PRP Records

Probable Primes Top 10000

(293510 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 ?
4001(88*10^128324-637)/9128325Robert Price11/2020
4002(491*10^128285+31)/9128287Robert Price04/2022
400339103^1908+1908^39103128281Hans Havermann04/2021
40042^426043+35128252Robert Price11/2015
4005(4*10^128244-19)/3128245Robert Price03/2018
400635489^4102+4102^35489128222Hans Havermann04/2021
400734721^4926+4926^34721128208Hans Havermann04/2021
4008(305*10^128198+1)/9128200Robert Price02/2020
40092^425808-459959128181Enzo Doria06/2015
401030632^15291+15291^30632128178Hans Havermann04/2021
401135981^3648+3648^35981128167Hans Havermann04/2021
40122^425627-113605128127Enzo Doria08/2014
4013(4*10^128109+119)/3128110Robert Price12/2021
4014(22*10^128094+53)/3128095Robert Price07/2019
4015(86*10^128086-221)/9128087Robert Price09/2019
401618565^30002-30002^18565128070Norbert Schneider01/2015
4017(2^425287-9)/2737128021Lelio R Paula05/2015
4018(3*2^425233-1)/25128007Lelio R Paula05/2014
4019Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
40202^425205+4911128000Marek Hubal02/2017
402129241^23836+23836^29241127995Hans Havermann04/2021
40222^425118-113663127974Enzo Doria08/2014
4023(86*10^127967-329)/9127968Robert Price01/2020
40242^425061+1869761127957Enzo Doria05/2016
4025746^44541+44541^746127955Norbert Schneider07/2019
402630236^17043+17043^30236127946Hans Havermann03/2021
40272^424938+212419127920Enzo Doria08/2023
40282^424918-21141127914Enzo Doria07/2013
4029(62*10^127903+91)/9127904Robert Price07/2021
40302^424864-29489127897Enzo Doria08/2015
403130438^15893+15893^30438127877Hans Havermann02/2021
4032(97*10^127858-1)/3127860Serge Batalov12/2014
403328929^26258+26258^28929127845Hans Havermann03/2021
403430563^15220+15220^30563127828Hans Havermann03/2021
40352^424632-2786639127827Enzo Doria03/2016
403610^127821-700001127821Robert Price08/2021
40372^424577-113755127811Enzo Doria09/2014
4038(7*2^424512-1)/3127792Lelio R Paula05/2014
4039(56*10^127752+691)/9127753Robert Price05/2019
404011^122629-720127705Enzo Doria11/2012
404122*10^127645+3127647Robert Price01/2020
404228715^27844+27844^28715127631Hans Havermann03/2021
4043(56*10^127612+187)/9127613Robert Price10/2021
4044(5*36^81995+821)/7127609Eric Chen01/2021
40454*10^127562-39127563Robert Price09/2020
404632595^8186+8186^32595127547Hans Havermann03/2021
40472^423696-21429127546Enzo Doria07/2013
40482^423664-1864559127536Enzo Doria03/2016
404937889^2322+2322^37889127530Hans Havermann03/2021
405037668^2429+2429^37668127523Hans Havermann03/2021
40513^267267-4127519Henri Lifchitz10/2014
4052fibonacci(610144)-2127513Jon Grantham08/2023
4053(103*10^127491+17)/3127493Robert Price08/2020
405429376^21869+21869^29376127487Hans Havermann03/2021
405531186^12241+12241^31186127483Hans Havermann02/2021
4056(19^99689+5^99689)/24127477Robert Price09/2013
4057(21*2^423372+1)/101127447Lelio R Paula05/2014
405830594^14645+14645^30594127446Hans Havermann03/2021
40592^423328-21537127435Enzo Doria07/2013
4060(67*10^127413-7)/3127415Robert Price01/2020
4061(5*34^83193+700233)/11127408Eric Chen08/2023
4062(2*10^127407+73)/3127407Robert Price09/2020
4063(2^423165-7)/25127384Lelio R Paula05/2015
4064(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
4065(4*10^127349+17)/3127350Tyler Busby01/2023
406629512^20647+20647^29512127341Hans Havermann03/2021
40672^422987-3001935127332Paul Bourdelais07/2023
4068(112*10^127324+17)/3127326Robert Price03/2020
406929565^20252+20252^29565127321Hans Havermann03/2021
4070fibonacci(609165)-3127308Jon Grantham08/2023
4072(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
4071(5^182099-3^182099)/2127282Kellen Shenton05/2022
4073(16*10^127259+197)/3127260Robert Price04/2019
4074(26*10^127240+61)/3127241Robert Price10/2019
4075(234483*27^88884-145)/26127230Curtis Bright05/2015
40762^422515-114997127190Enzo Doria06/2015
40775*10^127179-3127180Robert Price07/2015
407831678^10343+10343^31678127176Hans Havermann03/2021
4079(44*10^127169-233)/9127170Robert Price01/2019
408034947^4352+4352^34947127162Hans Havermann03/2021
40816*10^127158+19127159Robert Price11/2021
408230469^14902+14902^30469127155Hans Havermann03/2021
