PRP Records

Probable Primes Top 10000

(291910 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
3501(5*10^131090+37)/3131091Robert Price03/2018
35022^435468+75631131089Enzo Doria04/2016
350337^83588-2131083Lelio R Paula08/2015
3504(4^217720+11)/3131081Robert Price02/2017
350530407^20448+20448^30407131074Hans Havermann04/2021
3506(22*10^131070+179)/3131071Robert Price02/2022
350729487^27836+27836^29487131059Hans Havermann04/2021
350829962^23615+23615^29962131030Hans Havermann03/2021
35092^435202-113193131009Enzo Doria07/2014
351041705^1384+1384^41705131002Hans Havermann04/2021
35119*10^130998-19130999Robert Price07/2019
351236243^4108+4108^36243130969Hans Havermann04/2021
3513floor((sqrt(5)-1)/2*10^130911)130911Serge Batalov06/2017
35142^434835-111937130899Enzo Doria05/2014
3515(62*10^130895-629)/9130896Robert Price07/2021
35162^434685+72257130854Enzo Doria04/2016
3517(7*10^130825+113)/3130826Robert Price02/2018
35182^434539-29317130810Enzo Doria07/2015
3519(74*10^130791+637)/9130792Robert Price01/2022
35202^434469-114259130789Enzo Doria01/2015
3521(5*10^130763+103)/9130763Robert Price04/2022
35222^434246+33130722Robert Price11/2015
352330156^21599+21599^30156130710Hans Havermann04/2021
3524(17*10^130695-161)/9130695Robert Price02/2021
352530513^19148+19148^30513130661Hans Havermann03/2021
352629736^24761+24761^29736130654Hans Havermann04/2021
35279*10^130638+41130639Robert Price08/2020
35282^433911-91130621Lelio R Paula06/2017
352930786^17449+17449^30786130588Hans Havermann03/2021
35302^433744-114419130570Enzo Doria02/2015
35322^433708+1869451130560Enzo Doria05/2016
35312^433710+93130560Lelio R Paula06/2017
35337*10^130535-27130536Robert Price11/2022
3534(9629^32768+1)/120501441265666130520Kellen Shenton05/2021
3535(29*2^433547-1)/27130511Lelio R Paula06/2015
35363^273521+10130503Tyler NeSmith01/2021
353741659^1356+1356^41659130487Hans Havermann03/2021
35384*10^130480+9130481Robert Price05/2015
3539(23*2^433449-1)/75130481Lelio R Paula06/2015
3540(23*2^433334-1)/3731130445Lelio R Paula06/2015
3541(31*10^130414-49)/9130415Robert Price11/2021
354233481^7848+7848^33481130401Hans Havermann03/2021
3543(22*10^130392+203)/9130393Robert Price10/2021
354429773^23950+23950^29773130386Hans Havermann04/2021
35452^433023-113497130353Enzo Doria08/2014
354631175^15178+15178^31175130350Hans Havermann04/2021
35472^433002+1179379130347Enzo Doria06/2016
35482^432974+19130339Robert Price08/2015
354931903^12168+12168^31903130331Hans Havermann04/2021
355029387^27112+27112^29387130278Hans Havermann04/2021
355129577^25370+25370^29577130267Hans Havermann04/2021
355231738^12685+12685^31738130231Hans Havermann03/2021
355344235^878+878^44235130206Hans Havermann04/2021
355432160^11171+11171^32160130187Hans Havermann04/2021
355529489^25956+25956^29489130172Hans Havermann04/2021
3556(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
355733005^8766+8766^33005130133Hans Havermann04/2021
3558(35*10^130132-611)/9130133Robert Price02/2022
35592^432217+41130111Lelio R Paula06/2017
3560(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
3561((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
356297^65480-2130094Lelio R Paula05/2017
356336007^4102+4102^36007130094Hans Havermann04/2021
35644*10^130088-89130089Robert Price11/2018
35652^432117-113215130081Enzo Doria07/2014
3566(4*10^130080+41)/9130080Serge Batalov11/2022
35672^431804+72511129986Enzo Doria04/2016
3568(13*10^129896+137)/3129897Robert Price06/2021
3569(13*10^129890+71)/3129891Robert Price06/2021
357029048^29101-29101^29048129882Norbert Schneider03/2022
357137832^2709+2709^37832129871Hans Havermann04/2021
357231055^15184+15184^31055129853Hans Havermann04/2021
3573(3^272141-3^136071+1)/7129844Serge Batalov03/2014
357431385^13702+13702^31385129833Hans Havermann04/2021
357528901^29102-29102^28901129822Norbert Schneider03/2022
3576(47*10^129789-119)/9129790Robert Price05/2019
3577(9*2^431141+1)/17129787Lelio R Paula06/2015
3578(166*10^129712+17)/3129714Robert Price07/2022
3579(29*2^430881-1)/21129709Lelio R Paula06/2015
35802^430807+1869563129686Enzo Doria05/2016
35812^430721-21429129660Enzo Doria07/2013
