PRP Records

Probable Primes Top 10000

(290751 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 ?
500125368^19333+19333^25368108735Hans Havermann11/2020
5002(2^361195+3618)/2108731Stefano Morozzi09/2020
50032^361153-111546435108718Paul Bourdelais10/2021
500414^94849-61108710Lelio R Paula05/2017
500527267^9700+9700^27267108708Hans Havermann11/2020
5006(19^85009-5^85009)/14108705Robert Price07/2013
500724832^23853+23853^24832108704Hans Havermann11/2020
500827502^8963+8963^27502108701Hans Havermann11/2020
500925807^16278+16278^25807108689Hans Havermann11/2020
5010(11*2^361027+1)/40463108677Lelio R Paula03/2014
50112^360973+1299108664Lelio R Paula04/2017
50122^360959-109101108660Enzo Doria04/2014
50136*5^155454+7108659Lelio R Paula11/2014
501410^108656+79108657Lelio R Paula02/2017
501510^108656-50001108656Patrick De Geest03/2017
50162^360918-35108648Lelio R Paula01/2012
50174*10^108646-47108647Robert Price10/2021
5018(11*2^360886-1)/7108638Lelio R Paula03/2014
50193*10^108624-49108625Robert Price07/2018
5020(2^360831+666)/2108621Stefano Morozzi09/2020
5021(134*10^108610+7)/3108612Robert Price02/2020
50222*10^108609+29108610Robert Price02/2021
5023(10^108604+7)/71/191108600Alfred Reich06/2021
5024(2^360742+3222)/2108594Stefano Morozzi09/2020
50252^360706-458903108584Enzo Doria04/2015
502631112^3087+3087^31112108567Hans Havermann11/2020
50272^360641-113185108564Enzo Doria07/2014
5028(29*10^108559-71)/3108560Robert Price07/2021
50292^360618+75019108557Enzo Doria04/2016
50302^360607-216367108554Harrison Mesh06/2022
5031(14*10^108545-221)/9108546Robert Price04/2018
5032(44*10^108544-233)/9108545Robert Price01/2019
50333*5^155286+2108541Lelio R Paula11/2014
50347^128422+4108530Lelio R Paula11/2014
50357^128421-80108529Lelio R Paula03/2017
50362^360497+53807108521Yves Minet07/2010
50372^360468-4559108512Yves Minet03/2019
5038(2^360451+578)/2108507Stefano Morozzi09/2020
50392^360366+1459108481Lelio R Paula09/2011
50402^360364-1499108481Yves Minet05/2013
504125662^16871+16871^25662108477Hans Havermann10/2020
504225009^21748+21748^25009108475Hans Havermann10/2020
504314^94642-23108472Lelio R Paula05/2017
5044(197*10^108446-11)/3108448Robert Price03/2020
5045(2^360229+1290)/2108440Stefano Morozzi01/2021
50464*10^108412+9108413Robert Price05/2015
5047(259*10^108409-1)/3108411Robert Price12/2020
5048(2^360122+1194)/2108408Stefano Morozzi09/2020
5049133^51042-132108406Norbert Schneider02/2019
50502^360093-351103108399Enzo Doria06/2015
50512^360042+723108384Lelio R Paula01/2012
505285^56164-2108364Lelio R Paula10/2013
50532^359937-29323108352Enzo Doria07/2015
5054(2^359922+1762)/2108348Stefano Morozzi09/2020
5055(2^359903+758)/2108342Stefano Morozzi09/2020
50562^359898-19997108341Enzo Doria06/2013
5057(2^359886+2122)/2108337Stefano Morozzi09/2020
50582*5^154948-7108305Lelio R Paula11/2014
505910^108303+13108304Lelio R Paula02/2017
506010^108303-207959108303Patrick De Geest03/2017
50617*10^108300+69108301Robert Price07/2019
50622^359730+753108290Lelio R Paula12/2011
5063(8*10^108273+13)/3108274Robert Price06/2018
50642^359650-19797108266Enzo Doria06/2013
5065(47*10^108261+259)/9108262Robert Price03/2022
506691^55259-90^55259108255Robert Price07/2015
506710^108251+85749108252Patrick De Geest02/2021
506810^108251-50000000001108251Robert Price12/2020
506910^108251-252081108251Patrick De Geest02/2021
50704*10^108238-71108239Robert Price12/2018
50713^226845+68108233Lelio R Paula03/2017
507231836^2509+2509^31836108227Hans Havermann10/2020
50735^154822-12866108216Enzo Doria05/2014
5074(9*2^359480+1)/5108215Lelio R Paula03/2014
50752^359454-177108207Lelio R Paula12/2011
5076(19*10^108184+191)/3108185Robert Price05/2019
50776^139022-59108181Lelio R Paula02/2017
5078(19*10^108176-43)/3108177Robert Price05/2019
50792^359352-179108176Lelio R Paula12/2011
50802^359338-1858781108172Enzo Doria04/2016
508112^100230-97108167Lelio R Paula03/2017
508227028^10043+10043^27028108163Hans Havermann11/2020
5083(25*2^359297-1)/137108159Lelio R Paula03/2014
5084(2^359262-509203)/9108148Lelio R Paula12/2013
508526583^11702+11702^26583108147Hans Havermann11/2020
5086(3^226648-8)/352715633108131Lelio R Paula12/2013
50876^138956-59108129Lelio R Paula02/2017
50882^359184+30285108126Lelio R Paula04/2017
508913^97059+10108119Lelio R Paula03/2017
50902^359137-81108112Lelio R Paula12/2011
5092(15185*2^359105-1)/567108103Lelio R Paula05/2015
50912^359110-11655108103Lelio R Paula04/2017
