PRP Records

Probable Primes Top 10000

(294627 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 ?
501(22071^94249-1)/(22071^307-1)408068Ryan Propper11/2023
5022^1349535+218783406251Enzo Doria03/2024
503(55766^85849-1)/(55766^293-1)406081Ryan Propper11/2023
5042^1348956+24241406077Enzo Doria11/2023
505(88^208739+1)/89405888Paul Bourdelais12/2020
506(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
5072^1347744-3405712Paul Bourdelais07/2019
5089*10^404644-11404645Mischa Rodermond04/2023
5091215^131072+242^131072404302Kellen Shenton08/2022
5102^1341908+212911403955Enzo Doria09/2023
5111196^131072+595^131072403405Kellen Shenton08/2022
51210^400000+1415223400001Patrick De Geest10/2020
51310^400000-339233400000Patrick De Geest10/2020
5142^1323373+27317398375Enzo Doria01/2024
515Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
5162^1320423+24293397487Enzo Doria11/2023
5172^1320057+211517397377Enzo Doria08/2023
5182^1319770+1884949397291Enzo Doria06/2017
5192^1314741+219257395777Enzo Doria03/2024
5202^1313062+1888849395272Enzo Doria08/2017
521(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
522(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
5232^1311618+783529394837Enzo Doria01/2017
5242^1308992+28111394046Enzo Doria02/2024
5252^1308000+1883521393748Enzo Doria02/2017
5262^1307262+28759393526Enzo Doria02/2024
527(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
528(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
529(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
530(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
531(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
532(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
5332^1303102+1866409392273Enzo Doria09/2017
5342^1302818+283429392188Enzo Doria01/2017
5352^1301430+22669391770Enzo Doria10/2023
536(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
5372^1299181+1886867391093Enzo Doria04/2017
538(37^249341-1)/36391016Paul Bourdelais08/2020
5392^1298304+1882891390829Enzo Doria01/2017
54095196^12497+12497^95196390000Hans Havermann12/2021
54186206^33381+33381^86206389953Hans Havermann05/2023
5422^1294324+25171389631Enzo Doria12/2023
543(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
544(7^457871-5^457871)/2386946Jon Grantham08/2023
54579455^73828+73828^79455386805Hans Havermann03/2023
54681650^54369+54369^81650386642Yusuf AttarBashi06/2021
54780565^62824+62824^80565386561Hans Havermann08/2021
54883747^41272+41272^83747386548Hans Havermann08/2021
54915^328574+328574^15386434Serge Batalov05/2014
5502^1280078+1885099385342Enzo Doria08/2017
5512^1279921+17385295Stefano Morozzi10/2022
5522^1276977+71657384409Enzo Doria08/2023
553(76803^78961-1)/(76803^281-1)384382Ryan Propper11/2023
5542^1276571+26213384287Enzo Doria12/2023
5552^1274941+1880717383796Enzo Doria10/2016
5562^1272632+383431383101Enzo Doria01/2017
5572^1271346+1889839382714Enzo Doria08/2017
5582^1271173+219587382662Enzo Doria03/2024
5595*3^798534-2^798534380999Jon Grantham08/2023
560(10^380976-7)/3380976Leonid Durman01/2012
5612^1264748+23221380728Enzo Doria11/2023
562(4*10^380056+11)/3380057Tyler Busby03/2023
5632^1257787+1447761378632Makoto Morimoto10/2013
564(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
5652^1257728+20851378614Enzo Doria08/2023
566(77^200657-1)/76378536Paul Bourdelais08/2020
567(98^189619+1)/99377573Paul Bourdelais02/2021
568F(1803059)376817Henri Lifchitz06/2009
569(10^376417-3^376417)/7376417Jon Grantham08/2023
5702^1246724+213961375302Enzo Doria10/2023
5712^1245230+19374852Stefano Morozzi10/2022
5727^442674+4374103Paul Bourdelais02/2021
573(97^187393-1)/96372306Paul Bourdelais09/2020
57410^371696+7371697Alfred Reich05/2021
5752^1234709+883127371685Enzo Doria12/2016
5762^1234119+21803371507Enzo Doria09/2023
577(67^203431+1)/68371479Paul Bourdelais09/2021
5782^1233971+216593371463Enzo Doria12/2023
5792^1233212+27301371234Enzo Doria12/2023
5802^1231466+283819370709Enzo Doria07/2017
5812^1229766+26659370197Enzo Doria12/2023
