PRP Records

Probable Primes Top 10000

(294627 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 ?
4501(97*10^127858-1)/3127860Serge Batalov12/2014
450228929^26258+26258^28929127845Hans Havermann03/2021
450330563^15220+15220^30563127828Hans Havermann03/2021
45042^424632-2786639127827Enzo Doria03/2016
450510^127821-700001127821Robert Price08/2021
45062^424577-113755127811Enzo Doria09/2014
4507(7*2^424512-1)/3127792Lelio R Paula05/2014
4508(56*10^127752+691)/9127753Robert Price05/2019
450911^122629-720127705Enzo Doria11/2012
451022*10^127645+3127647Robert Price01/2020
451128715^27844+27844^28715127631Hans Havermann03/2021
4512(56*10^127612+187)/9127613Robert Price10/2021
4513(5*36^81995+821)/7127609Eric Chen01/2021
45144*10^127562-39127563Robert Price09/2020
451532595^8186+8186^32595127547Hans Havermann03/2021
45162^423696-21429127546Enzo Doria07/2013
45172^423664-1864559127536Enzo Doria03/2016
451837889^2322+2322^37889127530Hans Havermann03/2021
451937668^2429+2429^37668127523Hans Havermann03/2021
45203^267267-4127519Henri Lifchitz10/2014
4521fibonacci(610144)-2127513Jon Grantham08/2023
4522(103*10^127491+17)/3127493Robert Price08/2020
452329376^21869+21869^29376127487Hans Havermann03/2021
452431186^12241+12241^31186127483Hans Havermann02/2021
4525(19^99689+5^99689)/24127477Robert Price09/2013
452627069^28754-28754^27069127452Frank Doornink01/2024
4527(21*2^423372+1)/101127447Lelio R Paula05/2014
452830594^14645+14645^30594127446Hans Havermann03/2021
45292^423328-21537127435Enzo Doria07/2013
4530(67*10^127413-7)/3127415Robert Price01/2020
4531(5*34^83193+700233)/11127408Eric Chen08/2023
4532(2*10^127407+73)/3127407Robert Price09/2020
4533(2^423165-7)/25127384Lelio R Paula05/2015
4534(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
4535(4*10^127349+17)/3127350Tyler Busby01/2023
453629512^20647+20647^29512127341Hans Havermann03/2021
45372^422987-3001935127332Paul Bourdelais07/2023
4538(112*10^127324+17)/3127326Robert Price03/2020
453929565^20252+20252^29565127321Hans Havermann03/2021
4540fibonacci(609165)-3127308Jon Grantham08/2023
4542(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
4541(5^182099-3^182099)/2127282Kellen Shenton05/2022
4543(16*10^127259+197)/3127260Robert Price04/2019
4544(26*10^127240+61)/3127241Robert Price10/2019
4545(234483*27^88884-145)/26127230Curtis Bright05/2015
45462^422515-114997127190Enzo Doria06/2015
45475*10^127179-3127180Robert Price07/2015
454831678^10343+10343^31678127176Hans Havermann03/2021
4549(44*10^127169-233)/9127170Robert Price01/2019
455034947^4352+4352^34947127162Hans Havermann03/2021
45516*10^127158+19127159Robert Price11/2021
455230469^14902+14902^30469127155Hans Havermann03/2021
45535*10^127153+77127154Robert Price12/2018
455429941^17620+17620^29941127130Hans Havermann02/2021
455531607^10516+10516^31607127119Hans Havermann03/2021
4556(19*10^127118-97)/3127119Robert Price10/2021
4557(29*10^127111+691)/9127112Robert Price08/2021
4558736^44335+44335^736127104Norbert Schneider07/2019
455933040^7023+7023^33040127090Hans Havermann03/2021
4560(4*10^127081+167)/9127081Robert Price03/2022
456129748^18661+18661^29748127052Hans Havermann03/2021
4562-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
4563(78^67141-1)/77127036Paul Bourdelais09/2017
4564(14*10^127014-137)/3127015Robert Price04/2021
456531436^10965+10965^31436127002Hans Havermann03/2021
456628905^24758+24758^28905127001Hans Havermann03/2021
45672^421860-113285126993Enzo Doria07/2014
4568(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
4569(2^421827-7)/11126982Lelio R Paula05/2015
457011^121910-840126957Enzo Doria12/2012
4571(56*10^126935+187)/9126936Robert Price10/2021
457228915^24538+24538^28915126933Hans Havermann03/2021
4573(29*10^126928-77)/3126929Robert Price02/2020
4574(259*10^126919-1)/3126921Robert Price12/2020
457510^126919+204567126920Patrick De Geest05/2021
4576(2^421617+100280245065)126920Paul Bourdelais05/2022
457710^126919-100001126919Robert Price07/2020
457828340^28503+28503^28340126907Norbert Schneider02/2021
45792^421534-3001935126895Paul Bourdelais07/2023
4580(71^68539+1)/72126882Paul Bourdelais09/2017
4581(5*10^126871-119)/3126872Robert Price03/2018