40835*10^127153+77127154Robert Price12/2018
408429941^17620+17620^29941127130Hans Havermann02/2021
408531607^10516+10516^31607127119Hans Havermann03/2021
4086(19*10^127118-97)/3127119Robert Price10/2021
4087(29*10^127111+691)/9127112Robert Price08/2021
4088736^44335+44335^736127104Norbert Schneider07/2019
408933040^7023+7023^33040127090Hans Havermann03/2021
4090(4*10^127081+167)/9127081Robert Price03/2022
409129748^18661+18661^29748127052Hans Havermann03/2021
4092-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
4093(78^67141-1)/77127036Paul Bourdelais09/2017
4094(14*10^127014-137)/3127015Robert Price04/2021
409531436^10965+10965^31436127002Hans Havermann03/2021
409628905^24758+24758^28905127001Hans Havermann03/2021
40972^421860-113285126993Enzo Doria07/2014
4098(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
4099(2^421827-7)/11126982Lelio R Paula05/2015
410011^121910-840126957Enzo Doria12/2012
4101(56*10^126935+187)/9126936Robert Price10/2021
410228915^24538+24538^28915126933Hans Havermann03/2021
4103(29*10^126928-77)/3126929Robert Price02/2020
4104(259*10^126919-1)/3126921Robert Price12/2020
410510^126919+204567126920Patrick De Geest05/2021
4106(2^421617+100280245065)126920Paul Bourdelais05/2022
410710^126919-100001126919Robert Price07/2020
410828340^28503+28503^28340126907Norbert Schneider02/2021
41092^421534-3001935126895Paul Bourdelais07/2023
4110(71^68539+1)/72126882Paul Bourdelais09/2017
4111(5*10^126871-119)/3126872Robert Price03/2018
4112331^50339-10004126846Enzo Doria07/2012
41132^421363-2790757126843Enzo Doria03/2016
4114(106*10^126839-1)/3126841Serge Batalov12/2014
411537938^2203+2203^37938126828Hans Havermann03/2021
4116(13*10^126819+77)/9126820Robert Price07/2022
4117(7*2^421243+1)/39126807Lelio R Paula05/2014
4119(14*10^126784-83)/3126785Robert Price12/2018
41182^421169-3001935126785Paul Bourdelais07/2023
41202^421161-286183126783Enzo Doria06/2015
4121(106*10^126726+17)/3126728Robert Price04/2021
412230718^13347+13347^30718126724Hans Havermann03/2021
41232^420939-113935126716Enzo Doria10/2014
412411*23^93048+356126708Eric Chen08/2023
4125177^56363-2126703Lelio R Paula10/2017
41262^420741-113659126656Enzo Doria08/2014
41272^420694-21126642Lelio R Paula05/2017
4128(13*10^126638+437)/9126639Robert Price04/2018
4129(167*10^126637-17)/3126639Robert Price03/2020
41304*10^126625+87126626Robert Price08/2018
4131(31*2^420556+1)/7126601Lelio R Paula05/2014
41327*10^126600-99126601Robert Price06/2019
41332^420424-59189126561Enzo Doria10/2015
413428717^25534+25534^28717126560Hans Havermann03/2021
4135(86*10^126542+103)/9126543Robert Price12/2021
413628922^23655+23655^28922126503Hans Havermann03/2021
41372^420126+71893126471Enzo Doria04/2016
4138(43*10^126441+47)/9126442Robert Price12/2018
41398*10^126408+71126409Robert Price05/2022
41402^419866+1877059126393Enzo Doria07/2016
414129315^20484+20484^29315126390Hans Havermann03/2021
414229433^19676+19676^29433126384Hans Havermann03/2021
4143F(604711)126377Henri Lifchitz02/2005
41442^419757+72707126360Enzo Doria04/2016
41452^419720-21569126349Enzo Doria07/2013
41462^419637+29126324Henri Lifchitz02/2006
414731004^11865+11865^31004126319Hans Havermann03/2021
41482^419612+1876741126316Enzo Doria07/2016
41492^419520+2793271126289Enzo Doria03/2016
4150(2^419447-5)/369126264Lelio R Paula05/2014
41512^419328-1859939126231Enzo Doria03/2016
41522^419282-1851507126217Enzo Doria08/2015
4153(133*10^126212+17)/3126214Robert Price11/2021
41542^419251+1866143126208Enzo Doria03/2016
415511^121185+2126202Robert Price05/2014
415628203^28352+28352^28203126175Norbert Schneider01/2021
4157(23*2^419036-1)/1393126141Lelio R Paula05/2014
41582^418851+23126087Robert Price09/2015
4159(2^418849-9)/2681126083Lelio R Paula05/2014
41602^418829+167126081Lelio R Paula01/2012
416131037^11530+11530^31037126067Hans Havermann03/2021
41624*10^126064-69126065Robert Price01/2022
4163(31*2^418782-1)/75891126063Lelio R Paula05/2014
4164(19*2^418754-1)/15126058Lelio R Paula05/2014
4165(35*10^126048-323)/9126049Robert Price10/2021
416633016^6551+6551^33016126000Hans Havermann03/2021
41672^418548-111546435125996Paul Bourdelais10/2021