582(49627^78961-1)/(49627^281-1)369460Ryan Propper11/2023
5832^1226987+28163369360Enzo Doria02/2024
58473^197880+197880368715Kellen Shenton06/2023
5855*3^771723-2^771723368207Jon Grantham08/2023
5862^1222211+22703367923Enzo Doria11/2023
587(2^1222097+19)/3367888Stefano Morozzi09/2022
5882^1220335+1881263367358Enzo Doria11/2016
5892^1218344+215641366759Enzo Doria12/2023
5902^1217510+220039366508Enzo Doria03/2024
5912^1216694+1884769366262Enzo Doria02/2017
5922^1215889-3366020Paul Bourdelais06/2019
5932^1215296+1885441365841Enzo Doria03/2017
594(80^192133+1)/81365645Paul Bourdelais01/2021
5952^1214307+1888115365543Enzo Doria05/2017
5962^1213815+3365395Paul Bourdelais06/2019
597(80^191953+1)/81365302Paul Bourdelais01/2021
5982^1213313+215837365244Enzo Doria11/2023
5992^1208276+22201363728Enzo Doria09/2023
6002^1207345+1882577363448Enzo Doria12/2016
6012^1207336+217801363445Enzo Doria03/2024
6022^1207073+883727363366Enzo Doria03/2017
6033^761457-2363308Ryan Propper07/2015
604(10^363030+7)/337/443363025Alfred Reich12/2021
6052^1200972+141811361529Stefano Morozzi10/2022
606(2^1200924+324730)/2361514Stefano Morozzi06/2021
607(2^1200912+274110)/2361511Stefano Morozzi01/2021
6082^1200906+165249361509Stefano Morozzi07/2022
6092^1200890+166339361504Stefano Morozzi01/2023
610(2^1200887+344126)/2361503Stefano Morozzi10/2020
6112^1200877+186755361500Stefano Morozzi09/2022
6122^1200861+198521361495Stefano Morozzi11/2021
613(2^1200856+305790)/2361494Stefano Morozzi10/2020
614(2^1200853+372822)/2361493Stefano Morozzi06/2021
6152^1200812+324178)/2361481Stefano Morozzi06/2021
616(2^1200768+380458)/2361467Stefano Morozzi01/2021
6172^1200756+140917361464Stefano Morozzi05/2022
6182^1200741+184781361460Stefano Morozzi09/2022
619(2^1200741+293402)/2361459Stefano Morozzi07/2021
6202^1200734+142653361457Stefano Morozzi02/2023
6222^1200672+1880881361439Enzo Doria10/2016
6212^1200672+141535361439Stefano Morozzi09/2022
6232^1200669+178805361438Stefano Morozzi11/2022
6242^1200660+198555361435Stefano Morozzi12/2021
6252^1200657+164837361434Stefano Morozzi05/2022
6262^1200631+166431361426Stefano Morozzi02/2023
6272^1200627+150669361425Stefano Morozzi02/2023
628(2^1200603+356030)/2361418Stefano Morozzi10/2020
629(2^1200590+275854)/2361414Stefano Morozzi03/2021
6302^1200550+139297361402Stefano Morozzi10/2021
6312^1200486+172855361383Stefano Morozzi01/2023
632(2^1200456+320526)/2361373Stefano Morozzi10/2020
6332^1200443+142121361370Stefano Morozzi01/2023
6342^1200416+164065361362Stefano Morozzi01/2022
6352^1200331+155429361336Stefano Morozzi10/2021
637(2^1200289+348366)/2361323Stefano Morozzi10/2020
6362^1200289+141885361323Stefano Morozzi11/2022
638(2^1200284+273162)/2361322Stefano Morozzi10/2020
6392^1200252+194535361312Stefano Morozzi11/2021
640(2^1200250+364230)/2361311Stefano Morozzi10/2020
6412^1200227+156881361305Stefano Morozzi05/2022
642(2^1200209+305990)/2361299Stefano Morozzi10/2020
643(2^1200210+376278)/2361299Stefano Morozzi10/2020
6442^1200202+216499361297Enzo Doria12/2023
645(2^1200182+274462)/2361291Stefano Morozzi01/2021
6462^1200178+149193361290Stefano Morozzi07/2022
6472^1200168+140403361287Stefano Morozzi03/2022
648(2^1200162+275910)/2361285Stefano Morozzi03/2021
6492^1200157+168927361284Stefano Morozzi02/2023
6502^1200134+141385361277Stefano Morozzi08/2022
651(2^1200131+360150)/2361276Stefano Morozzi10/2020
652(2^1200118+290718)/2361272Stefano Morozzi01/2021
6532^1200022+192777361243Stefano Morozzi09/2022
6542^1200021+149777361243Stefano Morozzi10/2022
655(64*10^360173-1)/243360173Serge Batalov09/2014
656(59^203309+1)/60360029Paul Bourdelais09/2021
657(2*10^359860-11)/9359860Rytis Slatkevicius01/2023
6582^1195093+1882577359759Enzo Doria12/2016
6593^753451+5*2^753451359488Jon Grantham08/2023
660(6^461108-11)/5358812Paul Bourdelais04/2019
6612^1191375+8543358640Phil Moore06/2008
6622^1190972+1880191358519Enzo Doria11/2016
6632^1189930+28549358205Enzo Doria03/2024
664(45^216551-1)/44358004Paul Bourdelais08/2020
665(50^210319-1)/49357324Paul Bourdelais08/2020
