PRP Records

Probable Primes Top 10000

(295149 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 ?
5012^1398726+7421059Stefano Morozzi10/2022
5022^1398269+131595420921Makoto Morimoto10/2013
5032^1397071+684443420561Enzo Doria07/2017
504953^141023-952^141023420121Jean-Louis Charton10/2016
5052^1393111+1867211419369Enzo Doria09/2023
506(3^877843-1)/2418838Paul Bourdelais07/2010
5072^1389628+28651418320Enzo Doria03/2024
5082^1386321+60299417325Enzo Doria02/2018
5092^1386320+184531417324Enzo Doria09/2017
5102^1382074+1883587416046Enzo Doria01/2017
5112^1380651+215843415618Enzo Doria12/2023
5122^1379907+1885223415394Enzo Doria03/2017
5132^1379111+29693415154Enzo Doria05/2024
5142^1376707+25763414431Enzo Doria12/2023
5152^1375751+24443414143Enzo Doria12/2023
5162^1375574+1886719414090Enzo Doria04/2017
5172^1373111+1884833413348Enzo Doria02/2017
5182^1372996+15413313Stefano Morozzi10/2022
5192^1372515+32393413169Enzo Doria05/2024
5202^1369171+216593412162Enzo Doria01/2024
5212^1368632+1889731412000Enzo Doria10/2017
522(65245^85849-1)/(65245^293-1)411914Ryan Propper11/2023
523(89*10^411590+1)/9411591Serge Batalov09/2014
524F(1968721)411439Henri Lifchitz11/2009
5252^1366066+683749411227Enzo Doria02/2017
5262^1364401+217727410726Enzo Doria02/2024
5272^1364303+219533410697Enzo Doria03/2024
5282^1363434+27589410435Enzo Doria02/2024
5292^1359550+25819409266Enzo Doria12/2023
5302^1355826+15408145Stefano Morozzi10/2022
5312^1355790+1888939408134Enzo Doria07/2017
5322^1355635+1884203408087Enzo Doria01/2017
533(22071^94249-1)/(22071^307-1)408068Ryan Propper11/2023
5342^1349535+218783406251Enzo Doria03/2024
535(55766^85849-1)/(55766^293-1)406081Ryan Propper11/2023
5362^1348956+24241406077Enzo Doria11/2023
537(88^208739+1)/89405888Paul Bourdelais12/2020
538(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
5392^1347744-3405712Paul Bourdelais07/2019
5409*10^404644-11404645Mischa Rodermond04/2023
5411215^131072+242^131072404302Kellen Shenton08/2022
5422^1341908+212911403955Enzo Doria09/2023
5431196^131072+595^131072403405Kellen Shenton08/2022
5442^1339302+29389403171Enzo Doria04/2024
5452^1330371+28313400482Enzo Doria03/2024
54610^400000+1415223400001Patrick De Geest10/2020
54710^400000-339233400000Patrick De Geest10/2020
5482^1323373+27317398375Enzo Doria01/2024
549Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
5502^1320423+24293397487Enzo Doria11/2023
5512^1320057+211517397377Enzo Doria08/2023
5522^1319770+1884949397291Enzo Doria06/2017
5532^1319616+30091397244Enzo Doria04/2024
5542^1317657+31367396655Enzo Doria04/2024
5552^1314741+219257395777Enzo Doria03/2024
5562^1313062+1888849395272Enzo Doria08/2017
557(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
5582^1312349+221177395057Enzo Doria04/2024
559(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
5602^1311618+783529394837Enzo Doria01/2017
5612^1308992+28111394046Enzo Doria02/2024
5622^1308000+1883521393748Enzo Doria02/2017
5632^1307262+28759393526Enzo Doria02/2024
564(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
565(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
566(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
567(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
568(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
569(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
5702^1303102+1866409392273Enzo Doria09/2017
5712^1302818+283429392188Enzo Doria01/2017
5722^1301430+22669391770Enzo Doria10/2023
5732^1301229+222467391709Enzo Doria04/2024
574(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
5752^1299181+1886867391093Enzo Doria04/2017
576(37^249341-1)/36391016Paul Bourdelais08/2020
5772^1298304+1882891390829Enzo Doria01/2017
57895196^12497+12497^95196390000Hans Havermann12/2021
57986206^33381+33381^86206389953Hans Havermann05/2023
5802^1294324+25171389631Enzo Doria12/2023
581(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
5822^1289624+32551388216Enzo Doria05/2024
