIME | View |
1(21)798 | (12*10{1597}21)/99 | HR | Jun 17 2001 | PRIME | View |
1(21)989 | (12*10{1979}21)/99 | CR | ___ __ 1997 | PRIME | View |
1(21)3904 | (12*10780921)/99 | CR | ___ __ 2001 | PROBABLE PRIME |
View |
1(21)7029 | (12*101405921)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
1(21)23249 | (12*10{46499}21)/99 | RC | Oct 12 2010 | PROBABLE PRIME |
View |
¬ | | ||||
1(31)1 | (13*10{3}31)/99 | JH | Feb 09 2001 | PRIME | View |
1(31)12 | (13*102531)/99 | JH | Feb 09 2001 | PRIME | View |
A062210 ¬ | | ||||
1(41)5 | (14*10{11}41)/99 | JH | Feb 09 2001 | PRIME | View |
1(41)138 | (14*10{277}41)/99 | JH | Feb 09 2001 | PRIME | View |
1(41)239 | (14*10{479}41)/99 | JH | Feb 09 2001 | PRIME | View |
1(41)291 | (14*1058341)/99 | JH | Feb 09 2001 | PRIME | View |
1(41)815 | (14*10163141)/99 | HR | Aug 09 2001 | PRIME | View |
1(41)3171 | (14*10{6343}41)/99 | DB | Dec 22 2002 | PRIME | View |
1(41)7344 | (14*101468941)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
A062211 ¬ | | ||||
1(51)1 | (15*10{3}51)/99 | JH | Feb 09 2001 | PRIME | View |
1(51)7 | (15*101551)/99 | JH | Feb 09 2001 | PRIME | View |
1(51)31 | (15*106351)/99 | JH | Feb 09 2001 | PRIME | View |
1(51)44 | (15*10{89}51)/99 | JH | Feb 09 2001 | PRIME | View |
1(51)122 | (15*1024551)/99 | JH | Feb 09 2001 | PRIME | View |
1(51)291 | (15*1058351)/99 | JH | Feb 09 2001 | PRIME | View |
1(51)895 | (15*10179151)/99 | HR | Jun 17 2001 | PRIME | View |
1(51)1061 | (15*10212351)/99 | HR | Aug 09 2001 | PRIME | View |
1(51)3616 | (15*10723351)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
1(51)12393 | (15*102478751)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
1(51)22326 | (15*104465351)/99 | RC | Oct 04 2010 | PROBABLE PRIME |
View |
A062212 ¬ | | ||||
1(61)3 | (16*10{7}61)/99 | JH | Feb 09 2001 | PRIME | View |
1(61)27 | (16*105561)/99 | JH | Feb 09 2001 | PRIME | View |
1(61)54 | (16*10{109}61)/99 | JH | Feb 09 2001 | PRIME | View |
1(61)72 | (16*1014561)/99 | JH | Feb 09 2001 | PRIME | View |
1(61)114 | (16*10{229}61)/99 | JH | Feb 09 2001 | PRIME | View |
1(61)480 | (16*1096161)/99 | HR | Jun 04 2001 | PRIME | View |
A062213 ¬ | | ||||
1(71)15 | (17*10{31}71)/99 | JH | Feb 09 2001 | PRIME | View |
1(71)18 | (17*10{37}71)/99 | JH | Feb 09 2001 | PRIME | View |
1(71)2442 | (17*10488571)/99 | HR | Oct 27 2002 | PRIME | View |
A062214 ¬ | | ||||
1(81)1 | (18*10{3}81)/99 | JH | Feb 09 2001 | PRIME | View |
1(81)2 | (18*10{5}81)/99 | JH | Feb 09 2001 | PRIME | View |
1(81)38 | (18*107781)/99 | JH | Feb 09 2001 | PRIME | View |
1(81)81 | (18*10{163}81)/99 | JH | Feb 09 2001 | PRIME | View |
1(81)739 | (18*10147981)/99 | HR | Aug 09 2001 | PRIME | View |
1(81)1828 | (18*10365781)/99 | HR | Feb 11 2002 | PRIME | View |
1(81)2286 | (18*10457381)/99 | HR | Aug 08 2002 | PRIME | View |
1(81)4157 | (18*10831581)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
1(81)15129 | (18*10{30259}81)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
1(81)15531 | (18*10{31063}81)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
1(81)15927 | (18*103185581)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
1(81)18457 | (18*103691581)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
1(81)33328 | (18*106665781)/99 | RC | Jan 31 2011 | PROBABLE PRIME |
View |
A062215 ¬ | | ||||
1(91)1 | (19*10{3}91)/99 | JH | Feb 09 2001 | PRIME | View |
1(91)16 | (19*103391)/99 | JH | Feb 09 2001 | PRIME | View |
1(91)66 | (19*1013391)/99 | JH | Feb 09 2001 | PRIME | View |
1(91)984 | (19*10196991)/99 | HR | Jul 08 2001 | PRIME | View |
1(91)1167 | (19*10233591)/99 | HR | Sep 04 2001 | PRIME | View |
A062216 ¬ | | ||||
3(13)1 | (31*10{3}13)/99 | JH | Feb 09 2001 | PRIME | View |
