PRP Records

Probable Primes Top 10000

(291192 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 ?
35018*10^128651-37128652Robert Price03/2022
3502(68*10^128645-257)/9128646Robert Price07/2019
35032^427269-113635128621Enzo Doria08/2014
35042^427130+1877569128579Enzo Doria08/2016
35052^427016-115349128545Enzo Doria07/2015
3506(4*10^128510+137)/3128511Robert Price03/2018
35072^426889-112879128507Enzo Doria06/2014
35082^426804+1869931128481Enzo Doria05/2016
35092^426750+77635128465Enzo Doria05/2016
351036988^2969+2969^36988128445Hans Havermann03/2021
351136664^3185+3185^36664128439Hans Havermann03/2021
351232618^8649+8649^32618128416Hans Havermann04/2021
351328883^27874+27874^28883128391Hans Havermann04/2021
35142^426425-91128367Lelio R Paula05/2017
3515(15*2^426398-1)/11128359Lelio R Paula05/2014
35162^426352+74971128345Enzo Doria04/2016
3517(199*10^128343-7)/3128345Robert Price05/2020
35184*10^128343-21128344Robert Price09/2018
3519(65*10^128338+493)/9128339Robert Price08/2021
352035632^3997+3997^35632128337Hans Havermann04/2021
35212^426300-1863689128330Enzo Doria03/2016
35222^426293+1881017128327Enzo Doria11/2016
3523(88*10^128324-637)/9128325Robert Price11/2020
3524(491*10^128285+31)/9128287Robert Price04/2022
352539103^1908+1908^39103128281Hans Havermann04/2021
35262^426043+35128252Robert Price11/2015
3527(4*10^128244-19)/3128245Robert Price03/2018
352835489^4102+4102^35489128222Hans Havermann04/2021
352934721^4926+4926^34721128208Hans Havermann04/2021
3530(305*10^128198+1)/9128200Robert Price02/2020
35312^425808-459959128181Enzo Doria06/2015
353230632^15291+15291^30632128178Hans Havermann04/2021
353335981^3648+3648^35981128167Hans Havermann04/2021
35342^425627-113605128127Enzo Doria08/2014
3535(4*10^128109+119)/3128110Robert Price12/2021
3536(22*10^128094+53)/3128095Robert Price07/2019
3537(86*10^128086-221)/9128087Robert Price09/2019
353818565^30002-30002^18565128070Norbert Schneider01/2015
3539(2^425287-9)/2737128021Lelio R Paula05/2015
3540(3*2^425233-1)/25128007Lelio R Paula05/2014
3541Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
35422^425205+4911128000Marek Hubal02/2017
354329241^23836+23836^29241127995Hans Havermann04/2021
35442^425118-113663127974Enzo Doria08/2014
3545(86*10^127967-329)/9127968Robert Price01/2020
35462^425061+1869761127957Enzo Doria05/2016
3547746^44541+44541^746127955Norbert Schneider07/2019
354830236^17043+17043^30236127946Hans Havermann03/2021
35492^424918-21141127914Enzo Doria07/2013
3550(62*10^127903+91)/9127904Robert Price07/2021
35512^424864-29489127897Enzo Doria08/2015
355230438^15893+15893^30438127877Hans Havermann02/2021
3553(97*10^127858-1)/3127860Serge Batalov12/2014
355428929^26258+26258^28929127845Hans Havermann03/2021
355530563^15220+15220^30563127828Hans Havermann03/2021
35562^424632-2786639127827Enzo Doria03/2016
355710^127821-700001127821Robert Price08/2021
35582^424577-113755127811Enzo Doria09/2014
3559(7*2^424512-1)/3127792Lelio R Paula05/2014
3560(56*10^127752+691)/9127753Robert Price05/2019
356111^122629-720127705Enzo Doria11/2012
356222*10^127645+3127647Robert Price01/2020
356328715^27844+27844^28715127631Hans Havermann03/2021
3564(56*10^127612+187)/9127613Robert Price10/2021
3565(5*36^81995+821)/7127609Eric Chen01/2021
35664*10^127562-39127563Robert Price09/2020
356732595^8186+8186^32595127547Hans Havermann03/2021
35682^423696-21429127546Enzo Doria07/2013
35692^423664-1864559127536Enzo Doria03/2016
357037889^2322+2322^37889127530Hans Havermann03/2021
357137668^2429+2429^37668127523Hans Havermann03/2021
35723^267267-4127519Henri Lifchitz10/2014
3573(103*10^127491+17)/3127493Robert Price08/2020
357429376^21869+21869^29376127487Hans Havermann03/2021
357531186^12241+12241^31186127483Hans Havermann02/2021
3576(19^99689+5^99689)/24127477Robert Price09/2013
3577(21*2^423372+1)/101127447Lelio R Paula05/2014
357830594^14645+14645^30594127446Hans Havermann03/2021
35792^423328-21537127435Enzo Doria07/2013
3580(67*10^127413-7)/3127415Robert Price01/2020
3581(2*10^127407+73)/3127407Robert Price09/2020
3582(2^423165-7)/25127384Lelio R Paula05/2015
3583(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