416834736^4227+4227^34736125954Hans Havermann03/2021
41692^418319-109501125927Enzo Doria04/2014
41702^418316-112373125926Enzo Doria06/2014
417140398^1309+1309^40398125919Hans Havermann03/2021
4172(8*10^125894-29)/3125895Robert Price07/2018
4173(26*10^125886-413)/9125887Robert Price05/2018
417410^(2*62938+1)-7*10^62938-1125877Robert Price07/2023
417555*10^125847+9125849Robert Price03/2022
41764*10^125832+57125833Robert Price05/2022
41772^417968+1869811125821Enzo Doria06/2016
41782^417902+63125802Lelio R Paula09/2015
4179(10^125792-91)/9125792Serge Batalov12/2014
418030438^13573+13573^30438125791Hans Havermann03/2021
418132867^6714+6714^32867125782Hans Havermann03/2021
418231155^10892+10892^31155125777Hans Havermann03/2021
4183(35*10^125754-593)/9125755Robert Price07/2018
418430455^13464+13464^30455125754Hans Havermann03/2021
4185(32*10^125751-77)/9125752Robert Price06/2018
41862^417704+77011125742Enzo Doria05/2016
418729755^16816+16816^29755125737Hans Havermann03/2021
4188(22*10^125734+203)/9125735Robert Price10/2021
418929918^15915+15915^29918125710Hans Havermann03/2021
4190(10^125706+149)/3125706Serge Batalov12/2014
419128531^25368+25368^28531125659Hans Havermann03/2021
41922^417419-115309125656Enzo Doria07/2015
4193(46*10^125642+593)/9125643Robert Price04/2022
41942^417300+77281125620Enzo Doria05/2016
419530638^12537+12537^30638125561Hans Havermann03/2021
41962^417095-1657125559Yves Minet07/2014
419730162^14525+14525^30162125538Hans Havermann03/2021
4198(56*10^125535+583)/9125536Robert Price08/2021
4199(23*10^125517-179)/3125518Robert Price06/2022
42009*10^125516+29125517Robert Price03/2022
4201(88*10^125492-637)/9125493Robert Price11/2020
420228958^21525+21525^28958125474Hans Havermann02/2021
42042^416773-25125462Lelio R Paula09/2015
4203(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
420533889^5032+5032^33889125449Hans Havermann03/2021
4206(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
4207(11*2^416691+1)/43125436Lelio R Paula05/2014
4208(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
42092^416641-2*416641+1125422Robert Price05/2018
421033392^5697+5697^33392125409Hans Havermann03/2021
4211(21*2^416566-1)/17125399Lelio R Paula05/2014
42122^416530+1870429125389Enzo Doria05/2016
4213(56*10^125385+691)/9125386Robert Price05/2019
421427953^28198+28198^27953125381Norbert Schneider01/2021
421531074^10837+10837^31074125381Hans Havermann03/2021
421633745^5194+5194^33745125380Hans Havermann03/2021
42172^416490+1875109125376Enzo Doria09/2016
421828360^26331+26331^28360125365Hans Havermann03/2021
42192^416416-114929125354Enzo Doria05/2015
4220(77*10^125330-293)/9125331Robert Price09/2019
4221(172*10^125292-1)/9125294Serge Batalov12/2014
42222^416134+1865899125269Enzo Doria03/2016
4223153^57337-152125264Norbert Schneider12/2018
4224(599*10^125224+13)/9125226Robert Price02/2022
4225(9*2^415992+1)/13560845125220Lelio R Paula05/2014
422630054^14657+14657^30054125207Hans Havermann03/2021
4227(23^91943-1)/22125201Robert Price01/2012
42282^415884-933075125194Paul Bourdelais06/2021
422943125^27010-106125185Enzo Doria08/2012
4230(38*10^125166+349)/9125167Robert Price10/2018
423110^125166-5001125166Robert Price12/2021
42322^415765-112603125158Enzo Doria06/2014
42338*10^125088-13125089Robert Price08/2019
4234(25*10^125076-13)/3125077Robert Price09/2019
4235(11*10^125054+73)/3125055Robert Price08/2021
4236(29*10^125021-113)/3125022Robert Price10/2019
42372^415290-113591125015Enzo Doria08/2014
42382^415276-460919125011Enzo Doria06/2015
42392^415259+77243125006Enzo Doria05/2016
4240(67*10^124990+77)/9124991Robert Price10/2021
42412^415144-3683124971Yves Minet10/2011
42422^415092+111546435124956Paul Bourdelais10/2021
424331936^8173+8173^31936124946Hans Havermann03/2021
42445^178715-4124916Tyler NeSmith07/2021
424529767^15700+15700^29767124900Hans Havermann03/2021
42462^414874+79124890Lelio R Paula01/2015
4247(2^414765+7)/1389124854Lelio R Paula05/2014
42482^414618+79459124813Enzo Doria06/2016
4249(61*10^124809-1)/3124811Robert Price01/2020
4250(29*10^124765-71)/3124766Robert Price07/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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