666(531^131072+25^131072)/2357184Kellen Shenton03/2021
6672^1184565+21227356590Enzo Doria08/2023
6682^1180159+22823355264Enzo Doria11/2023
6692^1179836+1885021355167Enzo Doria02/2017
6702^1177053+28607354329Enzo Doria02/2024
671(19*10^353884-91)/9353885Alfred Reich02/2023
672(10^353884*19-91)/9353885Alfred Reich10/2023
67320^271951+3353817Paul Bourdelais01/2021
6742^1173095+21353137Stefano Morozzi10/2022
675(63^195893-1)/62352477Paul Bourdelais08/2020
6762^1170331+27293352305Enzo Doria01/2024
6772^1170326+7352304Stefano Morozzi10/2022
678numbpart(100000135540)352269Serge Batalov04/2017
679(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
6805*3^737931-2^737931352084Jon Grantham08/2023
6812^1168554+783529351770Enzo Doria01/2017
682(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
6832^1166152+1882411351047Enzo Doria12/2016
6842^1163972+20971350391Enzo Doria08/2023
6852^1163272+22411350180Enzo Doria10/2023
68610^350071+7350072Alfred Reich05/2021
6872^1162154+1890207349844Enzo Doria08/2017
688(7*10^348724-61)/9348724Erik Branger09/2016
689(4*10^348453+41)/9348453Serge Batalov11/2022
690(127^165601-1)/126348390Alexander Zhirkov09/2015
6912^1155085+213377347716Enzo Doria09/2023
6922^1153083+1883693347113Enzo Doria04/2017
693(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
6942^1145882+80779344945Enzo Doria09/2016
6952^1141813+27047343720Enzo Doria12/2023
6962^1138296+27541342662Enzo Doria01/2024
6972^1136462+1887289342110Enzo Doria05/2017
698F(1636007)341905Henri Lifchitz03/2009
699(2^1135567+13)/3341840Stefano Morozzi09/2022
7002^1133678+782569341272Enzo Doria11/2016
701(11^327001+1)/12340536Paul Bourdelais09/2013
7022^1128621+25919339749Enzo Doria12/2023
703(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
704Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
7052^1126380-3339075Paul Bourdelais06/2019
7062^1125784+24331338895Enzo Doria10/2023
7072^1125446+1885099338794Enzo Doria08/2017
708(63^188147+1)/64338539Paul Bourdelais12/2020
7092^1124549+143807338523Enzo Doria10/2016
710(4*10^338476+23)/9338476Serge Batalov11/2022
7112^1121187+1886783337511Enzo Doria04/2017
712(48^200443-1)/47336992Paul Bourdelais08/2020
713(2*10^336405+43)/9336405Rytis Slatkevicius01/2023
714(94^170371-1)/93336162Paul Bourdelais09/2020
7152^1116184+1883521336005Enzo Doria02/2017
7162^1115727+27683335868Enzo Doria01/2024
7172^1114974+28759335641Enzo Doria02/2024
7182^1114517+1880087335504Enzo Doria10/2016
719(5*10^335480+31)/9335480Serge Batalov11/2022
7205*3^701688+2^701688334791Jon Grantham08/2023
721(101^166849+1)/102334418Paul Bourdelais12/2020
722(3^700897+1)/4334413Paul Bourdelais04/2010
7232^1104500+22411332488Enzo Doria10/2023
7242^1104408-114539332460Enzo Doria03/2015
7252^1101921+82085331712Enzo Doria10/2016
7262^1101895+29963331704Enzo Doria03/2024
7272^1100655+683513331331Enzo Doria01/2017
728(10^330906+71)/9330906Serge Batalov07/2015
7292^1098346+482899330636Enzo Doria11/2016
730(2^1096212+19)/5329992Stefano Morozzi09/2022
7312^1095679+1878713329833Enzo Doria09/2016
7322^1094874+27499329590Enzo Doria01/2024
7332^1094740-1851539329550Enzo Doria08/2015
7342^1092242+19328798Stefano Morozzi10/2022
7352^1091469-379369328565Enzo Doria03/2014
7362^1090801+24227328364Enzo Doria10/2023
737(69^178093-1)/68327485Paul Bourdelais08/2020
738(10^326884+7)/421326882Alfred Reich12/2021
7392^1085750+582349326844Enzo Doria11/2016
740(54308^69169-1)/(54308^263-1)326261Ryan Propper11/2023
7412^1083596+483061326195Enzo Doria12/2016
742(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
7432^1082908+583561325988Enzo Doria05/2017
74430^220411-29^220411325574Jean-Louis Charton10/2018
7452^1081308+7325507Stefano Morozzi10/2022
7462^1080032+25171325123Enzo Doria11/2023
7472^1078242+1881649324584Enzo Doria11/2016
7482^1077737+1880117324432Enzo Doria10/2016
7493^679017-5*2^679017323974Jon Grantham08/2023
7502^1075425+1880117323736Enzo Doria10/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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