PRP Records

Probable Primes Top 10000

(294613 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(88^208739+1)/89405888Paul Bourdelais12/2020
502(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
5032^1347744-3405712Paul Bourdelais07/2019
5049*10^404644-11404645Mischa Rodermond04/2023
5051215^131072+242^131072404302Kellen Shenton08/2022
5062^1341908+212911403955Enzo Doria09/2023
5071196^131072+595^131072403405Kellen Shenton08/2022
50810^400000+1415223400001Patrick De Geest10/2020
50910^400000-339233400000Patrick De Geest10/2020
5102^1323373+27317398375Enzo Doria01/2024
511Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
5122^1320423+24293397487Enzo Doria11/2023
5132^1320057+211517397377Enzo Doria08/2023
5142^1319770+1884949397291Enzo Doria06/2017
5152^1313062+1888849395272Enzo Doria08/2017
516(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
517(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
5182^1311618+783529394837Enzo Doria01/2017
5192^1308992+28111394046Enzo Doria02/2024
5202^1308000+1883521393748Enzo Doria02/2017
5212^1307262+28759393526Enzo Doria02/2024
522(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
523(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
524(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
525(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
526(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
527(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
5282^1303102+1866409392273Enzo Doria09/2017
5292^1302818+283429392188Enzo Doria01/2017
5302^1301430+22669391770Enzo Doria10/2023
531(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
5322^1299181+1886867391093Enzo Doria04/2017
533(37^249341-1)/36391016Paul Bourdelais08/2020
5342^1298304+1882891390829Enzo Doria01/2017
53595196^12497+12497^95196390000Hans Havermann12/2021
53686206^33381+33381^86206389953Hans Havermann05/2023
5372^1294324+25171389631Enzo Doria12/2023
538(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
539(7^457871-5^457871)/2386946Jon Grantham08/2023
54079455^73828+73828^79455386805Hans Havermann03/2023
54181650^54369+54369^81650386642Yusuf AttarBashi06/2021
54280565^62824+62824^80565386561Hans Havermann08/2021
54383747^41272+41272^83747386548Hans Havermann08/2021
54415^328574+328574^15386434Serge Batalov05/2014
5452^1280078+1885099385342Enzo Doria08/2017
5462^1279921+17385295Stefano Morozzi10/2022
5472^1276977+71657384409Enzo Doria08/2023
548(76803^78961-1)/(76803^281-1)384382Ryan Propper11/2023
5492^1276571+26213384287Enzo Doria12/2023
5502^1274941+1880717383796Enzo Doria10/2016
5512^1272632+383431383101Enzo Doria01/2017
5522^1271346+1889839382714Enzo Doria08/2017
5532^1271173+219587382662Enzo Doria03/2024
5545*3^798534-2^798534380999Jon Grantham08/2023
555(10^380976-7)/3380976Leonid Durman01/2012
5562^1264748+23221380728Enzo Doria11/2023
557(4*10^380056+11)/3380057Tyler Busby03/2023
5582^1257787+1447761378632Makoto Morimoto10/2013
559(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
5602^1257728+20851378614Enzo Doria08/2023
561(77^200657-1)/76378536Paul Bourdelais08/2020
562(98^189619+1)/99377573Paul Bourdelais02/2021
563F(1803059)376817Henri Lifchitz06/2009
564(10^376417-3^376417)/7376417Jon Grantham08/2023
5652^1246724+213961375302Enzo Doria10/2023
5662^1245230+19374852Stefano Morozzi10/2022
5677^442674+4374103Paul Bourdelais02/2021
568(97^187393-1)/96372306Paul Bourdelais09/2020
56910^371696+7371697Alfred Reich05/2021
5702^1234709+883127371685Enzo Doria12/2016
5712^1234119+21803371507Enzo Doria09/2023
572(67^203431+1)/68371479Paul Bourdelais09/2021
5732^1233971+216593371463Enzo Doria12/2023
5742^1233212+27301371234Enzo Doria12/2023
5752^1231466+283819370709Enzo Doria07/2017
5762^1229766+26659370197Enzo Doria12/2023
577(49627^78961-1)/(49627^281-1)369460Ryan Propper11/2023
5782^1226987+28163369360Enzo Doria02/2024
57973^197880+197880368715Kellen Shenton06/2023
5805*3^771723-2^771723368207Jon Grantham08/2023
5812^1222211+22703367923Enzo Doria11/2023
