PRP Records

Probable Primes Top 10000

(303109 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 ?
10012^1307262+28759393526Enzo Doria02/2024
1002(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
10032^1306643+47333393339Enzo Doria07/2025
10042^1305860+35461393104Enzo Doria08/2024
1005(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
10062^1305333+47717392945Enzo Doria06/2025
10072^1305200+54571392905Enzo Doria01/2026
1008(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
1009(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
1010(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
10112^1304675+243713392747Enzo Doria01/2026
1012(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
10132^1303816+38251392488Enzo Doria11/2024
10142^1303257+48527392320Enzo Doria07/2025
10152^1303102+1866409392273Enzo Doria09/2017
10162^1302818+283429392188Enzo Doria01/2017
10172^1301430+22669391770Enzo Doria10/2023
10182^1301229+222467391709Enzo Doria04/2024
10192^1300835+232523391591Enzo Doria03/2025
1020(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
10212^1299181+1886867391093Enzo Doria04/2017
1022(37^249341-1)/36391016Paul Bourdelais08/2020
10232^1298304+1882891390829Enzo Doria01/2017
10242^1297732+228721390657Enzo Doria11/2024
1025Phi(87181,13#)390354Henri Lifchitz02/2026
10262^1295728+240751390053Enzo Doria09/2025
102795196^12497+12497^95196390000Hans Havermann12/2021
10282^1295539+35633389997Enzo Doria08/2024
102986206^33381+33381^86206389953Hans Havermann05/2023
10302^1294976+236731389827Enzo Doria06/2025
10312^1294324+25171389631Enzo Doria12/2023
10322^1294298+243649389623Enzo Doria01/2026
1033(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
10342^1292338+229249389033Enzo Doria11/2024
10352^1289624+32551388216Enzo Doria05/2024
10362^1286857+37967387383Enzo Doria10/2024
10372^1285458+46159386962Enzo Doria06/2025
10382^1285456+230611386961Enzo Doria01/2025
1039(7^457871-5^457871)/2386946Jon Grantham08/2023
104079455^73828+73828^79455386805Hans Havermann03/2023
104181650^54369+54369^81650386642Yusuf AttarBashi06/2021
104280565^62824+62824^80565386561Hans Havermann08/2021
104383747^41272+41272^83747386548Hans Havermann08/2021
104415^328574+328574^15386434Serge Batalov05/2014
10452^1283304+53551386313Enzo Doria01/2026
10462^1283177+57887386275Enzo Doria06/2026
10472^1283147+54833386266Enzo Doria02/2026
10482^1282676+30493386124Enzo Doria12/2024
10492^1280078+1885099385342Enzo Doria08/2017
10502^1279921+17385295Stefano Morozzi10/2022
10512^1279245+224087385092Enzo Doria07/2024
10522^1278091+47963384744Enzo Doria07/2025
10532^1277980+231391384711Enzo Doria01/2025
10542^1277688+231241384623Enzo Doria01/2025
10552^1277142+234979384459Enzo Doria04/2025
10562^1276977+71657384409Enzo Doria08/2023
1057(76803^78961-1)/(76803^281-1)384382Ryan Propper11/2023
10582^1276571+26213384287Enzo Doria12/2023
1059MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832,26908)384166Sergey Batalov05/2024
10602^1274941+1880717383796Enzo Doria10/2016
10612^1272632+383431383101Enzo Doria01/2017
10622^1271346+1889839382714Enzo Doria08/2017
10632^1271173+219587382662Enzo Doria03/2024
10642^1266263+239783381184Enzo Doria09/2025
10655*3^798534-2^798534380999Jon Grantham08/2023
1066(10^380976-7)/3380976Leonid Durman01/2012
10672^1264748+23221380728Enzo Doria11/2023
10682^1262877+56897380164Enzo Doria04/2026
1069(4*10^380056+11)/3380057Tyler Busby03/2023
10702^1262504+242821380052Enzo Doria12/2025
10712^1262431+228353380030Enzo Doria11/2024
10722^1260859+222683379557Enzo Doria06/2024
10732^1258313+43727378790Enzo Doria03/2025
10742^1257787+1447761378632Makoto Morimoto10/2013
1075(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
10762^1257728+20851378614Enzo Doria08/2023
1077(77^200657-1)/76378536Paul Bourdelais08/2020
10782^1257107+45413378427Enzo Doria05/2025
10792^1254797+229487377732Enzo Doria11/2024
1080(98^189619+1)/99377573Paul Bourdelais02/2021
1081Phi(17#,12492)377546Henri Lifchitz10/2025