4582331^50339-10004126846Enzo Doria07/2012
45832^421363-2790757126843Enzo Doria03/2016
4584(106*10^126839-1)/3126841Serge Batalov12/2014
458537938^2203+2203^37938126828Hans Havermann03/2021
4586(13*10^126819+77)/9126820Robert Price07/2022
4587(7*2^421243+1)/39126807Lelio R Paula05/2014
4589(14*10^126784-83)/3126785Robert Price12/2018
45882^421169-3001935126785Paul Bourdelais07/2023
45902^421161-286183126783Enzo Doria06/2015
4591(106*10^126726+17)/3126728Robert Price04/2021
459230718^13347+13347^30718126724Hans Havermann03/2021
45932^420939-113935126716Enzo Doria10/2014
459411*23^93048+356126708Eric Chen08/2023
4595177^56363-2126703Lelio R Paula10/2017
45962^420741-113659126656Enzo Doria08/2014
45972^420694-21126642Lelio R Paula05/2017
4598(13*10^126638+437)/9126639Robert Price04/2018
4599(167*10^126637-17)/3126639Robert Price03/2020
46004*10^126625+87126626Robert Price08/2018
4601(31*2^420556+1)/7126601Lelio R Paula05/2014
46027*10^126600-99126601Robert Price06/2019
46032^420424-59189126561Enzo Doria10/2015
460428717^25534+25534^28717126560Hans Havermann03/2021
4605(86*10^126542+103)/9126543Robert Price12/2021
4606(19*10^126517-7)/3126518Robert Price12/2023
460728922^23655+23655^28922126503Hans Havermann03/2021
46082^420126+71893126471Enzo Doria04/2016
4609(43*10^126441+47)/9126442Robert Price12/2018
46108*10^126408+71126409Robert Price05/2022
46112^419866+1877059126393Enzo Doria07/2016
461229315^20484+20484^29315126390Hans Havermann03/2021
461329433^19676+19676^29433126384Hans Havermann03/2021
4614F(604711)126377Henri Lifchitz02/2005
46152^419757+72707126360Enzo Doria04/2016
46162^419720-21569126349Enzo Doria07/2013
46172^419637+29126324Henri Lifchitz02/2006
461831004^11865+11865^31004126319Hans Havermann03/2021
46192^419612+1876741126316Enzo Doria07/2016
46202^419520+2793271126289Enzo Doria03/2016
4621(2^419447-5)/369126264Lelio R Paula05/2014
46222^419328-1859939126231Enzo Doria03/2016
46232^419282-1851507126217Enzo Doria08/2015
4624(133*10^126212+17)/3126214Robert Price11/2021
46252^419251+1866143126208Enzo Doria03/2016
462611^121185+2126202Robert Price05/2014
462728203^28352+28352^28203126175Norbert Schneider01/2021
4628(23*2^419036-1)/1393126141Lelio R Paula05/2014
46292^418851+23126087Robert Price09/2015
4630(2^418849-9)/2681126083Lelio R Paula05/2014
46312^418829+167126081Lelio R Paula01/2012
463231037^11530+11530^31037126067Hans Havermann03/2021
46334*10^126064-69126065Robert Price01/2022
4634(31*2^418782-1)/75891126063Lelio R Paula05/2014
4635(19*2^418754-1)/15126058Lelio R Paula05/2014
4636(35*10^126048-323)/9126049Robert Price10/2021
463733016^6551+6551^33016126000Hans Havermann03/2021
46382^418548-111546435125996Paul Bourdelais10/2021
463925134^28625-28625^25134125958Frank Doornink12/2023
464034736^4227+4227^34736125954Hans Havermann03/2021
46412^418319-109501125927Enzo Doria04/2014
46422^418316-112373125926Enzo Doria06/2014
464340398^1309+1309^40398125919Hans Havermann03/2021
4644(8*10^125894-29)/3125895Robert Price07/2018
4645(26*10^125886-413)/9125887Robert Price05/2018
464610^(2*62938+1)-7*10^62938-1125877Robert Price07/2023
464755*10^125847+9125849Robert Price03/2022
46484*10^125832+57125833Robert Price05/2022
46492^417968+1869811125821Enzo Doria06/2016
46502^417902+63125802Lelio R Paula09/2015
4651(10^125792-91)/9125792Serge Batalov12/2014
465230438^13573+13573^30438125791Hans Havermann03/2021
465332867^6714+6714^32867125782Hans Havermann03/2021
465431155^10892+10892^31155125777Hans Havermann03/2021
4655(35*10^125754-593)/9125755Robert Price07/2018
465630455^13464+13464^30455125754Hans Havermann03/2021
4657(32*10^125751-77)/9125752Robert Price06/2018
46582^417704+77011125742Enzo Doria05/2016
465929755^16816+16816^29755125737Hans Havermann03/2021
4660(22*10^125734+203)/9125735Robert Price10/2021
466129918^15915+15915^29918125710Hans Havermann03/2021
4662(10^125706+149)/3125706Serge Batalov12/2014
466328531^25368+25368^28531125659Hans Havermann03/2021
46642^417419-115309125656Enzo Doria07/2015
4665(46*10^125642+593)/9125643Robert Price04/2022
46662^417315+213953125625Enzo Doria10/2023
46672^417300+77281125620Enzo Doria05/2016