583(7^457871-5^457871)/2386946Jon Grantham08/2023
58479455^73828+73828^79455386805Hans Havermann03/2023
58581650^54369+54369^81650386642Yusuf AttarBashi06/2021
58680565^62824+62824^80565386561Hans Havermann08/2021
58783747^41272+41272^83747386548Hans Havermann08/2021
58815^328574+328574^15386434Serge Batalov05/2014
5892^1280078+1885099385342Enzo Doria08/2017
5902^1279921+17385295Stefano Morozzi10/2022
5912^1276977+71657384409Enzo Doria08/2023
592(76803^78961-1)/(76803^281-1)384382Ryan Propper11/2023
5932^1276571+26213384287Enzo Doria12/2023
5942^1274941+1880717383796Enzo Doria10/2016
5952^1272632+383431383101Enzo Doria01/2017
5962^1271346+1889839382714Enzo Doria08/2017
5972^1271173+219587382662Enzo Doria03/2024
5985*3^798534-2^798534380999Jon Grantham08/2023
599(10^380976-7)/3380976Leonid Durman01/2012
6002^1264748+23221380728Enzo Doria11/2023
601(4*10^380056+11)/3380057Tyler Busby03/2023
6022^1257787+1447761378632Makoto Morimoto10/2013
603(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
6042^1257728+20851378614Enzo Doria08/2023
605(77^200657-1)/76378536Paul Bourdelais08/2020
606(98^189619+1)/99377573Paul Bourdelais02/2021
607F(1803059)376817Henri Lifchitz06/2009
6082^1250590+29389376466Enzo Doria03/2024
609(10^376417-3^376417)/7376417Jon Grantham08/2023
6102^1246724+213961375302Enzo Doria10/2023
6112^1245230+19374852Stefano Morozzi10/2022
6127^442674+4374103Paul Bourdelais02/2021
613(97^187393-1)/96372306Paul Bourdelais09/2020
61410^371696+7371697Alfred Reich05/2021
6152^1234709+883127371685Enzo Doria12/2016
6162^1234119+21803371507Enzo Doria09/2023
617(67^203431+1)/68371479Paul Bourdelais09/2021
6182^1233971+216593371463Enzo Doria12/2023
6192^1233212+27301371234Enzo Doria12/2023
6202^1231466+283819370709Enzo Doria07/2017
6212^1229766+26659370197Enzo Doria12/2023
6222^1228899+30713369936Enzo Doria03/2024
623(49627^78961-1)/(49627^281-1)369460Ryan Propper11/2023
6242^1226987+28163369360Enzo Doria02/2024
6252^1226569+30857369235Enzo Doria03/2024
62673^197880+197880368715Kellen Shenton06/2023
6275*3^771723-2^771723368207Jon Grantham08/2023
6282^1222473+221597368002Enzo Doria04/2024
6292^1222211+22703367923Enzo Doria11/2023
630(2^1222097+19)/3367888Stefano Morozzi09/2022
6312^1220335+1881263367358Enzo Doria11/2016
6322^1218344+215641366759Enzo Doria12/2023
6332^1217510+220039366508Enzo Doria03/2024
6342^1216694+1884769366262Enzo Doria02/2017
6352^1215889-3366020Paul Bourdelais06/2019
6362^1215296+1885441365841Enzo Doria03/2017
637(80^192133+1)/81365645Paul Bourdelais01/2021
6382^1214307+1888115365543Enzo Doria05/2017
6392^1213815+3365395Paul Bourdelais06/2019
640(80^191953+1)/81365302Paul Bourdelais01/2021
6412^1213313+215837365244Enzo Doria11/2023
6422^1208276+22201363728Enzo Doria09/2023
6432^1207345+1882577363448Enzo Doria12/2016
6442^1207336+217801363445Enzo Doria03/2024
6452^1207073+883727363366Enzo Doria03/2017
6463^761457-2363308Ryan Propper07/2015
647(10^363030+7)/337/443363025Alfred Reich12/2021
6482^1200972+141811361529Stefano Morozzi10/2022
649(2^1200924+324730)/2361514Stefano Morozzi06/2021
650(2^1200912+274110)/2361511Stefano Morozzi01/2021
6512^1200906+165249361509Stefano Morozzi07/2022
6522^1200890+166339361504Stefano Morozzi01/2023
653(2^1200887+344126)/2361503Stefano Morozzi10/2020
6542^1200877+186755361500Stefano Morozzi09/2022
6552^1200861+198521361496Stefano Morozzi11/2021
656(2^1200856+305790)/2361494Stefano Morozzi10/2020
657(2^1200853+372822)/2361493Stefano Morozzi06/2021
6582^1200812+324178)/2361481Stefano Morozzi06/2021
659(2^1200768+380458)/2361467Stefano Morozzi01/2021
6602^1200756+140917361464Stefano Morozzi05/2022
6612^1200741+184781361460Stefano Morozzi09/2022
662(2^1200741+293402)/2361459Stefano Morozzi07/2021
6632^1200734+142653361457Stefano Morozzi02/2023
6652^1200672+1880881361439Enzo Doria10/2016
6642^1200672+141535361439Stefano Morozzi09/2022
6662^1200669+178805361438Stefano Morozzi11/2022
6672^1200660+198555361435Stefano Morozzi12/2021
6682^1200657+164837361434Stefano Morozzi05/2022
