PRP Records

Probable Primes Top 10000

(277054 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
3501numbpart(10^10+76282)111391Serge Batalov04/2015
35022^369974+733111374Lelio R Paula05/2013
3503121^53470+120111367Norbert Schneider10/2018
35042^369915-286267111356Enzo Doria07/2015
35052^369855-1615111338Lelio R Paula05/2017
35067*10^111325+3111326Robert Price08/2015
350751^65176+2111293Lelio R Paula08/2013
35082^369643-1865767111274Enzo Doria03/2016
35092^369603+885111262Lelio R Paula05/2017
351025555^22564+22564^25555111252Hans Havermann10/2020
3511L(532277)111240Renaud Lifchitz03/2004
3512105^55033-2111233Lelio R Paula10/2017
3513(35*10^111232-737)/9111233Robert Price07/2018
351426970^13307+13307^26970111227Hans Havermann10/2020
351525419^23716+23716^25419111210Hans Havermann10/2020
35169*10^111201-29111202Robert Price09/2019
35172^369392+29835111199Lelio R Paula05/2017
35183^233059+16111198Robert Price03/2020
35192^369354-3413111187Yves Minet12/2016
35202^369296-27111170Lelio R Paula02/2013
35212^369239-109837111153Enzo Doria05/2014
35222^369224-291839111148Enzo Doria07/2015
35232^369216+2798881111146Enzo Doria04/2016
352426842^13817+13817^26842111137Hans Havermann11/2020
352510^111111+163849111112Patrick De Geest03/2017
352610^111111-312911111111Patrick De Geest03/2017
35272^369092-216923111108Enzo Doria05/2014
35282^369081-55111105Lelio R Paula02/2013
3529(2^369047+3618)/2111094Stefano Morozzi09/2020
353088^57124-87111077Norbert Schneider11/2015
35312^368980+753111075Lelio R Paula05/2013
35322^368946-3623111064Yves Minet03/2017
35332^368929+29835111059Lelio R Paula05/2017
35344^184463-3^184463111058Jean-Louis Charton12/2004
3535111^54298+110111057Norbert Schneider04/2017
3536(4*10^111032-7)/3111033Ray Chandler04/2011
353735799^1262+1262^35799111015Hans Havermann10/2020
3538(298*10^111004+11)/3111006Robert Price11/2020
353927648^10349+10349^27648111004Hans Havermann11/2020
354028899^6932+6932^28899110997Hans Havermann11/2020
35412^368641-460303110972Enzo Doria06/2015
35422^368619-109087110966Enzo Doria04/2014
3543(74*10^110961+313)/9110962Robert Price06/2019
354425258^24711+24711^25258110956Hans Havermann11/2020
3545(2^368539+1290)/2110941Stefano Morozzi01/2021
35463*2^368489+7110927Lelio R Paula09/2014
3547(14*10^110922+61)/3110923Robert Price12/2018
354897411!4-2110913Robert Price07/2017
3549(9179*2^368330-1)/35110881Lelio R Paula05/2015
355025830^19619+19619^25830110880Hans Havermann10/2020
3551(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
355226022^18191+18191^26022110850Hans Havermann10/2020
3553(2^368211+2250)/2110843Stefano Morozzi01/2021
35542^368050-64875110795Lelio R Paula05/2017
35552^368048+25110794Lelio R Paula02/2013
355669^60239-2110771Lelio R Paula10/2013
3557(23*2^367952+1)/15717110762Lelio R Paula03/2014
35582^367924-69110757Lelio R Paula02/2013
3559(2^367779+3750)/2110713Stefano Morozzi01/2021
35602^367709-109723110692Enzo Doria04/2014
3561(3*2^367644-1)/107110671Lelio R Paula03/2014
3562(2^367626+3514)/2110667Stefano Morozzi09/2020
3563(23*2^367398+1)/57963110595Lelio R Paula03/2014
3564140^51515-139110558Norbert Schneider04/2019
35652^367215+1879223110543Enzo Doria09/2016
356625782^19375+19375^25782110534Hans Havermann10/2020
356726117^17058+17058^26117110526Hans Havermann10/2020
35682^367141+41110521Lelio R Paula02/2013
35692^367126+29835110516Lelio R Paula05/2017
3570(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
3571(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
3572(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
3573(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
3574(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
3575(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
3576(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
3577(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
3578(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
3579(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
3580(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
35813*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
35823*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
35833*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