3(13)25 | (31*105113)/99 | JH | Feb 09 2001 | PRIME | View |
3(13)41 | (31*10{83}13)/99 | JH | Feb 09 2001 | PRIME | View |
3(13)112 | (31*1022513)/99 | JH | Feb 09 2001 | PRIME | View |
3(13)280 | (31*1056113)/99 | JH | Feb 09 2001 | PRIME | View |
3(13)5209 | (31*101041913)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
3(13)9127 | (31*101825513)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
3(13)21934 | (31*104386913)/99 | RC | Sep 30 2010 | PROBABLE PRIME |
View |
A062217 ¬ | | ||||
3(23)2 | (32*10{5}23)/99 | JH | Feb 09 2001 | PRIME | View |
3(23)4 | (32*10923)/99 | JH | Feb 09 2001 | PRIME | View |
3(23)5 | (32*10{11}23)/99 | JH | Feb 09 2001 | PRIME | View |
3(23)1507 | (32*10301523)/99 | HR | Sep 04 2001 | PRIME | View |
3(23)1703 | (32*10{3407}23)/99 | HR | Oct 19 2001 | PRIME | View |
3(23)3479 | (32*10{6959}23)/99 | HR | Jul 08 2003 | PRIME | View |
3(23)4799 | (32*10959923)/99 | HR | Jun 04 2001 | RECORD PROVEN PRIME |
View |
3(23)5699 | (32*10{11399}23)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
3(23)8296 | (32*101659323)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
3(23)12941 | (32*102588323)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
¬ | | ||||
3(43)w | (34*10n43)/99 | | Mon day year | | View |
A062218 ¬ | | ||||
3(53)1 | (35*10{3}53)/99 | JH | Feb 09 2001 | PRIME | View |
3(53)2 | (35*10{5}53)/99 | JH | Feb 09 2001 | PRIME | View |
3(53)11 | (35*10{23}53)/99 | JH | Feb 09 2001 | PRIME | View |
3(53)1088 | (35*10217753)/99 | HR | Jun 17 2001 | PRIME | View |
3(53)1573 | (35*10314753)/99 | HR | Oct 19 2001 | PRIME | View |
3(53)2078 | (35*10{4157}53)/99 | HR | Feb 11 2002 | PRIME | View |
3(53)11356 | (35*102271353)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
3(53)14192 | (35*102838553)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
A062219 ¬ | | ||||
3(73)1 | (37*10{3}73)/99 | JH | Feb 09 2001 | PRIME | View |
3(73)10 | (37*102173)/99 | JH | Feb 09 2001 | PRIME | View |
3(73)13 | (37*102773)/99 | JH | Feb 09 2001 | PRIME | View |
3(73)40 | (37*108173)/99 | JH | Feb 09 2001 | PRIME | View |
3(73)157 | (37*1031573)/99 | JH | Feb 09 2001 | PRIME | View |
3(73)424 | (37*1084973)/99 | HR | Jun 04 2001 | PRIME | View |
3(73)946 | (37*10189373)/99 | HR | Jul 08 2001 | PRIME | View |
3(73)1441 | (37*10288373)/99 | LN | ___ __ 1997 | PRIME | View |
3(73)4795 | (37*10959173)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
3(73)7345 | (37*101469173)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
A062220 ¬ | | ||||
3(83)1 | (38*10{3}83)/99 | JH | Feb 09 2001 | PRIME | View |
3(83)4 | (38*10983)/99 | JH | Feb 09 2001 | PRIME | View |
3(83)7 | (38*101583)/99 | JH | Feb 09 2001 | PRIME | View |
3(83)8 | (38*10{17}83)/99 | JH | Feb 09 2001 | PRIME | View |
3(83)10 | (38*102183)/99 | JH | Feb 09 2001 | PRIME | View |
3(83)28 | (38*105783)/99 | JH | Feb 09 2001 | PRIME | View |
3(83)2116 | (38*10423383)/99 | HR | Apr 02 2002 | PRIME | View |
3(83)2167 | (38*10433583)/99 | HR | Aug 08 2002 | PRIME | View |
3(83)6610 | (38*101322183)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
3(83)13223 | (38*102644783)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
3(83)14948 | (38*102989783)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
3(83)45998 | (38*10{91997}83)/99 | RC | Jul 29 2011 | PROBABLE PRIME |
View |
¬ | | ||||
7(17)w | (71*10n17)/99 | | Mon day year | | View |
A062221 ¬ | n ⩾ 100001 (PDG, September 13, 2004) | ||||
7(27)1 | (72*10{3}27)/99 | JH | Feb 09 2001 | PRIME | View |
7(27)2 | (72*10{5}27)/99 | JH | Feb 09 2001 | PRIME | View |
7(27)4 | (72*10927)/99 | JH | Feb 09 2001 | PRIME | View |
7(27)8 | (72*10{17}27)/99 | JH | Feb 09 2001 | PRIME | View |
7(27)35 | (72*10{71}27)/99 | JH | Feb 09 2001 | PRIME | View |