3582(4*10^129618+89)/3129619Robert Price08/2021
35832^430415-276271129568Enzo Doria07/2015
358432282^10311+10311^32282129558Hans Havermann04/2021
358529486^24741+24741^29486129545Hans Havermann04/2021
3586(29*10^129543+313)/9129544Robert Price04/2021
358737095^3104+3104^37095129533Hans Havermann04/2021
358831132^14459+14459^31132129514Hans Havermann04/2021
358932582^9435+9435^32582129506Hans Havermann03/2021
359030442^17953+17953^30442129505Hans Havermann03/2021
3591(199*10^129487-7)/3129489Robert Price05/2020
35922^430142-2791721129486Enzo Doria03/2016
3593(7*10^129472-13)/3129473Robert Price07/2018
3594(8*10^129469+79)/3129470Robert Price10/2020
359531678^12213+12213^31678129463Hans Havermann04/2021
3596(772*10^129406-7)/9129408Robert Price06/2022
359731100^14439+14439^31100129362Hans Havermann04/2021
359833009^8288+8288^33009129345Hans Havermann04/2021
359929675^22804+22804^29675129324Hans Havermann04/2021
360029068^28099+28099^29068129315Hans Havermann04/2021
36012^429568-21017129313Enzo Doria07/2013
3602(10^129295+83)/3129295Robert Price08/2021
3603(853*10^129274-7)/9129276Robert Price07/2021
360430958^14961+14961^30958129249Hans Havermann04/2021
3605(11*10^129239-179)/3129240Robert Price09/2018
360628659^28988+28988^28659129208Norbert Schneider02/2021
360729423^24616+24616^29423129203Hans Havermann03/2021
36082^429194-112685129201Enzo Doria06/2014
36092^429145-2780449129186Enzo Doria04/2016
361032500^9427+9427^32500129168Hans Havermann04/2021
361133577^7014+7014^33577129136Hans Havermann03/2021
36122^428892-113453129110Enzo Doria07/2014
3613(11*2^428881-7)/15129106Renaud Lifchitz03/2011
36142^428727-113959129060Enzo Doria10/2014
3615(7*2^428725-1)/13129059Lelio R Paula05/2014
3616(10^129051-31)/3129051Serge Batalov12/2014
3617(134*10^129038+7)/3129040Robert Price02/2020
36182^428564+71161129011Enzo Doria04/2016
361928781^28930+28930^28781129002Norbert Schneider02/2021
362029065^27424+27424^29065128995Hans Havermann04/2021
36212^428502-113285128992Enzo Doria07/2014
36222^428421-21373128968Enzo Doria06/2013
3623L(616787)128901Henri Lifchitz09/2008
362420^99055-3128874Paul Bourdelais12/2020
362591^65772-2128851Lelio R Paula05/2017
36262^428022+43128848Lelio R Paula05/2017
36272^427999-459397128841Enzo Doria05/2015
36282^427993+76847128839Enzo Doria05/2016
362931059^14060+14060^31059128833Hans Havermann03/2021
363010^128805+152871128806Patrick De Geest05/2021
363110^128805-10001128805Robert Price02/2021
36322^427824-1851507128788Enzo Doria08/2015
36332^427807-21469128783Enzo Doria07/2013
363429082^26783+26783^29082128772Hans Havermann04/2021
363540055^1638+1638^40055128750Hans Havermann04/2021
363611^123594-240128710Enzo Doria09/2012
36372^427504-21503128692Enzo Doria07/2013
363837727^2574+2574^37727128673Hans Havermann04/2021
363929686^21591+21591^29686128668Hans Havermann04/2021
364010^128668-70000000001128668Robert Price08/2021
36412^427420+91128667Lelio R Paula05/2017
36428*10^128651-37128652Robert Price03/2022
3643(68*10^128645-257)/9128646Robert Price07/2019
36442^427269-113635128621Enzo Doria08/2014
36452^427130+1877569128579Enzo Doria08/2016
36462^427016-115349128545Enzo Doria07/2015
3647(4*10^128510+137)/3128511Robert Price03/2018
36482^426889-112879128507Enzo Doria06/2014
36492^426804+1869931128481Enzo Doria05/2016
36502^426750+77635128465Enzo Doria05/2016
365136988^2969+2969^36988128445Hans Havermann03/2021
365236664^3185+3185^36664128439Hans Havermann03/2021
365332618^8649+8649^32618128416Hans Havermann04/2021
365428883^27874+27874^28883128391Hans Havermann04/2021
36552^426425-91128367Lelio R Paula05/2017
3656(15*2^426398-1)/11128359Lelio R Paula05/2014
36572^426352+74971128345Enzo Doria04/2016
3658(199*10^128343-7)/3128345Robert Price05/2020
36594*10^128343-21128344Robert Price09/2018
3660(65*10^128338+493)/9128339Robert Price08/2021
366135632^3997+3997^35632128337Hans Havermann04/2021
36622^426300-1863689128330Enzo Doria03/2016
36632^426293+1881017128327Enzo Doria11/2016
3664(88*10^128324-637)/9128325Robert Price11/2020
3665(491*10^128285+31)/9128287Robert Price04/2022
366639103^1908+1908^39103128281Hans Havermann04/2021
36672^426043+35128252Robert Price11/2015
