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) !!!


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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 ?
525125021^20026+20026^25021107631Hans Havermann11/2020
52522^357521+1870217107625Enzo Doria05/2016
52532^357477-1203107612Lelio R Paula03/2017
525426008^13693+13693^26008107583Hans Havermann10/2020
525525432^16991+16991^25432107583Hans Havermann10/2020
5256(2^357371+3726)/2107580Stefano Morozzi09/2020
52575^153894-18107568Lelio R Paula02/2017
52582^357324-69059107566Enzo Doria11/2015
5259467^40296+40296^467107563Norbert Schneider03/2019
526029446^4495+4495^29446107559Hans Havermann10/2020
5261(8*10^107556-149)/3107557Robert Price12/2021
52622^357283-869688105107553Lelio R Paula01/2017
52632^357280-16805107552Enzo Doria05/2013
526410^107547+481719107548Patrick De Geest03/2017
526510^107547-47107547Lelio R Paula02/2017
5266(23*10^107540+37)/3107541Robert Price02/2022
526717^87396-32107537Lelio R Paula04/2017
5268(746*10^107505+1)/9107507Robert Price03/2020
5269(2^357125+1730)/2107506Stefano Morozzi09/2020
52702^357081+107107493Lelio R Paula12/2011
52712^357058-3911107486Yves Minet04/2017
52723^225274+64107484Lelio R Paula03/2017
52735*10^107482-57107483Robert Price03/2021
527418^85619-95107476Lelio R Paula04/2017
5275(2^357013+2526)/2107472Stefano Morozzi09/2020
52763^225248-130107471Lelio R Paula03/2017
5277(5*2^356961+1)/143107455Lelio R Paula03/2014
527827029^9448+9448^27029107450Hans Havermann11/2020
52792^356935-18085107449Enzo Doria05/2013
528055396^87+87^55396107442Hans Havermann10/2020
5281(14*10^107439-137)/3107440Robert Price04/2021
528210^107409+37107410Lelio R Paula02/2017
528310^107409-329633107409Patrick De Geest03/2017
5284(2^356799+3134)/2107407Stefano Morozzi09/2020
52852^356787-109027107404Enzo Doria04/2014
5286(2^356767+78557)/5107397Lelio R Paula12/2013
52873*10^107389+77107390Robert Price09/2018
52885^153622-42107378Lelio R Paula02/2017
52892^356699-97305107378Lelio R Paula03/2017
52902^356654+85107364Lelio R Paula11/2011
52912^356641-19921107360Enzo Doria06/2013
52925*10^107355+11107356Robert Price08/2019
52932^356623-465107355Lelio R Paula03/2017
529419^83945-92107345Lelio R Paula02/2017
529525491^16246+16246^25491107337Hans Havermann11/2020
529610^107334+28149107335Patrick De Geest03/2017
529710^107334-83107334Lelio R Paula02/2017
52982^356518+885107323Lelio R Paula03/2017
5299(59*10^107322+391)/9107323Robert Price03/2021
5300(3*2^356506-1)/467107317Lelio R Paula03/2014
5301(2^356468+1162)/2107308Stefano Morozzi09/2020
53022^356442-114713107300Enzo Doria04/2015
53032^356425+72257107295Enzo Doria04/2016
53042^356351-112237107273Enzo Doria06/2014
5306(6^137845-11)/5107264Paul Bourdelais11/2011
53052^356322+74539107264Enzo Doria04/2016
53072^356274+1874479107250Enzo Doria06/2016
530824606^22819+22819^24606107241Hans Havermann10/2020
5309(2^356243+3686)/2107240Stefano Morozzi09/2020
531020^82422-93107234Lelio R Paula02/2017
53112^356157-20365107214Enzo Doria06/2013
53128*10^107209+99107210Robert Price03/2021
53132^356129-18949107206Enzo Doria05/2013
53142^356100-109587107197Enzo Doria04/2014
53152*10^107173-37107174Robert Price11/2021
5316(2^355978+3262)/2107160Stefano Morozzi02/2021
5317(31*2^355970+1)/5107159Lelio R Paula03/2014
53182^355968-64875107158Lelio R Paula01/2017
53192^355952+1870321107153Enzo Doria05/2016
532027069^9088+9088^27069107152Hans Havermann11/2020
53212^355915-117107142Lelio R Paula11/2011
5322(16*10^107140+77)/3107141Robert Price03/2019
532324628^22369+22369^24628107124Hans Havermann11/2020
5324(19*2^355838-1)/15107119Lelio R Paula03/2014
53253^224495-8107112Lelio R Paula12/2013
53263*10^107096+23107097Robert Price03/2022
532725077^18632+18632^25077107086Hans Havermann10/2020
53287^126691-44107067Lelio R Paula03/2017
53294^177830-8243107065Mike Oakes02/2011
5330(509*10^107057+13)/9107059Robert Price05/2022
5331(2^355562+1702)/2107035Stefano Morozzi09/2020
533210^107028+3593037107029Paul Bourdelais10/2021