7(27)49 | (72*109927)/99 | JH | Feb 09 2001 | PRIME | View |
7(27)121 | (72*1024327)/99 | JH | Feb 09 2001 | PRIME | View |
7(27)3797 | (72*10759527)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
7(27)4636 | (72*10927327)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
7(27)26923 | (72*105384727)/99 | PDG | Aug 06 2004 | PROBABLE PRIME |
View |
A062222 ¬ | | ||||
7(37)7 | (73*101537)/99 | JH | Feb 09 2001 | PRIME | View |
7(37)19 | (73*103937)/99 | JH | Feb 09 2001 | PRIME | View |
7(37)283 | (73*1056737)/99 | JH | Feb 09 2001 | PRIME | View |
7(37)1264 | (73*10252937)/99 | HR | Sep 04 2001 | PRIME | View |
7(37)7168 | (73*101433737)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
A062223 ¬ | | ||||
7(47)2 | (74*10{5}47)/99 | JH | Feb 09 2001 | PRIME | View |
7(47)8 | (74*10{17}47)/99 | JH | Feb 09 2001 | PRIME | View |
7(47)1034 | (74*10{2069}47)/99 | HR | Aug 09 2001 | PRIME | View |
7(47)3407 | (74*10681547)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
7(47)10208 | (74*102041747)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
7(47)12872 | (74*102574547)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
A062224 ¬ | | ||||
7(57)1 | (75*10{3}57)/99 | JH | Feb 09 2001 | PRIME | View |
7(57)8 | (75*10{17}57)/99 | JH | Feb 09 2001 | PRIME | View |
7(57)38 | (75*107757)/99 | JH | Feb 09 2001 | PRIME | View |
7(57)71 | (75*1014357)/99 | JH | Feb 09 2001 | PRIME | View |
7(57)74 | (75*10{149}57)/99 | JH | Feb 09 2001 | PRIME | View |
7(57)256 | (75*1051357)/99 | JH | Feb 09 2001 | PRIME | View |
7(57)539 | (75*10107957)/99 | HR | Aug 09 2001 | PRIME | View |
7(57)707 | (75*10141557)/99 | HR | Aug 09 2001 | PRIME | View |
7(57)3124 | (75*10624957)/99 | HR | Aug 21 2003 | PRIME | View |
7(57)6632 | (75*101326557)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
7(57)7289 | (75*101457957)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
7(57)7646 | (75*101529357)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
7(57)20828 | (75*104165757)/99 | RC | Sep 16 2010 | PROBABLE PRIME |
View |
7(57)36470 | (75*107294157)/99 | RC | Mar 24 2011 | PROBABLE PRIME |
View |
A062225 ¬ | | ||||
7(87)1 | (78*10{3}87)/99 | JH | Feb 09 2001 | PRIME | View |
7(87)2 | (78*10{5}87)/99 | JH | Feb 09 2001 | PRIME | View |
7(87)10 | (78*102187)/99 | JH | Feb 09 2001 | PRIME | View |
7(87)13 | (78*102787)/99 | JH | Feb 09 2001 | PRIME | View |
7(87)47 | (78*109587)/99 | JH | Feb 09 2001 | PRIME | View |
7(87)1037 | (78*10207587)/99 | HR | Aug 09 2001 | PRIME | View |
7(87)1082 | (78*10216587)/99 | HR | Aug 09 2001 | PRIME | View |
7(87)1523 | (78*10304787)/99 | HR | Oct 19 2001 | PRIME | View |
7(87)1751 | (78*10350387)/99 | HR | Feb 11 2002 | PRIME | View |
7(87)8395 | (78*101679187)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
7(87)17441 | (78*10{34883}87)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
A062226 ¬ | | ||||
7(97)1 | (79*10{3}97)/99 | JH | Feb 09 2001 | PRIME | View |
7(97)178 | (79*1035797)/99 | JH | Feb 09 2001 | PRIME | View |
7(97)268 | (79*1053797)/99 | JH | Feb 09 2001 | PRIME | View |
7(97)838 | (79*10167797)/99 | HR | Aug 09 2001 | PRIME | View |
7(97)1528 | (79*10305797)/99 | HR | Oct 19 2001 | PRIME | View |
7(97)25831 | (79*105166397)/99 | RC | Nov 3 2010 | PROBABLE PRIME |
View |
7(97)33223 | (79*106644797)/99 | RC | Jan 29 2011 | PROBABLE PRIME |
View |
A062227 ¬ | | ||||
9(19)1 | (91*10{3}19)/99 | JH | Feb 09 2001 | PRIME | View |
9(19)4 | (91*10919)/99 | JH | Feb 09 2001 | PRIME | View |
9(19)5 | (91*10{11}19)/99 | JH | Feb 09 2001 | PRIME | View |
9(19)8 | (91*10{17}19)/99 | JH | Feb 09 2001 | PRIME | View |
9(19)11 | (91*10{23}19)/99 | JH | Feb 09 2001 | PRIME | View |
9(19)12614 | (91*10{25229}19)/99 | HR | Jun 15 2001 | PROBABLE PRIME |