3668(4*10^128244-19)/3128245Robert Price03/2018
366935489^4102+4102^35489128222Hans Havermann04/2021
367034721^4926+4926^34721128208Hans Havermann04/2021
3671(305*10^128198+1)/9128200Robert Price02/2020
36722^425808-459959128181Enzo Doria06/2015
367330632^15291+15291^30632128178Hans Havermann04/2021
367435981^3648+3648^35981128167Hans Havermann04/2021
36752^425627-113605128127Enzo Doria08/2014
3676(4*10^128109+119)/3128110Robert Price12/2021
3677(22*10^128094+53)/3128095Robert Price07/2019
3678(86*10^128086-221)/9128087Robert Price09/2019
367918565^30002-30002^18565128070Norbert Schneider01/2015
3680(2^425287-9)/2737128021Lelio R Paula05/2015
3681(3*2^425233-1)/25128007Lelio R Paula05/2014
3682Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
36832^425205+4911128000Marek Hubal02/2017
368429241^23836+23836^29241127995Hans Havermann04/2021
36852^425118-113663127974Enzo Doria08/2014
3686(86*10^127967-329)/9127968Robert Price01/2020
36872^425061+1869761127957Enzo Doria05/2016
3688746^44541+44541^746127955Norbert Schneider07/2019
368930236^17043+17043^30236127946Hans Havermann03/2021
36902^424918-21141127914Enzo Doria07/2013
3691(62*10^127903+91)/9127904Robert Price07/2021
36922^424864-29489127897Enzo Doria08/2015
369330438^15893+15893^30438127877Hans Havermann02/2021
3694(97*10^127858-1)/3127860Serge Batalov12/2014
369528929^26258+26258^28929127845Hans Havermann03/2021
369630563^15220+15220^30563127828Hans Havermann03/2021
36972^424632-2786639127827Enzo Doria03/2016
369810^127821-700001127821Robert Price08/2021
36992^424577-113755127811Enzo Doria09/2014
3700(7*2^424512-1)/3127792Lelio R Paula05/2014
3701(56*10^127752+691)/9127753Robert Price05/2019
370211^122629-720127705Enzo Doria11/2012
370322*10^127645+3127647Robert Price01/2020
370428715^27844+27844^28715127631Hans Havermann03/2021
3705(56*10^127612+187)/9127613Robert Price10/2021
3706(5*36^81995+821)/7127609Eric Chen01/2021
37074*10^127562-39127563Robert Price09/2020
370832595^8186+8186^32595127547Hans Havermann03/2021
37092^423696-21429127546Enzo Doria07/2013
37102^423664-1864559127536Enzo Doria03/2016
371137889^2322+2322^37889127530Hans Havermann03/2021
371237668^2429+2429^37668127523Hans Havermann03/2021
37133^267267-4127519Henri Lifchitz10/2014
3714(103*10^127491+17)/3127493Robert Price08/2020
371529376^21869+21869^29376127487Hans Havermann03/2021
371631186^12241+12241^31186127483Hans Havermann02/2021
3717(19^99689+5^99689)/24127477Robert Price09/2013
3718(21*2^423372+1)/101127447Lelio R Paula05/2014
371930594^14645+14645^30594127446Hans Havermann03/2021
37202^423328-21537127435Enzo Doria07/2013
3721(67*10^127413-7)/3127415Robert Price01/2020
3722(2*10^127407+73)/3127407Robert Price09/2020
3723(2^423165-7)/25127384Lelio R Paula05/2015
3724(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
3725(4*10^127349+17)/3127350Tyler Busby01/2023
372629512^20647+20647^29512127341Hans Havermann03/2021
3727(112*10^127324+17)/3127326Robert Price03/2020
372829565^20252+20252^29565127321Hans Havermann03/2021
3730(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
3729(5^182099-3^182099)/2127282Kellen Shenton05/2022
3731(16*10^127259+197)/3127260Robert Price04/2019
3732(26*10^127240+61)/3127241Robert Price10/2019
3733(234483*27^88884-145)/26127230Curtis Bright05/2015
37342^422515-114997127190Enzo Doria06/2015
37355*10^127179-3127180Robert Price07/2015
373631678^10343+10343^31678127176Hans Havermann03/2021
3737(44*10^127169-233)/9127170Robert Price01/2019
373834947^4352+4352^34947127162Hans Havermann03/2021
37396*10^127158+19127159Robert Price11/2021
374030469^14902+14902^30469127155Hans Havermann03/2021
37415*10^127153+77127154Robert Price12/2018
374229941^17620+17620^29941127130Hans Havermann02/2021
374331607^10516+10516^31607127119Hans Havermann03/2021
3744(19*10^127118-97)/3127119Robert Price10/2021
3745(29*10^127111+691)/9127112Robert Price08/2021
3746736^44335+44335^736127104Norbert Schneider07/2019
374733040^7023+7023^33040127090Hans Havermann03/2021
3748(4*10^127081+167)/9127081Robert Price03/2022
374929748^18661+18661^29748127052Hans Havermann03/2021
3750-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!