53332^355524-21237107024Enzo Doria06/2013
5335(10223*2^355515+1)/4855107022Lelio R Paula07/2014
533424843^20320+20320^24843107022Hans Havermann10/2020
53362^355494-19901107015Enzo Doria06/2013
53372^355454-869688105107003Lelio R Paula01/2017
53384*10^106997+13106998Robert Price02/2021
5339(8*10^106985-629)/9106985Robert Price01/2022
53402^355366+54615106976Lelio R Paula01/2017
5341(31*2^355346-1)/1563106969Lelio R Paula03/2014
53422^355275-19861106949Enzo Doria06/2013
534327503^7738+7738^27503106949Hans Havermann11/2020
5344(85*10^106943+77)/9106944Robert Price07/2022
5345(9179*2^355234-1)/1915106937Lelio R Paula05/2015
53464*10^106914-93106915Robert Price07/2020
53474*10^106892-3106893Robert Price10/2015
5348(66^58741+1)/67106881Paul Bourdelais08/2017
53492^354946-3106850M. Frind & P. Underwood08/2002
5350(2^354945+3134)/2106849Stefano Morozzi09/2020
53512^354873-18693106828Enzo Doria05/2013
5352(2^354831+3186)/2106815Stefano Morozzi09/2020
53542^354828+4257106814Lelio R Paula01/2017
535325216^17217+17217^25216106814Hans Havermann10/2020
5355(2^354799+1218)/2106805Stefano Morozzi09/2020
5356436^40459+40459^436106791Norbert Schneider03/2019
5357(21^80761+1)/22106783Paul Bourdelais03/2010
5358(115*10^106772-7)/9106774Robert Price02/2020
53592^354640-354640+1106758Robert Price10/2014
5360(2^354603+2606)/2106746Stefano Morozzi09/2020
53612^354585+95106741Lelio R Paula10/2011
5362(206*10^106737+1)/9106739Robert Price04/2022
53632^354553+189106732Lelio R Paula10/2011
5364(2^354546+1338)/2106729Stefano Morozzi02/2021
53652^354514-109031106720Enzo Doria04/2014
53662^354509-109465106718Enzo Doria04/2014
5367(15*2^354478-1)/26983106706Lelio R Paula03/2014
5368Phi(217618,10)/899798636917106693Makoto Kamada06/2019
536915^90710+28106684Lelio R Paula04/2017
53707^126237+34106683Lelio R Paula03/2017
53712^354385-115315106681Enzo Doria06/2015
53722^354327-19305106664Enzo Doria06/2013
5373(35*10^106649+1)/9106650Serge Batalov11/2010
537410^106636+97106637Lelio R Paula02/2017
537510^106636-22923106636Patrick De Geest03/2017
53762^354220-57106631Lelio R Paula10/2011
5377(68*10^106628-329)/9106629Robert Price03/2021
5378(29*10^106620-77)/3106621Robert Price02/2020
5379(746*10^106618+1)/9106620Robert Price03/2020
53802*10^106613+29106614Robert Price02/2021
53812^354157-17041106612Enzo Doria05/2013
538212^98778+73106600Lelio R Paula02/2017
538333333^1576+1576^33333106585Hans Havermann11/2020
53842^354064+1870651106584Enzo Doria05/2016
538524568^21779+21779^24568106577Hans Havermann11/2020
53862^353992-57106563Lelio R Paula10/2011
53879*10^106559+59106560Robert Price01/2020
53887*10^106553+27106554Robert Price11/2020
538928847^4938+4938^28847106548Hans Havermann10/2020
5390NSW(139160)106535Robert Price12/2018
5391(7*10^106516+113)/3106517Robert Price02/2018
53922^353832-1853849106515Enzo Doria09/2015
5393(7^126037-1)/6106513Paul Bourdelais09/2008
53942^353794-18453106503Enzo Doria05/2013
5395(2^353761+2094)/2106493Stefano Morozzi09/2020
53962^353728+7695106483Lelio R Paula01/2017
539726476^10509+10509^26476106475Hans Havermann10/2020
53982^353672-303106466Yves Minet02/2012
53996^136811+101106460Lelio R Paula02/2017
54002^353641+1871981106457Enzo Doria05/2016
5401(8*10^106454-29)/3106455Robert Price07/2018
540227845^6654+6654^27845106454Hans Havermann11/2020
540310^106449-700001106449Robert Price08/2021
540425316^16017+16017^25316106444Hans Havermann11/2020
54052^353553+54615106431Lelio R Paula01/2017
54062^353544-18897106428Enzo Doria05/2013
540728894^4823+4823^28894106426Hans Havermann11/2020
5408(19*10^106422+29)/3106423Robert Price12/2021
5409(694*10^106418+53)/9106420Robert Price02/2022
54106*10^106412-13106413Robert Price07/2022
541125696^13829+13829^25696106402Hans Havermann11/2020
54126^136729-133106396Lelio R Paula02/2017
54132^353418+1605106390Lelio R Paula01/2017
54142^353387+65106381Lelio R Paula10/2011
54152^353372+74311106376Enzo Doria04/2016
54162^353344-3693106368Yves Minet03/2017
5417(772*10^106365-7)/9106367Robert Price06/2022