View |
A062228 ¬ | | ||||
9(29)1 | (92*10{3}29)/99 | JH | Feb 09 2001 | PRIME | View |
9(29)4 | (92*10929)/99 | JH | Feb 09 2001 | PRIME | View |
9(29)97 | (92*1019529)/99 | JH | Feb 09 2001 | PRIME | View |
9(29)257 | (92*1051529)/99 | JH | Feb 09 2001 | PRIME | View |
9(29)428 | (92*10{857}29)/99 | HR | Jun 04 2001 | PRIME | View |
9(29)5696 | (92*10{11393}29)/99 | HR | Jun 04 2001 | PROBABLE PRIME |
View |
A062229 ¬ | | ||||
9(49)2 | (94*10{5}49)/99 | JH | Feb 09 2001 | PRIME | View |
9(49)8 | (94*10{17}49)/99 | JH | Feb 09 2001 | PRIME | View |
9(49)32 | (94*106549)/99 | JH | Feb 09 2001 | PRIME | View |
9(49)71 | (94*1014349)/99 | JH | Feb 09 2001 | PRIME | View |
9(49)275 | (94*1055149)/99 | JH | Feb 09 2001 | PRIME | View |
9(49)46490 | (94*109298149)/99 | RC | Jul 30 2011 | RECORD PROBABLE PRIME |
View |
A062230 ¬ | | ||||
9(59)2 | (95*10{5}59)/99 | JH | Feb 09 2001 | PRIME | View |
9(59)8 | (95*10{17}59)/99 | JH | Feb 09 2001 | PRIME | View |
9(59)104 | (95*1020959)/99 | JH | Feb 09 2001 | PRIME | View |
9(59)647 | (95*10129559)/99 | HR | Aug 09 2001 | PRIME | View |
A062231 ¬ | | ||||
9(79)4 | (97*10979)/99 | JH | Feb 09 2001 | PRIME | View |
9(79)13 | (97*102779)/99 | JH | Feb 09 2001 | PRIME | View |
9(79)22 | (97*104579)/99 | JH | Feb 09 2001 | PRIME | View |
9(79)118 | (97*1023779)/99 | JH | Feb 09 2001 | PRIME | View |
A062232 ¬ | | ||||
9(89)4 | (98*10989)/99 | JH | Feb 09 2001 | PRIME | View |
9(89)80 | (98*1016189)/99 | JH | Feb 09 2001 | PRIME | View |
9(89)109 | (98*1021989)/99 | JH | Feb 09 2001 | PRIME | View |
9(89)2429 | (98*10485989)/99 | HR | Oct 19 2001 | PRIME | View |
9(89)10994 | (98*102198989)/99 | HR | Oct 19 2001 | PROBABLE PRIME |
View |
9(89)26465 | (98*105293189)/99 | RC | Nov 9 2010 | PROBABLE PRIME |
View |
9(89)44297 | (98*108859589)/99 | RC | Jul 23 2011 | PROBABLE PRIME |
View |
The reference table for Near Smoothly Undulating Primes Cases with 2-digit undulators derived from the composite set of SUP's | |||||
This collection is complete for probable primes up to 30,000 digits. | PDG = Patrick De Geest | ||||
NSUP | Formula Accolades = prime exp | Who | When | Status | Prime Certificat |
¬ | | ||||
2(12)1/22 = [53](03)0 | (21*10{3}12)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)3/22 = [53](03)2 | (21*10{7}12)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)10/22 = [53](03)9 | (21*102112)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)38/22 = [53](03)37 | (21*107712)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)51/22 = [53](03)50 | (21*10{103}12)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)71/22 = [53](03)70 | (21*1014312)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)260/22 = [53](03)259 | (21*10{521}12)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)632/22 = [53](03)631 | (21*10126512)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)673/22 = [53](03)672 | (21*10134712)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)2508/22 = [53](03)2507 | (21*10501712)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)4513/22 = [53](03)4512 | (21*10902712)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(12)7868/22 = [53](03)7867 | (21*10{15737}12)/(99*4) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
2(32)91/25 = [726](01)89 | (23*1018332)/(99*32) | PDG | Aug 01 2022 | PRP | View |
2(32)721/25 = [726](01)719 | (23*10144332)/(99*32) | PDG | Aug 01 2022 | PRP | View |
2(32)3000/25 = [726](01)2998 | (23*10600132)/(99*32) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