582(2^1222097+19)/3367888Stefano Morozzi09/2022
5832^1220335+1881263367358Enzo Doria11/2016
5842^1218344+215641366759Enzo Doria12/2023
5852^1217510+220039366508Enzo Doria03/2024
5862^1216694+1884769366262Enzo Doria02/2017
5872^1215889-3366020Paul Bourdelais06/2019
5882^1215296+1885441365841Enzo Doria03/2017
589(80^192133+1)/81365645Paul Bourdelais01/2021
5902^1214307+1888115365543Enzo Doria05/2017
5912^1213815+3365395Paul Bourdelais06/2019
592(80^191953+1)/81365302Paul Bourdelais01/2021
5932^1213313+215837365244Enzo Doria11/2023
5942^1208276+22201363728Enzo Doria09/2023
5952^1207345+1882577363448Enzo Doria12/2016
5962^1207336+217801363445Enzo Doria03/2024
5972^1207073+883727363366Enzo Doria03/2017
5983^761457-2363308Ryan Propper07/2015
599(10^363030+7)/337/443363025Alfred Reich12/2021
6002^1200972+141811361529Stefano Morozzi10/2022
601(2^1200924+324730)/2361514Stefano Morozzi06/2021
602(2^1200912+274110)/2361511Stefano Morozzi01/2021
6032^1200906+165249361509Stefano Morozzi07/2022
6042^1200890+166339361504Stefano Morozzi01/2023
605(2^1200887+344126)/2361503Stefano Morozzi10/2020
6062^1200877+186755361500Stefano Morozzi09/2022
6072^1200861+198521361495Stefano Morozzi11/2021
608(2^1200856+305790)/2361494Stefano Morozzi10/2020
609(2^1200853+372822)/2361493Stefano Morozzi06/2021
6102^1200812+324178)/2361481Stefano Morozzi06/2021
611(2^1200768+380458)/2361467Stefano Morozzi01/2021
6122^1200756+140917361464Stefano Morozzi05/2022
6132^1200741+184781361460Stefano Morozzi09/2022
614(2^1200741+293402)/2361459Stefano Morozzi07/2021
6152^1200734+142653361457Stefano Morozzi02/2023
6172^1200672+1880881361439Enzo Doria10/2016
6162^1200672+141535361439Stefano Morozzi09/2022
6182^1200669+178805361438Stefano Morozzi11/2022
6192^1200660+198555361435Stefano Morozzi12/2021
6202^1200657+164837361434Stefano Morozzi05/2022
6212^1200631+166431361426Stefano Morozzi02/2023
6222^1200627+150669361425Stefano Morozzi02/2023
623(2^1200603+356030)/2361418Stefano Morozzi10/2020
624(2^1200590+275854)/2361414Stefano Morozzi03/2021
6252^1200550+139297361402Stefano Morozzi10/2021
6262^1200486+172855361383Stefano Morozzi01/2023
627(2^1200456+320526)/2361373Stefano Morozzi10/2020
6282^1200443+142121361370Stefano Morozzi01/2023
6292^1200416+164065361362Stefano Morozzi01/2022
6302^1200331+155429361336Stefano Morozzi10/2021
632(2^1200289+348366)/2361323Stefano Morozzi10/2020
6312^1200289+141885361323Stefano Morozzi11/2022
633(2^1200284+273162)/2361322Stefano Morozzi10/2020
6342^1200252+194535361312Stefano Morozzi11/2021
635(2^1200250+364230)/2361311Stefano Morozzi10/2020
6362^1200227+156881361305Stefano Morozzi05/2022
637(2^1200209+305990)/2361299Stefano Morozzi10/2020
638(2^1200210+376278)/2361299Stefano Morozzi10/2020
6392^1200202+216499361297Enzo Doria12/2023
640(2^1200182+274462)/2361291Stefano Morozzi01/2021
6412^1200178+149193361290Stefano Morozzi07/2022
6422^1200168+140403361287Stefano Morozzi03/2022
643(2^1200162+275910)/2361285Stefano Morozzi03/2021
6442^1200157+168927361284Stefano Morozzi02/2023
6452^1200134+141385361277Stefano Morozzi08/2022
646(2^1200131+360150)/2361276Stefano Morozzi10/2020
647(2^1200118+290718)/2361272Stefano Morozzi01/2021
6482^1200022+192777361243Stefano Morozzi09/2022
6492^1200021+149777361243Stefano Morozzi10/2022
650(64*10^360173-1)/243360173Serge Batalov09/2014
651(59^203309+1)/60360029Paul Bourdelais09/2021
652(2*10^359860-11)/9359860Rytis Slatkevicius01/2023
6532^1195093+1882577359759Enzo Doria12/2016
6543^753451+5*2^753451359488Jon Grantham08/2023
655(6^461108-11)/5358812Paul Bourdelais04/2019
6562^1191375+8543358640Phil Moore06/2008
6572^1190972+1880191358519Enzo Doria11/2016
658(45^216551-1)/44358004Paul Bourdelais08/2020
659(50^210319-1)/49357324Paul Bourdelais08/2020
660(531^131072+25^131072)/2357184Kellen Shenton03/2021
6612^1184565+21227356590Enzo Doria08/2023
6622^1180159+22823355264Enzo Doria11/2023
6632^1179836+1885021355167Enzo Doria02/2017
6642^1177053+28607354329Enzo Doria02/2024
665(19*10^353884-91)/9353885Alfred Reich02/2023