1082F(1803059)376817Henri Lifchitz06/2009
10832^1250590+29389376466Enzo Doria03/2024
1084(10^376417-3^376417)/7376417Jon Grantham08/2023
10852^1250116+34951376323Enzo Doria08/2024
10862^1248318+51859375782Enzo Doria11/2025
10872^1248184-57329375741Enzo Doria05/2026
10882^1246724+213961375302Enzo Doria10/2023
10892^1246340+54961375186Enzo Doria02/2026
10902^1245610+237919374966Enzo Doria06/2025
10912^1245230+19374852Stefano Morozzi10/2022
10922^1244480+52021374626Enzo Doria11/2025
10932^1244368+247771374593Enzo Doria04/2026
10942^1244263+230033374561Enzo Doria01/2025
10957^442674+4374103Paul Bourdelais02/2021
10962^1242374+240919373992Enzo Doria09/2025
10972^1242268+239641373960Enzo Doria08/2025
10982^1239939+242513373259Enzo Doria12/2025
10992^1239151+35633373022Enzo Doria08/2024
11002^1238732+39181372896Enzo Doria11/2024
11012^1237699+34703372585Enzo Doria07/2024
1102(97^187393-1)/96372306Paul Bourdelais09/2020
11032^1235070+46219371794Enzo Doria05/2025
110410^371696+7371697Alfred Reich05/2021
11052^1234709+883127371685Enzo Doria12/2016
11062^1234688+237151371679Enzo Doria08/2025
11072^1234119+21803371507Enzo Doria09/2023
1108(67^203431+1)/68371479Paul Bourdelais09/2021
11092^1233971+216593371463Enzo Doria12/2023
11102^1233212+27301371234Enzo Doria12/2023
11112^1231847+244103370823Enzo Doria01/2026
11122^1231529+237557370728Enzo Doria06/2025
11132^1231466+283819370709Enzo Doria07/2017
11142^1229766+26659370197Enzo Doria12/2023
11152^1228899+30713369936Enzo Doria03/2024
11162^1228892+223831369934Enzo Doria06/2024
11172^1227635+45413369555Enzo Doria05/2025
1118(49627^78961-1)/(49627^281-1)369460Ryan Propper11/2023
11192^1227060+226663369382Enzo Doria09/2024
11202^1226987+28163369360Enzo Doria02/2024
11212^1226725+234887369282Enzo Doria04/2025
11222^1226569+30857369235Enzo Doria03/2024
11232^1225268+46591368843Enzo Doria05/2025
112473^197880+197880368715Kellen Shenton06/2023
11252^1223601+242357368341Enzo Doria11/2025
11265*3^771723-2^771723368207Jon Grantham08/2023
11272^1222741+231707368082Enzo Doria02/2025
11282^1222473+221597368002Enzo Doria04/2024
11292^1222211+22703367923Enzo Doria11/2023
1130(2^1222097+19)/3367888Stefano Morozzi09/2022
11312^1220335+1881263367358Enzo Doria11/2016
11322^1219565+49967367126Enzo Doria03/2026
11332^1219561+47897367125Enzo Doria09/2025
11342^1219351+240773367062Enzo Doria09/2025
11352^1219016+53041366961Enzo Doria12/2025
11362^1218344+215641366759Enzo Doria12/2023
11372^1217510+220039366508Enzo Doria03/2024
11382^1217500+226321366505Enzo Doria09/2024
1139(233^154787-1)/232366434Anonymous05/2024
11402^1216694+1884769366262Enzo Doria02/2017
11412^1216267+45143366133Enzo Doria05/2025
11422^1215889-3366020Paul Bourdelais06/2019
11432^1215296+1885441365841Enzo Doria03/2017
1144(80^192133+1)/81365645Paul Bourdelais01/2021
11452^1214307+1888115365543Enzo Doria05/2017
11462^1213815+3365395Paul Bourdelais06/2019
1147(80^191953+1)/81365302Paul Bourdelais01/2021
11482^1213313+215837365244Enzo Doria11/2023
11492^1208816+55081363890Enzo Doria02/2026
11502^1208276+22201363728Enzo Doria09/2023
11512^1207345+1882577363448Enzo Doria12/2016
11522^1207336+217801363445Enzo Doria03/2024
11532^1207073+883727363366Enzo Doria03/2017
11543^761457-2363308Ryan Propper07/2015
1155(10^363030+7)/337/443363025Alfred Reich12/2021
11562^1204869+224885362702Enzo Doria07/2024
11572^1204540+237541362603Enzo Doria07/2025
11582^1203721+44117362357Enzo Doria04/2025
11592^1203309+54857362233Enzo Doria02/2026
11602^1200972+141811361529Stefano Morozzi10/2022
1161(2^1200924+324730)/2361514Stefano Morozzi06/2021
1162(2^1200912+274110)/2361511Stefano Morozzi01/2021
11632^1200906+165249361509Stefano Morozzi07/2022
11642^1200890+166339361504Stefano Morozzi01/2023
1165(2^1200887+344126)/2361503Stefano Morozzi10/2020
11662^1200877+186755361500Stefano Morozzi09/2022
11672^1200861+198521361496Stefano Morozzi11/2021
1168(2^1200856+305790)/2361494Stefano Morozzi10/2020
1169(2^1200853+372822)/2361493Stefano Morozzi06/2021
11702^1200812+324178)/2361481Stefano Morozzi06/2021