358429512^20647+20647^29512127341Hans Havermann03/2021
3585(112*10^127324+17)/3127326Robert Price03/2020
358629565^20252+20252^29565127321Hans Havermann03/2021
3588(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
3587(5^182099-3^182099)/2127282Kellen Shenton05/2022
3589(16*10^127259+197)/3127260Robert Price04/2019
3590(26*10^127240+61)/3127241Robert Price10/2019
3591(234483*27^88884-145)/26127230Curtis Bright05/2015
35922^422515-114997127190Enzo Doria06/2015
35935*10^127179-3127180Robert Price07/2015
359431678^10343+10343^31678127176Hans Havermann03/2021
3595(44*10^127169-233)/9127170Robert Price01/2019
359634947^4352+4352^34947127162Hans Havermann03/2021
35976*10^127158+19127159Robert Price11/2021
359830469^14902+14902^30469127155Hans Havermann03/2021
35995*10^127153+77127154Robert Price12/2018
360029941^17620+17620^29941127130Hans Havermann02/2021
360131607^10516+10516^31607127119Hans Havermann03/2021
3602(19*10^127118-97)/3127119Robert Price10/2021
3603(29*10^127111+691)/9127112Robert Price08/2021
3604736^44335+44335^736127104Norbert Schneider07/2019
360533040^7023+7023^33040127090Hans Havermann03/2021
3606(4*10^127081+167)/9127081Robert Price03/2022
360729748^18661+18661^29748127052Hans Havermann03/2021
3608-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
3609(78^67141-1)/77127036Paul Bourdelais09/2017
3610(14*10^127014-137)/3127015Robert Price04/2021
361131436^10965+10965^31436127002Hans Havermann03/2021
361228905^24758+24758^28905127001Hans Havermann03/2021
36132^421860-113285126993Enzo Doria07/2014
3614(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
3615(2^421827-7)/11126982Lelio R Paula05/2015
361611^121910-840126957Enzo Doria12/2012
3617(56*10^126935+187)/9126936Robert Price10/2021
361828915^24538+24538^28915126933Hans Havermann03/2021
3619(29*10^126928-77)/3126929Robert Price02/2020
3620(259*10^126919-1)/3126921Robert Price12/2020
362110^126919+204567126920Patrick De Geest05/2021
3622(2^421617+100280245065)126920Paul Bourdelais05/2022
362310^126919-100001126919Robert Price07/2020
362428340^28503+28503^28340126907Norbert Schneider02/2021
3625(71^68539+1)/72126882Paul Bourdelais09/2017
3626(5*10^126871-119)/3126872Robert Price03/2018
3627331^50339-10004126846Enzo Doria07/2012
36282^421363-2790757126843Enzo Doria03/2016
3629(106*10^126839-1)/3126841Serge Batalov12/2014
363037938^2203+2203^37938126828Hans Havermann03/2021
3631(13*10^126819+77)/9126820Robert Price07/2022
3632(7*2^421243+1)/39126807Lelio R Paula05/2014
3633(14*10^126784-83)/3126785Robert Price12/2018
36342^421161-286183126783Enzo Doria06/2015
3635(106*10^126726+17)/3126728Robert Price04/2021
363630718^13347+13347^30718126724Hans Havermann03/2021
36372^420939-113935126716Enzo Doria10/2014
3638177^56363-2126703Lelio R Paula10/2017
36392^420741-113659126656Enzo Doria08/2014
36402^420694-21126642Lelio R Paula05/2017
3641(13*10^126638+437)/9126639Robert Price04/2018
3642(167*10^126637-17)/3126639Robert Price03/2020
36434*10^126625+87126626Robert Price08/2018
3644(31*2^420556+1)/7126601Lelio R Paula05/2014
36457*10^126600-99126601Robert Price06/2019
36462^420424-59189126561Enzo Doria10/2015
364728717^25534+25534^28717126560Hans Havermann03/2021
3648(86*10^126542+103)/9126543Robert Price12/2021
364928922^23655+23655^28922126503Hans Havermann03/2021
36502^420126+71893126471Enzo Doria04/2016
3651(43*10^126441+47)/9126442Robert Price12/2018
36528*10^126408+71126409Robert Price05/2022
36532^419866+1877059126393Enzo Doria07/2016
365429315^20484+20484^29315126390Hans Havermann03/2021
365529433^19676+19676^29433126384Hans Havermann03/2021
3656F(604711)126377Henri Lifchitz02/2005
36572^419757+72707126360Enzo Doria04/2016
36582^419720-21569126349Enzo Doria07/2013
36592^419637+29126324Henri Lifchitz02/2006
366031004^11865+11865^31004126319Hans Havermann03/2021
36612^419612+1876741126316Enzo Doria07/2016
36622^419520+2793271126289Enzo Doria03/2016
3663(2^419447-5)/369126264Lelio R Paula05/2014
36642^419328-1859939126231Enzo Doria03/2016
36652^419282-1851507126217Enzo Doria08/2015
3666(133*10^126212+17)/3126214Robert Price11/2021
36672^419251+1866143126208Enzo Doria03/2016