35843*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
35853*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
35863*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
35873*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
35887*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
35897*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
35907*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
35917*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
35927*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
35937*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
35947*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
35957*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
35967*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
35977*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
35987*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
35997*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
36007*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
36017*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
36027*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
3603(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
3604(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
3605(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
3606(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
3607(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
3608(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
3609(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
3610(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
3611(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
3612(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
3613(11*10^110496+49)/3110497Robert Price07/2018
361425447^21958+21958^25447110481Hans Havermann11/2020
3615(31*2^366976+1)/7110472Lelio R Paula03/2014
36167*10^110468-23110469Robert Price07/2019
36172^366853+5711110434Lelio R Paula05/2017
3618(21181*2^366833+1)/3110432Lelio R Paula07/2014
36192^366816+315110423Lelio R Paula05/2017
36202^366775-2787037110411Enzo Doria03/2016
3621(112*10^110405-1)/3110407Serge Batalov12/2014
36222^366751+2797553110404Enzo Doria03/2016
362325276^23331+23331^25276110404Hans Havermann10/2020
36242^366748+255110403Lelio R Paula05/2017
36252^366738-2985110400Yves Minet09/2014
3626(23*2^366739+1)/74575110396Lelio R Paula03/2014
36272^366716+1871791110393Enzo Doria05/2016
36282^366649+1871687110373Enzo Doria05/2016
36292^366629-351205110367Enzo Doria06/2015
36302^366558+1874479110345Enzo Doria06/2016
363125132^24581+24581^25132110345Hans Havermann10/2020
3632(2^366539+770)/2110339Stefano Morozzi09/2020
363326368^15285+15285^26368110331Hans Havermann10/2020
3634(23*10^110290+19)/3110291Robert Price07/2019
363518^87853-4409110280Enzo Doria03/2013
363628490^7419+7419^28490110267Hans Havermann11/2020
36372^366218-23110243Lelio R Paula02/2013
3638(21*2^366193-1)/197110235Lelio R Paula03/2014
36392^366178-343991110231Enzo Doria07/2015
364025777^18798+18798^25777110174Hans Havermann10/2020
36412^365944+1871341110161Enzo Doria05/2016
36422^365838-461267110129Enzo Doria07/2015
364330152^4491+4491^30152110126Hans Havermann11/2020
364410^110111-40001110111Robert Price01/2021
36452^365763-6555110106Lelio R Paula04/2017
3646(2^365689+2^182845+1)/511008311/2006
36472^365666-459161110077Enzo Doria05/2015
36483*10^110076-7110077Robert Price08/2015
364913^98785-72110041Lelio R Paula03/2017
3650(25^78707+1)/26110027Robert Price06/2013
3651(16*10^110014-73)/3110015Robert Price07/2020
3652(7*10^110006-151)/9110006Robert Price02/2018
36536^141361-7110001Lelio R Paula11/2014
365420^84536+81109984Lelio R Paula03/2017
36555*2^365347-9109982Lelio R Paula09/2014
36569*6^141303+7109957Lelio R Paula11/2014
365727635^9522+9522^27635109953Hans Havermann11/2020
365878^58099+77109929Norbert Schneider02/2015
36592*10^109928-7109929Robert Price10/2015
366030580^3933+3933^30580109927Hans Havermann11/2020
366126380^14689+14689^26380109926Hans Havermann11/2020
3662(2^365161+1130)/2109925Stefano Morozzi09/2020
3663(27*2^365137-1)/2021109916Lelio R Paula03/2014
3664(4441*29^75152-24)/7109905Curtis Bright05/2015