666(10^353884*19-91)/9353885Alfred Reich10/2023
66720^271951+3353817Paul Bourdelais01/2021
6682^1173095+21353137Stefano Morozzi10/2022
669(63^195893-1)/62352477Paul Bourdelais08/2020
6702^1170331+27293352305Enzo Doria01/2024
6712^1170326+7352304Stefano Morozzi10/2022
672numbpart(100000135540)352269Serge Batalov04/2017
673(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
6745*3^737931-2^737931352084Jon Grantham08/2023
6752^1168554+783529351770Enzo Doria01/2017
676(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
6772^1166152+1882411351047Enzo Doria12/2016
6782^1163972+20971350391Enzo Doria08/2023
6792^1163272+22411350180Enzo Doria10/2023
68010^350071+7350072Alfred Reich05/2021
6812^1162154+1890207349844Enzo Doria08/2017
682(7*10^348724-61)/9348724Erik Branger09/2016
683(4*10^348453+41)/9348453Serge Batalov11/2022
684(127^165601-1)/126348390Alexander Zhirkov09/2015
6852^1155085+213377347716Enzo Doria09/2023
6862^1153083+1883693347113Enzo Doria04/2017
687(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
6882^1145882+80779344945Enzo Doria09/2016
6892^1141813+27047343720Enzo Doria12/2023
6902^1138296+27541342662Enzo Doria01/2024
6912^1136462+1887289342110Enzo Doria05/2017
692F(1636007)341905Henri Lifchitz03/2009
693(2^1135567+13)/3341840Stefano Morozzi09/2022
6942^1133678+782569341272Enzo Doria11/2016
695(11^327001+1)/12340536Paul Bourdelais09/2013
6962^1128621+25919339749Enzo Doria12/2023
697(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
698Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
6992^1126380-3339075Paul Bourdelais06/2019
7002^1125784+24331338895Enzo Doria10/2023
7012^1125446+1885099338794Enzo Doria08/2017
702(63^188147+1)/64338539Paul Bourdelais12/2020
7032^1124549+143807338523Enzo Doria10/2016
704(4*10^338476+23)/9338476Serge Batalov11/2022
7052^1121187+1886783337511Enzo Doria04/2017
706(48^200443-1)/47336992Paul Bourdelais08/2020
707(2*10^336405+43)/9336405Rytis Slatkevicius01/2023
708(94^170371-1)/93336162Paul Bourdelais09/2020
7092^1116184+1883521336005Enzo Doria02/2017
7102^1115727+27683335868Enzo Doria01/2024
7112^1114974+28759335641Enzo Doria02/2024
7122^1114517+1880087335504Enzo Doria10/2016
713(5*10^335480+31)/9335480Serge Batalov11/2022
7145*3^701688+2^701688334791Jon Grantham08/2023
715(101^166849+1)/102334418Paul Bourdelais12/2020
716(3^700897+1)/4334413Paul Bourdelais04/2010
7172^1104500+22411332488Enzo Doria10/2023
7182^1104408-114539332460Enzo Doria03/2015
7192^1101921+82085331712Enzo Doria10/2016
7202^1101895+29963331704Enzo Doria03/2024
7212^1100655+683513331331Enzo Doria01/2017
722(10^330906+71)/9330906Serge Batalov07/2015
7232^1098346+482899330636Enzo Doria11/2016
724(2^1096212+19)/5329992Stefano Morozzi09/2022
7252^1095679+1878713329833Enzo Doria09/2016
7262^1094874+27499329590Enzo Doria01/2024
7272^1094740-1851539329550Enzo Doria08/2015
7282^1092242+19328798Stefano Morozzi10/2022
7292^1091469-379369328565Enzo Doria03/2014
7302^1090801+24227328364Enzo Doria10/2023
731(69^178093-1)/68327485Paul Bourdelais08/2020
732(10^326884+7)/421326882Alfred Reich12/2021
7332^1085750+582349326844Enzo Doria11/2016
734(54308^69169-1)/(54308^263-1)326261Ryan Propper11/2023
7352^1083596+483061326195Enzo Doria12/2016
736(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
7372^1082908+583561325988Enzo Doria05/2017
73830^220411-29^220411325574Jean-Louis Charton10/2018
7392^1081308+7325507Stefano Morozzi10/2022
7402^1080032+25171325123Enzo Doria11/2023
7412^1078242+1881649324584Enzo Doria11/2016
7422^1077737+1880117324432Enzo Doria10/2016
7433^679017-5*2^679017323974Jon Grantham08/2023
7442^1075425+1880117323736Enzo Doria10/2016
745(28^223381+1)/29323267Paul Bourdelais12/2020
74610^322999+187071323000Stefano Morozzi03/2019
74710^322999-143151322999Patrick De Geest05/2020
7482^1072146+1886869322749Enzo Doria04/2017
7492^1072118-7321953322740Enzo Doria02/2015
7502^1071026+1886869322411Enzo Doria04/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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