2(52)5/22 = [63](13)4 | (25*10{11}52)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(52)15/22 = [63](13)14 | (25*10{31}52)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(52)42/22 = [63](13)41 | (25*108552)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(52)204/22 = [63](13)203 | (25*10{409}52)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(52)702/22 = [63](13)701 | (25*10140552)/(99*4) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
2(72)3/23 = [34](09)2 | (27*10{7}72)/(99*8) | PDG | Aug 01 2022 | PRP | View |
2(72)12/23 = [34](09)11 | (27*102572)/(99*8) | PDG | Aug 01 2022 | PRP | View |
2(72)55/23 = [34](09)54 | (27*1011172)/(99*8) | PDG | Aug 01 2022 | PRP | View |
2(72)2941/23 = [34](09)2940 | (27*10588372)/(99*8) | PDG | Aug 01 2022 | PRP | View |
2(72)3853/23 = [34](09)3852 | (27*10770772)/(99*8) | PDG | Aug 01 2022 | PRP | View |
2(72)8487/23 = [34](09)8486 | (27*101697572)/(99*8) | PDG | Aug 01 2022 | PRP | View |
¬ | n ⩾ 67231 (PDG, August 8, 2022) | ||||
2(92)1/22 = [73](23)0 | (29*10{3}92)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(92)3/22 = [73](23)2 | (29*10{7}92)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(92)28/22 = [73](23)27 | (29*105792)/(99*4) | PDG | Aug 01 2022 | PRP | View |
2(92)226/22 = [73](23)225 | (29*1045392)/(99*4) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
4(14)0/2 = [2](07)0 | (41*10114)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(14)2/2 = [2](07)2 | (41*10{5}14)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(14)129/2 = [2](07)129 | (41*1025914)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(14)249/2 = [2](07)249 | (41*10{499}14)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(14)315/2 = [2](07)315 | (41*10{631}14)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(14)557/2 = [2](07)557 | (41*10111514)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(14)615/2 = [2](07)615 | (41*10{1231}14)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(14)965/2 = [2](07)965 | (41*10{1931}14)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(14)4605/2 = [2](07)4605 | (41*10921114)/(99*2) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
4(34)0/2 = [2](17)0 | (43*10134)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(34)3/2 = [2](17)3 | (43*10{7}34)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(34)6/2 = [2](17)6 | (43*10{13}34)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(34)45/2 = [2](17)45 | (43*109134)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(34)48/2 = [2](17)48 | (43*10{97}34)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(34)291/2 = [2](17)291 | (43*1058334)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(34)2388/2 = [2](17)2388 | (43*10477734)/(99*2) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
4(54)0/2 = [2](27)0 | (45*10154)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(54)1/2 = [2](27)1 | (45*10{3}54)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(54)2/2 = [2](27)2 | (45*10{5}54)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(54)3/2 = [2](27)3 | (45*10{7}54)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(54)8/2 = [2](27)8 | (45*10{17}54)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(54)486/2 = [2](27)486 | (45*1097354)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(54)497/2 = [2](27)497 | (45*1099554)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(54)703/2 = [2](27)703 | (45*10140754)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(54)14514/2 = [2](27)14514 | (45*102902954)/(99*2) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
4(74)0/2 = [2](37)0 | (47*10174)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(74)57/2 = [2](37)57 | (47*1011574)/(99*2) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
4(94)0/2 = [2](47)0 | (49*10194)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(94)336/2 = [2](47)336 | (49*10{673}94)/(99*2) | PDG | Aug 01 2022 | PRP | View |