6692^1200631+166431361426Stefano Morozzi02/2023
6702^1200627+150669361425Stefano Morozzi02/2023
671(2^1200603+356030)/2361418Stefano Morozzi10/2020
672(2^1200590+275854)/2361414Stefano Morozzi03/2021
6732^1200550+139297361402Stefano Morozzi10/2021
6742^1200486+172855361383Stefano Morozzi01/2023
675(2^1200456+320526)/2361373Stefano Morozzi10/2020
6762^1200443+142121361370Stefano Morozzi01/2023
6772^1200416+164065361362Stefano Morozzi01/2022
6782^1200331+155429361336Stefano Morozzi10/2021
680(2^1200289+348366)/2361323Stefano Morozzi10/2020
6792^1200289+141885361323Stefano Morozzi11/2022
681(2^1200284+273162)/2361322Stefano Morozzi10/2020
6822^1200252+194535361312Stefano Morozzi11/2021
683(2^1200250+364230)/2361311Stefano Morozzi10/2020
6842^1200227+156881361305Stefano Morozzi05/2022
685(2^1200209+305990)/2361299Stefano Morozzi10/2020
686(2^1200210+376278)/2361299Stefano Morozzi10/2020
6872^1200202+216499361297Enzo Doria12/2023
688(2^1200182+274462)/2361291Stefano Morozzi01/2021
6892^1200178+149193361290Stefano Morozzi07/2022
6902^1200168+140403361287Stefano Morozzi03/2022
691(2^1200162+275910)/2361285Stefano Morozzi03/2021
6922^1200157+168927361284Stefano Morozzi02/2023
6932^1200134+141385361277Stefano Morozzi08/2022
694(2^1200131+360150)/2361276Stefano Morozzi10/2020
695(2^1200118+290718)/2361272Stefano Morozzi01/2021
6962^1200022+192777361243Stefano Morozzi09/2022
6972^1200021+149777361243Stefano Morozzi10/2022
698(64*10^360173-1)/243360173Serge Batalov09/2014
699(59^203309+1)/60360029Paul Bourdelais09/2021
700(2*10^359860-11)/9359860Rytis Slatkevicius01/2023
7012^1195093+1882577359759Enzo Doria12/2016
7023^753451+5*2^753451359488Jon Grantham08/2023
703(6^461108-11)/5358812Paul Bourdelais04/2019
7042^1191375+8543358640Phil Moore06/2008
7052^1190972+1880191358519Enzo Doria11/2016
7062^1189930+28549358205Enzo Doria03/2024
707(45^216551-1)/44358004Paul Bourdelais08/2020
708(50^210319-1)/49357324Paul Bourdelais08/2020
709(531^131072+25^131072)/2357184Kellen Shenton03/2021
7102^1184565+21227356590Enzo Doria08/2023
7112^1180159+22823355264Enzo Doria11/2023
7122^1179836+1885021355167Enzo Doria02/2017
7132^1178942+32269354897Enzo Doria04/2024
7142^1177053+28607354329Enzo Doria02/2024
715(19*10^353884-91)/9353885Alfred Reich02/2023
716(10^353884*19-91)/9353885Alfred Reich10/2023
71720^271951+3353817Paul Bourdelais01/2021
71872722^72722+7^7353551Serge Batalov04/2024
7192^1173095+21353137Stefano Morozzi10/2022
7202^1170959+218945352494Enzo Doria03/2024
721(63^195893-1)/62352477Paul Bourdelais08/2020
7222^1170331+27293352305Enzo Doria01/2024
7232^1170326+7352304Stefano Morozzi10/2022
724numbpart(100000135540)352269Serge Batalov04/2017
725(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
7265*3^737931-2^737931352084Jon Grantham08/2023
7272^1168554+783529351770Enzo Doria01/2017
728(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
7292^1166950+30409351287Enzo Doria03/2024
7302^1166152+1882411351047Enzo Doria12/2016
7312^1163972+20971350391Enzo Doria08/2023
7322^1163272+22411350180Enzo Doria10/2023
73310^350071+7350072Alfred Reich05/2021
7342^1162154+1890207349844Enzo Doria08/2017
735(7*10^348724-61)/9348724Erik Branger09/2016
736(4*10^348453+41)/9348453Serge Batalov11/2022
737(127^165601-1)/126348390Alexander Zhirkov09/2015
7382^1155085+213377347716Enzo Doria09/2023
7392^1153083+1883693347113Enzo Doria04/2017
740(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
7412^1145882+80779344945Enzo Doria09/2016
7422^1143425+221177344206Enzo Doria03/2024
7432^1141813+27047343720Enzo Doria12/2023
7442^1141114+221869343510Enzo Doria04/2024
7452^1138296+27541342662Enzo Doria01/2024
7462^1136462+1887289342110Enzo Doria05/2017
747F(1636007)341905Henri Lifchitz03/2009
748(2^1135567+13)/3341840Stefano Morozzi09/2022
7492^1133678+782569341272Enzo Doria11/2016
750(11^327001+1)/12340536Paul Bourdelais09/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

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