1171(2^1200768+380458)/2361467Stefano Morozzi01/2021
11722^1200756+140917361464Stefano Morozzi05/2022
11732^1200741+184781361460Stefano Morozzi09/2022
1174(2^1200741+293402)/2361459Stefano Morozzi07/2021
11752^1200734+142653361457Stefano Morozzi02/2023
11772^1200672+1880881361439Enzo Doria10/2016
11762^1200672+141535361439Stefano Morozzi09/2022
11782^1200669+178805361438Stefano Morozzi11/2022
11792^1200660+198555361435Stefano Morozzi12/2021
11802^1200657+164837361434Stefano Morozzi05/2022
11812^1200631+166431361426Stefano Morozzi02/2023
11822^1200627+150669361425Stefano Morozzi02/2023
1183(2^1200603+356030)/2361418Stefano Morozzi10/2020
1184(2^1200590+275854)/2361414Stefano Morozzi03/2021
11852^1200550+139297361402Stefano Morozzi10/2021
11862^1200486+172855361383Stefano Morozzi01/2023
1187(2^1200456+320526)/2361373Stefano Morozzi10/2020
11882^1200443+142121361370Stefano Morozzi01/2023
11892^1200416+164065361362Stefano Morozzi01/2022
11902^1200331+155429361336Stefano Morozzi10/2021
1192(2^1200289+348366)/2361323Stefano Morozzi10/2020
11912^1200289+141885361323Stefano Morozzi11/2022
1193(2^1200284+273162)/2361322Stefano Morozzi10/2020
11942^1200252+194535361312Stefano Morozzi11/2021
1195(2^1200250+364230)/2361311Stefano Morozzi10/2020
11962^1200227+156881361305Stefano Morozzi05/2022
1197(2^1200209+305990)/2361299Stefano Morozzi10/2020
1198(2^1200210+376278)/2361299Stefano Morozzi10/2020
11992^1200202+216499361297Enzo Doria12/2023
1200(2^1200182+274462)/2361291Stefano Morozzi01/2021
12012^1200178+149193361290Stefano Morozzi07/2022
12022^1200168+140403361287Stefano Morozzi03/2022
1203(2^1200162+275910)/2361285Stefano Morozzi03/2021
12042^1200157+168927361284Stefano Morozzi02/2023
12052^1200134+141385361277Stefano Morozzi08/2022
1206(2^1200131+360150)/2361276Stefano Morozzi10/2020
1207(2^1200118+290718)/2361272Stefano Morozzi01/2021
12082^1200022+192777361243Stefano Morozzi09/2022
12092^1200021+149777361243Stefano Morozzi10/2022
1210Phi(451125,2^5)361236Henri Lifchitz12/2025
1211(64*10^360173-1)/243360173Serge Batalov09/2014
1212(59^203309+1)/60360029Paul Bourdelais09/2021
1213(2*10^359860-11)/9359860Rytis Slatkevicius01/2023
12142^1195093+1882577359759Enzo Doria12/2016
12153^753451+5*2^753451359488Jon Grantham08/2023
12162^1193505+238397359281Enzo Doria07/2025
12172^1192258+36739358906Enzo Doria09/2024
12182^1192251+47183358904Enzo Doria06/2025
1219(6^461108-11)/5358812Paul Bourdelais04/2019
12202^1191375+8543358640Phil Moore06/2008
12212^1191335+50783358628Enzo Doria10/2025
12222^1190972+1880191358519Enzo Doria11/2016
12232^1190752+245041358453Enzo Doria02/2026
12242^1189930+28549358205Enzo Doria03/2024
1225(45^216551-1)/44358004Paul Bourdelais08/2020
12262^1187473+237257357465Enzo Doria06/2025
12272^1187356+44641357430Enzo Doria06/2025
12282^1187005+230807357325Enzo Doria01/2025
1229(50^210319-1)/49357324Paul Bourdelais08/2020
1230(531^131072+25^131072)/2357184Kellen Shenton03/2021
12312^1186366+226747357132Enzo Doria09/2024
12322^1185014+241039356725Enzo Doria09/2025
12332^1184565+21227356590Enzo Doria08/2023
12342^1180312+44173355310Enzo Doria04/2025
12352^1180159+22823355264Enzo Doria11/2023
12362^1179944+238741355199Enzo Doria07/2025
12372^1179836+1885021355167Enzo Doria02/2017
12382^1178942+32269354897Enzo Doria04/2024
12392^1178474+43369354757Enzo Doria03/2025
12402^1177053+28607354329Enzo Doria02/2024
12412^1177027+234863354321Enzo Doria04/2025
1242(19*10^353884-91)/9353885Alfred Reich02/2023
1243(10^353884*19-91)/9353885Alfred Reich10/2023
124420^271951+3353817Paul Bourdelais01/2021
124572722^72722+7^7353551Serge Batalov04/2024
12462^1173095+21353137Stefano Morozzi10/2022
12472^1170959+218945352494Enzo Doria03/2024
12482^1170915+382623352481Boyan Hu08/2024
1249(63^195893-1)/62352477Paul Bourdelais08/2020
12502^1170575+238043352379Enzo Doria07/2025


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 09 2026 15:49 (Time in France)

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