366811^121185+2126202Robert Price05/2014
366928203^28352+28352^28203126175Norbert Schneider01/2021
3670(23*2^419036-1)/1393126141Lelio R Paula05/2014
36712^418851+23126087Robert Price09/2015
3672(2^418849-9)/2681126083Lelio R Paula05/2014
36732^418829+167126081Lelio R Paula01/2012
367431037^11530+11530^31037126067Hans Havermann03/2021
36754*10^126064-69126065Robert Price01/2022
3676(31*2^418782-1)/75891126063Lelio R Paula05/2014
3677(19*2^418754-1)/15126058Lelio R Paula05/2014
3678(35*10^126048-323)/9126049Robert Price10/2021
367933016^6551+6551^33016126000Hans Havermann03/2021
36802^418548-111546435125996Paul Bourdelais10/2021
368134736^4227+4227^34736125954Hans Havermann03/2021
36822^418319-109501125927Enzo Doria04/2014
36832^418316-112373125926Enzo Doria06/2014
368440398^1309+1309^40398125919Hans Havermann03/2021
3685(8*10^125894-29)/3125895Robert Price07/2018
3686(26*10^125886-413)/9125887Robert Price05/2018
368755*10^125847+9125849Robert Price03/2022
36884*10^125832+57125833Robert Price05/2022
36892^417968+1869811125821Enzo Doria06/2016
36902^417902+63125802Lelio R Paula09/2015
3691(10^125792-91)/9125792Serge Batalov12/2014
369230438^13573+13573^30438125791Hans Havermann03/2021
369332867^6714+6714^32867125782Hans Havermann03/2021
369431155^10892+10892^31155125777Hans Havermann03/2021
3695(35*10^125754-593)/9125755Robert Price07/2018
369630455^13464+13464^30455125754Hans Havermann03/2021
3697(32*10^125751-77)/9125752Robert Price06/2018
36982^417704+77011125742Enzo Doria05/2016
369929755^16816+16816^29755125737Hans Havermann03/2021
3700(22*10^125734+203)/9125735Robert Price10/2021
370129918^15915+15915^29918125710Hans Havermann03/2021
3702(10^125706+149)/3125706Serge Batalov12/2014
370328531^25368+25368^28531125659Hans Havermann03/2021
37042^417419-115309125656Enzo Doria07/2015
3705(46*10^125642+593)/9125643Robert Price04/2022
37062^417300+77281125620Enzo Doria05/2016
370730638^12537+12537^30638125561Hans Havermann03/2021
37082^417095-1657125559Yves Minet07/2014
370930162^14525+14525^30162125538Hans Havermann03/2021
3710(56*10^125535+583)/9125536Robert Price08/2021
3711(23*10^125517-179)/3125518Robert Price06/2022
37129*10^125516+29125517Robert Price03/2022
3713(88*10^125492-637)/9125493Robert Price11/2020
371428958^21525+21525^28958125474Hans Havermann02/2021
37162^416773-25125462Lelio R Paula09/2015
3715(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
371733889^5032+5032^33889125449Hans Havermann03/2021
3718(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
3719(11*2^416691+1)/43125436Lelio R Paula05/2014
3720(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
37212^416641-2*416641+1125422Robert Price05/2018
372233392^5697+5697^33392125409Hans Havermann03/2021
3723(21*2^416566-1)/17125399Lelio R Paula05/2014
37242^416530+1870429125389Enzo Doria05/2016
3725(56*10^125385+691)/9125386Robert Price05/2019
372627953^28198+28198^27953125381Norbert Schneider01/2021
372731074^10837+10837^31074125381Hans Havermann03/2021
372833745^5194+5194^33745125380Hans Havermann03/2021
37292^416490+1875109125376Enzo Doria09/2016
373028360^26331+26331^28360125365Hans Havermann03/2021
37312^416416-114929125354Enzo Doria05/2015
3732(77*10^125330-293)/9125331Robert Price09/2019
3733(172*10^125292-1)/9125294Serge Batalov12/2014
37342^416134+1865899125269Enzo Doria03/2016
3735153^57337-152125264Norbert Schneider12/2018
3736(599*10^125224+13)/9125226Robert Price02/2022
3737(9*2^415992+1)/13560845125220Lelio R Paula05/2014
373830054^14657+14657^30054125207Hans Havermann03/2021
3739(23^91943-1)/22125201Robert Price01/2012
37402^415884-933075125194Paul Bourdelais06/2021
374143125^27010-106125185Enzo Doria08/2012
3742(38*10^125166+349)/9125167Robert Price10/2018
374310^125166-5001125166Robert Price12/2021
37442^415765-112603125158Enzo Doria06/2014
37458*10^125088-13125089Robert Price08/2019
3746(25*10^125076-13)/3125077Robert Price09/2019
3747(11*10^125054+73)/3125055Robert Price08/2021
3748(29*10^125021-113)/3125022Robert Price10/2019
37492^415290-113591125015Enzo Doria08/2014
37502^415276-460919125011Enzo Doria06/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!