4(94)396/2 = [2](47)396 | (49*1079394)/(99*2) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
5(15)0/5 = [1](03)0 | (51*10115)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)1/5 = [1](03)1 | (51*10{3}15)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)2/5 = [1](03)2 | (51*10{5}15)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)4/5 = [1](03)4 | (51*10915)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)9/5 = [1](03)9 | (51*10{19}15)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)22/5 = [1](03)22 | (51*104515)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)28/5 = [1](03)28 | (51*105715)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)39/5 = [1](03)39 | (51*10{79}15)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)96/5 = [1](03)96 | (51*10{193}15)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)138/5 = [1](03)138 | (51*10{277}15)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)1532/5 = [1](03)1532 | (51*10306515)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)1553/5 = [1](03)1553 | (51*10310715)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)3022/5 = [1](03)3022 | (51*10604515)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)3325/5 = [1](03)3325 | (51*10665115)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(15)9888/5 = [1](03)9888 | (51*10{19777}15)/(99*5) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
5(25)3/52 = [21](01)2 | (52*10{7}25)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(25)18/52 = [21](01)17 | (52*10{37}25)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(25)170/52 = [21](01)169 | (52*1034125)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(25)227/52 = [21](01)226 | (52*1045525)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(25)3086/52 = [21](01)3085 | (52*10{6173}25)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(25)5840/52 = [21](01)5839 | (52*10{11681}25)/(99*25) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
5(35)1/5 = [1](07)1 | (53*10{3}35)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(35)4/5 = [1](07)4 | (53*10935)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(35)6/5 = [1](07)6 | (53*10{13}35)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(35)34/5 = [1](07)34 | (53*106935)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(35)1563/5 = [1](07)1563 | (53*10312735)/(99*5) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
5(45)0/5 = [1](09)0 | (54*10145)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(45)1/5 = [1](09)1 | (54*10{3}45)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(45)2/5 = [1](09)2 | (54*10{5}45)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(45)3/5 = [1](09)3 | (54*10{7}45)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(45)5/5 = [1](09)5 | (54*10{11}45)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(45)12/5 = [1](09)12 | (54*102545)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(45)716/5 = [1](09)716 | (54*10{1433}45)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(45)2867/5 = [1](09)2867 | (54*10573545)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(45)5738/5 = [1](09)5738 | (54*101147745)/(99*5) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
5(65)0/5 = [1](13)0 | (56*10165)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(65)1/5 = [1](13)1 | (56*10{3}65)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(65)6/5 = [1](13)6 | (56*10{13}65)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(65)10/5 = [1](13)10 | (56*102165)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(65)810/5 = [1](13)810 | (56*10{1621}65)/(99*5) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