466830638^12537+12537^30638125561Hans Havermann03/2021
46692^417095-1657125559Yves Minet07/2014
467030162^14525+14525^30162125538Hans Havermann03/2021
4671(56*10^125535+583)/9125536Robert Price08/2021
4672(23*10^125517-179)/3125518Robert Price06/2022
46739*10^125516+29125517Robert Price03/2022
4674(88*10^125492-637)/9125493Robert Price11/2020
467528958^21525+21525^28958125474Hans Havermann02/2021
46772^416773-25125462Lelio R Paula09/2015
4676(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
467833889^5032+5032^33889125449Hans Havermann03/2021
4679(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
4680(2861^36481+1)/(2861^191+1)125438Martin Hopf12/2023
4681(11*2^416691+1)/43125436Lelio R Paula05/2014
4682(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
46832^416641-2*416641+1125422Robert Price05/2018
468433392^5697+5697^33392125409Hans Havermann03/2021
4685(21*2^416566-1)/17125399Lelio R Paula05/2014
46862^416530+1870429125389Enzo Doria05/2016
4687(56*10^125385+691)/9125386Robert Price05/2019
468827953^28198+28198^27953125381Norbert Schneider01/2021
468931074^10837+10837^31074125381Hans Havermann03/2021
469033745^5194+5194^33745125380Hans Havermann03/2021
46912^416490+1875109125376Enzo Doria09/2016
469228360^26331+26331^28360125365Hans Havermann03/2021
46932^416416-114929125354Enzo Doria05/2015
4694(77*10^125330-293)/9125331Robert Price09/2019
4695(172*10^125292-1)/9125294Serge Batalov12/2014
46962^416134+1865899125269Enzo Doria03/2016
4697153^57337-152125264Norbert Schneider12/2018
4698(599*10^125224+13)/9125226Robert Price02/2022
4699(9*2^415992+1)/13560845125220Lelio R Paula05/2014
470030054^14657+14657^30054125207Hans Havermann03/2021
4701(23^91943-1)/22125201Robert Price01/2012
47022^415884-933075125194Paul Bourdelais06/2021
470343125^27010-106125185Enzo Doria08/2012
4704(38*10^125166+349)/9125167Robert Price10/2018
470510^125166-5001125166Robert Price12/2021
47062^415765-112603125158Enzo Doria06/2014
47078*10^125088-13125089Robert Price08/2019
4708(25*10^125076-13)/3125077Robert Price09/2019
4709(11*10^125054+73)/3125055Robert Price08/2021
4710(29*10^125021-113)/3125022Robert Price10/2019
47112^415290-113591125015Enzo Doria08/2014
47122^415276-460919125011Enzo Doria06/2015
47132^415259+77243125006Enzo Doria05/2016
4714(67*10^124990+77)/9124991Robert Price10/2021
47152^415144-3683124971Yves Minet10/2011
47162^415092+111546435124956Paul Bourdelais10/2021
471731936^8173+8173^31936124946Hans Havermann03/2021
47185^178715-4124916Tyler NeSmith07/2021
471929767^15700+15700^29767124900Hans Havermann03/2021
47202^414874+79124890Lelio R Paula01/2015
472125292^28361-28361^25292124874Frank Doornink01/2024
4722(2^414765+7)/1389124854Lelio R Paula05/2014
47232^414618+79459124813Enzo Doria06/2016
4724(61*10^124809-1)/3124811Robert Price01/2020
4725(29*10^124765-71)/3124766Robert Price07/2021
47262^414432-1846709124757Enzo Doria07/2015
47272*10^124751-51124752Robert Price04/2018
4728(56*10^124735+367)/9124736Robert Price06/2019
4729(13*2^414274-1)/153124708Lelio R Paula05/2014
4730(23*10^124690+37)/3124691Robert Price02/2022
473156*10^124656-3124658Robert Price03/2020
4732(7*10^124648+197)/3124649Robert Price07/2018
47342^414032-5124637Henri Lifchitz07/2006
47332^414032+1872331124637Enzo Doria05/2016
473537373^2158+2158^37373124604Hans Havermann03/2021
473629811^15112+15112^29811124590Hans Havermann03/2021
47372^413781-2023124561Riley Fisher09/2023
473814120^30009-30009^14120124533Norbert Schneider02/2015
473929757^15296+15296^29757124521Hans Havermann03/2021
474035056^3561+3561^35056124504Hans Havermann03/2021
474140588^1167+1167^40588124487Hans Havermann02/2021
4742(85*10^124485-49)/9124486Robert Price12/2020
474364^68909-63^68909124463Robert Price07/2013
474435016^3581+3581^35016124448Hans Havermann03/2021
47452^413387+76253124442Enzo Doria04/2016
474628749^21298+21298^28749124436Hans Havermann03/2021
47472^413352+524287124432Paul Underwood09/2018
4748287117#+391613124424Nicolas PALAU01/2017
4749(4*10^124420+83)/3124421Robert Price02/2018
475034578^3965+3965^34578124421Hans Havermann03/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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