5418(56*10^106351+619)/9106352Robert Price05/2021
54202^353277-20089106347Enzo Doria06/2013
54192^353275+72173106347Enzo Doria04/2016
54212^353268-17705106345Enzo Doria05/2013
54222^353267-19857106344Enzo Doria06/2013
5423(46*10^106343+143)/9106344Robert Price01/2019
5424(2^353189+3054)/2106321Stefano Morozzi09/2020
542535087^1072+1072^35087106321Hans Havermann10/2020
5426(2^353184+1290)/2106319Stefano Morozzi01/2021
542726985^8684+8684^26985106287Hans Havermann10/2020
5428(2^353051+606)/2106279Stefano Morozzi09/2020
5430222748^3+3^222748106278Anatoly F. Selevich12/2010
5429(46*10^106277+107)/9106278Robert Price06/2022
5431(9179*2^353019-1)/9106273Lelio R Paula05/2015
54322^353025+72257106272Enzo Doria04/2016
54352^352932-20345106244Enzo Doria06/2013
5433(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
543425628^13983+13983^25628106244Hans Havermann10/2020
54362^352883-187106229Lelio R Paula10/2011
543720^81649-19^81649106228Jean-Louis Charton03/2011
5438(55*10^106222+377)/9106223Robert Price02/2019
54392^352814-131106208Lelio R Paula10/2011
54402^352752+73951106189Enzo Doria04/2016
54416^136434+5106167Lelio R Paula11/2014
544225296^15737+15737^25296106166Hans Havermann09/2020
54438*10^106157-13106158Robert Price08/2019
54447*5^151872-8106155Lelio R Paula11/2014
5445105^52520-2106153Lelio R Paula10/2017
5446(23*10^106152-29)/3106153Robert Price03/2022
54472^352601-1604809106144Enzo Doria05/2015
544812^98353-43106141Lelio R Paula02/2017
54492^352585-18901106139Enzo Doria05/2013
545026363^10614+10614^26363106135Hans Havermann09/2020
5451(2^352554-3)/193106128Lelio R Paula12/2013
54522^352540+15015106126Lelio R Paula01/2017
545325068^17119+17119^25068106125Hans Havermann09/2020
54542^352524-3149106121Yves Minet10/2014
5455(7*10^106119-67)/3106120Robert Price10/2021
54562^352486-1858781106109Enzo Doria04/2016
54572^352444+12705106097Lelio R Paula01/2017
545828561^5182+5182^28561106090Hans Havermann10/2020
5459(182*10^106083+43)/9106085Robert Price02/2020
5460(266*10^106066+1)/3106068Robert Price04/2020
54612^352228-18953106032Enzo Doria05/2013
5462(2^352223+1118)/2106030Stefano Morozzi09/2020
5463(2^352212+2250)/2106027Stefano Morozzi01/2021
5464(2^352136+2638)/2106004Stefano Morozzi09/2020
54652^352107+1872533105995Enzo Doria05/2016
5466(2^352096+2086)/2105992Stefano Morozzi09/2020
54672^352066-2591105983Yves Minet07/2014
54682^352030+715105972Lelio R Paula10/2011
54699*6^136176-5105967Lelio R Paula11/2014
547017099*2^351991+58329105965Paul Vanderveen12/2017
547128582^5097+5097^28582105963Hans Havermann09/2020
5472155^48377+2105962Lelio R Paula08/2013
5473(23*10^105944-119)/3105945Robert Price07/2021
54742^351865+1869707105922Enzo Doria05/2016
547524974^17427+17427^24974105921Hans Havermann09/2020
547625163^16194+16194^25163105920Hans Havermann09/2020
54772^351831+23105912Lelio R Paula10/2011
5478(2^351818+3798)/2105908Stefano Morozzi02/2021
54799*2^351784-5105899Lelio R Paula09/2014
5480(2^351776+2766)/2105895Stefano Morozzi01/2021
5481(85*10^105881+203)/9105882Robert Price09/2020
54822^351671-112387105864Enzo Doria06/2014
54832^351669-109501105863Enzo Doria04/2014
54842^351644+74731105856Enzo Doria04/2016
548513^95025-42105853Lelio R Paula12/2016
54862^351599+15015105842Lelio R Paula01/2017
548719^82763+90105834Lelio R Paula01/2017
5488(205*10^105831-1)/3105833Robert Price11/2021
548926050^11551+11551^26050105832Hans Havermann09/2020
5490(9179*2^351540-1)/221105826Lelio R Paula05/2015
549120^81329-51105812Lelio R Paula01/2017
5492(5*10^105811+211)/9105811Robert Price02/2018
54932^351483+28425105807Lelio R Paula01/2017
549425231^15610+15610^25231105804Hans Havermann09/2020
549515^89960+86105802Lelio R Paula02/2017
54962^351460-17289105801Enzo Doria05/2013
549719^82735+22105798Lelio R Paula01/2017
54982^351435-109077105793Enzo Doria04/2014
54992^351393+1089105780Lelio R Paula01/2017
55002^351364+72631105772Enzo Doria04/2016


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

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