3665(2^365087+7)/6015109899Lelio R Paula01/2014
366629652^5083+5083^29652109894Mark Rodenkirch10/2020
3667(2^365049+722)/2109891Stefano Morozzi09/2020
366818^87533-11109878Lelio R Paula04/2017
36692^364982-5109871Henri Lifchitz04/2006
36703*10^109861+59109862Robert Price08/2018
36712^364936-1867979109857Enzo Doria04/2016
367227013^11652+11652^27013109846Hans Havermann10/2020
36732^364867-112087109836Enzo Doria06/2014
36744^182415-85061109825Mike Oakes06/2011
3675(2^364809+1034)/2109819Stefano Morozzi09/2020
367625708^18675+18675^25708109806Hans Havermann10/2020
3677(17^89227+16^89227)/33109788Robert Price08/2013
36782^364687-187109782Lelio R Paula01/2012
36792^364644+67109769Lelio R Paula01/2012
3680(9787*2^364625-1)/24947109763Lelio R Paula05/2015
3681(2^364616+5)/9109760Lelio R Paula01/2014
3682(55*10^109759+89)/9109760Robert Price03/2019
368312^101694+73109747Lelio R Paula03/2017
368413^98518-66109744Lelio R Paula03/2017
36862^364478-113261109719Enzo Doria07/2014
3685(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
3687(24737*2^364454+1)/3109716Lelio R Paula07/2014
368827814^8777+8777^27814109681Hans Havermann10/2020
3689(62*10^109673+1)/9109674Serge Batalov11/2010
36903^229824+340109654Lelio R Paula03/2017
3691(2*10^109645-71)/3109645Robert Price12/2017
36922^364169-112813109626Enzo Doria06/2014
369328822^6359+6359^28822109622Hans Havermann11/2020
369410^109615+21109616Lelio R Paula03/2017
369510^109615-456267109615Patrick De Geest03/2017
36962^364094-113109604Lelio R Paula01/2012
369725251^21898+21898^25251109600Hans Havermann11/2020
3698(4^182026+11)/3109591Robert Price02/2017
36992^364041-6883109588Lelio R Paula09/2011
370012^101545+11109586Lelio R Paula03/2017
370126536^13475+13475^26536109582Hans Havermann11/2020
37022^363842-2787101109528Enzo Doria03/2016
3703(2^363812+3570)/2109519Stefano Morozzi09/2020
3704(22699*2^363782+1)/763109511Lelio R Paula07/2014
37052^363769+5711109506Lelio R Paula04/2017
3706(31*2^363748+1)/49109499Lelio R Paula03/2014
3707p(22245)#/2-8109462Robert Price01/2017
37082^363556+55109442Lelio R Paula01/2012
3709(2^363437+1682)/2109406Stefano Morozzi09/2020
3710(55459*2^363411+1)/81109401Lelio R Paula07/2014
37112^363406+1871569109397Enzo Doria05/2016
3712(2^363349+7)/9109378Lelio R Paula01/2014
37133^229236+100109374Lelio R Paula03/2017
37142^363268-58695109355Lelio R Paula04/2017
37152^363191-112321109332Enzo Doria06/2014
371626231^14718+14718^26231109327Hans Havermann10/2020
371725461^19672+19672^25461109326Hans Havermann10/2020
37184*10^109316-63109317Robert Price10/2018
37192^363120+3109311Donovan Johnson04/2006
3720(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
37212^363042-114641109287Enzo Doria04/2015
37222^363020-112793109280Enzo Doria06/2014
3723(85*10^109253+203)/9109254Robert Price09/2020
372424990^23431+23431^24990109202Hans Havermann10/2020
3725(2^362746+3738)/2109198Stefano Morozzi09/2020
3726(2^362716+1282)/2109189Stefano Morozzi01/2021
3727(67607*2^362695+1)/70499109183Lelio R Paula07/2014
372825060^22737+22737^25060109180Hans Havermann10/2020
3729(9*2^362644+1)/5109167Lelio R Paula03/2014
37305^156181+38109166Lelio R Paula02/2017
3731(2^362623+3618)/2109161Stefano Morozzi09/2020
373225138^21993+21993^25138109157Hans Havermann10/2020
37334*10^109142+91109143Robert Price08/2018
37353^228750+68109142Lelio R Paula03/2017
3734(2^362561+786)/2109142Stefano Morozzi09/2020
37362*10^109100-49109101Robert Price09/2020
3737(10223*2^362376+1)/9109090Lelio R Paula07/2014
373865^60167-64^60167109078Robert Price08/2013
37397*3^228589-2109066Lelio R Paula09/2014
374024874^24243+24243^24874109063Hans Havermann11/2020
374129158^5495+5495^29158109050Hans Havermann11/2020
3742(78557*2^362188+1)/189109033Lelio R Paula07/2014
37432*7^129008+9109025Lelio R Paula11/2014
374488*10^109022+7109024Robert Price03/2020
374528194^7337+7337^28194108985Hans Havermann10/2020
3746(5*10^108960+91)/3108961Robert Price04/2018
37472^361957+76367108960Enzo Doria05/2016
37482^361873-1411108935Yves Minet01/2013
3749(24737*2^361857+1)/35108933Lelio R Paula07/2014
3750115^52842-114108892Norbert Schneider07/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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