5(75)1/52 = [23](03)0 | (57*10{3}75)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(75)3/52 = [23](03)2 | (57*10{7}75)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(75)7/52 = [23](03)6 | (57*101575)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(75)21/52 = [23](03)20 | (57*10{43}75)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(75)40/52 = [23](03)39 | (57*108175)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(75)60/52 = [23](03)59 | (57*1012175)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(75)73/52 = [23](03)72 | (57*1014775)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(75)571/52 = [23](03)570 | (57*10114375)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(75)783/52 = [23](03)782 | (57*10{1567}75)/(99*25) | PDG | Aug 01 2022 | PRP | View |
5(75)2980/52 = [23](03)2979 | (57*10596175)/(99*25) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
5(85)0/5 = [1](17)0 | (58*10185)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(85)2/5 = [1](17)2 | (58*10{5}85)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(85)6/5 = [1](17)6 | (58*10{13}85)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(85)12/5 = [1](17)12 | (58*102585)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(85)33/5 = [1](17)33 | (58*10{67}85)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(85)90/5 = [1](17)90 | (58*10{181}85)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(85)1262/5 = [1](17)1262 | (58*10252585)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(85)6872/5 = [1](17)6872 | (58*101374585)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(85)10365/5 = [1](17)10365 | (58*10{20731}85)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(85)13665/5 = [1](17)13665 | (58*102733185)/(99*5) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
5(95)0/5 = [1](19)0 | (59*10195)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(95)24/5 = [1](19)24 | (59*104995)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(95)381/5 = [1](19)381 | (59*1076395)/(99*5) | PDG | Aug 01 2022 | PRP | View |
5(95)9741/5 = [1](19)9741 | (59*10{19483}95)/(99*5) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
6(16)2/24 = [3851](01)0 | (61*10{5}16)/(99*16) | PDG | Aug 01 2022 | PRP | View |
6(16)5/24 = [3851](01)3 | (61*10{11}16)/(99*16) | PDG | Aug 01 2022 | PRP | View |
6(16)62/24 = [3851](01)60 | (61*1012516)/(99*16) | PDG | Aug 01 2022 | PRP | View |
6(16)926/24 = [3851](01)924 | (61*10185316)/(99*16) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
6(56)4/23 = [82](07)3 | (65*10956)/(99*8) | PDG | Aug 01 2022 | PRP | View |
6(56)10/23 = [82](07)9 | (65*102156)/(99*8) | PDG | Aug 01 2022 | PRP | View |
6(56)13/23 = [82](07)12 | (65*102756)/(99*8) | PDG | Aug 01 2022 | PRP | View |
6(56)37/23 = [82](07)36 | (65*107556)/(99*8) | PDG | Aug 01 2022 | PRP | View |
6(56)3047/23 = [82](07)3046 | (65*10609556)/(99*8) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
8(18)1/2 = [4](09)1 | (81*10{3}18)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)7/2 = [4](09)7 | (81*101518)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)14/2 = [4](09)14 | (81*10{29}18)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)58/2 = [4](09)58 | (81*1011718)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)143/2 = [4](09)143 | (81*1028718)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)383/2 = [4](09)383 | (81*1076718)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)488/2 = [4](09)488 | (81*10{977}18)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)499/2 = [4](09)499 | (81*1099918)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)1203/2 = [4](09)1203 | (81*10240718)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)8754/2 = [4](09)8754 | (81*10{17509}18)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(18)11708/2 = [4](09)11708 | (81*10{23417}18)/(99*2) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
8(38)1/2 = [4](19)1 | (83*10{3}38)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(38)3/2 = [4](19)3 | (83*10{7}38)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(38)43/2 = [4](19)43 | (83*108738)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(38)87/2 = [4](19)87 | (83*1017538)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(38)811/2 = [4](19)811 | (83*10162338)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(38)979/2 = [4](19)979 | (83*10195938)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(38)13372/2 = [4](19)13372 | (83*102674538)/(99*2) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
8(58)2/2 = [4](29)2 | (85*10{5}58)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(58)6/2 = [4](29)6 | (85*10{13}58)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(58)90/2 = [4](29)90 | (85*10{181}58)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(58)98/2 = [4](29)98 | (85*10{197}58)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(58)141/2 = [4](29)141 | (85*10{283}58)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(58)443/2 = [4](29)443 | (85*10{887}58)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(58)560/2 = [4](29)560 | (85*10112158)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(58)689/2 = [4](29)689 | (85*10137958)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(58)11393/2 = [4](29)11393 | (85*10{22787}58)/(99*2) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
8(78)1/2 = [4](39)1 | (87*10{3}78)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(78)10/2 = [4](39)10 | (87*102178)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(78)16/2 = [4](39)16 | (87*103378)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(78)37/2 = [4](39)37 | (87*107578)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(78)132/2 = [4](39)132 | (87*1026578)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(78)150/2 = [4](39)150 | (87*1030178)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(78)2716/2 = [4](39)2716 | (87*10543378)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(78)9922/2 = [4](39)9922 | (87*101984578)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(78)11370/2 = [4](39)11370 | (87*10{22741}78)/(99*2) | PDG | Aug 01 2022 | PRP | View |
¬ | | ||||
8(98)1/2 = [4](49)1 | (89*10{3}98)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)21/2 = [4](49)21 | (89*10{43}98)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)28/2 = [4](49)28 | (89*105798)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)43/2 = [4](49)43 | (89*108798)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)169/2 = [4](49)169 | (89*1033998)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)201/2 = [4](49)201 | (89*1040398)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)210/2 = [4](49)210 | (89*10{421}98)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)298/2 = [4](49)298 | (89*1059798)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)1948/2 = [4](49)1948 | (89*10389798)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)3351/2 = [4](49)3351 | (89*10{6703}98)/(99*2) | PDG | Aug 01 2022 | PRP | View |
8(98)13213/2 = [4](49)13213 | (89*102642798)/(99*2) | PDG | Aug 01 2022 | PRP | View |
Click here to view some entries to the table about palindromes. |
All of Hans Rosenthal's probable primes above 10000 digits are also
submitted to the PRP TOP records table maintained by Henri & Renaud Lifchitz.
See : http://www.primenumbers.net/prptop/prptop.php
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