50932^359069-933075108091Paul Bourdelais06/2021
509426227^13222+13222^26227108090Hans Havermann10/2020
50958*6^138875+5108067Lelio R Paula11/2014
50962^358987-216919108066Enzo Doria05/2014
5097(2^358977+2714)/2108063Stefano Morozzi09/2020
509839^67918-67918^39108062Norbert Schneider02/2017
509924^78283-1*78283^24108048Dylan Delgado12/2019
510025282^18767+18767^25282108040Hans Havermann11/2020
51012^358785-16933108006Enzo Doria05/2013
5102(2^358783+5)/33383108000Lelio R Paula12/2013
51036^138770-77107985Lelio R Paula02/2017
5104(2^358727-1017)/94178479107980Lelio R Paula12/2013
510510^107976+19107977Lelio R Paula02/2017
510610^107976-202103107976Patrick De Geest03/2017
51072^358684+75781107975Enzo Doria04/2016
510824928^21411+21411^24928107955Hans Havermann10/2020
510999^54094+2107952Lelio R Paula06/2013
5110(2^358583-9)/391107942Lelio R Paula12/2013
5111(2^358562+838)/2107938Stefano Morozzi02/2021
51122^358538+55107931Lelio R Paula12/2011
51132^358517-109009107925Enzo Doria03/2014
511426395^12258+12258^26395107914Hans Havermann10/2020
51153^226159+104107906Lelio R Paula03/2017
51162^358310-11655107863Lelio R Paula03/2017
5117(68*10^107852-329)/9107853Robert Price03/2021
51182^358275-112987107852Enzo Doria07/2014
51193^226038+4107848Tyler NeSmith01/2021
51202^358233-20005107839Enzo Doria06/2013
51212^358194+175107828Lelio R Paula12/2011
5122107^53125-106107812Norbert Schneider12/2016
5123(25*10^107804+161)/3107805Robert Price09/2019
51243^225922-2107793Lelio R Paula10/2013
512512^99874-95107783Lelio R Paula03/2017
5126(2^358042+3042)/2107782Stefano Morozzi09/2020
51272^358030-171107778Lelio R Paula12/2011
512811^103488-4170107772Enzo Doria12/2012
51292^357930-4547107748Yves Minet03/2019
51302^357911-20089107742Enzo Doria06/2013
51312^357885+12857107735Yves Minet07/2010
5132(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
51337^127473+40107728Lelio R Paula03/2017
51345*2^357850+9107725Lelio R Paula09/2014
51352^357786-291191107705Enzo Doria06/2015
513628907^5320+5320^28907107705Hans Havermann10/2020
513718^85798-23107700Lelio R Paula04/2017
51383*10^107697+61107698Robert Price09/2020
5139(14*10^107694-83)/3107695Robert Price12/2018
51402^357688-1854269107675Enzo Doria09/2015
51412^357671-112225107670Enzo Doria06/2014
514234323^1370+1370^34323107662Hans Havermann11/2020
51432^357618-21005107654Enzo Doria06/2013
51442^357615-17505107653Enzo Doria05/2013
514526350^12171+12171^26350107649Hans Havermann11/2020
5146(30^72871-1)/29107638Robert Price12/2011
514725021^20026+20026^25021107631Hans Havermann11/2020
51482^357521+1870217107625Enzo Doria05/2016
51492^357477-1203107612Lelio R Paula03/2017
515026008^13693+13693^26008107583Hans Havermann10/2020
515125432^16991+16991^25432107583Hans Havermann10/2020
5152(2^357371+3726)/2107580Stefano Morozzi09/2020
51535^153894-18107568Lelio R Paula02/2017
51542^357324-69059107566Enzo Doria11/2015
5155467^40296+40296^467107563Norbert Schneider03/2019
515629446^4495+4495^29446107559Hans Havermann10/2020
5157(8*10^107556-149)/3107557Robert Price12/2021
51582^357283-869688105107553Lelio R Paula01/2017
51592^357280-16805107552Enzo Doria05/2013
516010^107547+481719107548Patrick De Geest03/2017
516110^107547-47107547Lelio R Paula02/2017
5162(23*10^107540+37)/3107541Robert Price02/2022
516317^87396-32107537Lelio R Paula04/2017
5164(746*10^107505+1)/9107507Robert Price03/2020
5165(2^357125+1730)/2107506Stefano Morozzi09/2020
51662^357081+107107493Lelio R Paula12/2011
51672^357058-3911107486Yves Minet04/2017
51683^225274+64107484Lelio R Paula03/2017
51695*10^107482-57107483Robert Price03/2021
517018^85619-95107476Lelio R Paula04/2017
5171(2^357013+2526)/2107472Stefano Morozzi09/2020
51723^225248-130107471Lelio R Paula03/2017
5173(5*2^356961+1)/143107455Lelio R Paula03/2014
517427029^9448+9448^27029107450Hans Havermann11/2020
51752^356935-18085107449Enzo Doria05/2013
517655396^87+87^55396107442Hans Havermann10/2020
5177(14*10^107439-137)/3107440Robert Price04/2021
517810^107409+37107410Lelio R Paula02/2017
517910^107409-329633107409Patrick De Geest03/2017
5180(2^356799+3134)/2107407Stefano Morozzi09/2020
51812^356787-109027107404Enzo Doria04/2014
5182(2^356767+78557)/5107397Lelio R Paula12/2013
51833*10^107389+77107390Robert Price09/2018
51845^153622-42107378Lelio R Paula02/2017
51852^356699-97305107378Lelio R Paula03/2017
51862^356654+85107364Lelio R Paula11/2011
51872^356641-19921107360Enzo Doria06/2013
51885*10^107355+11107356Robert Price08/2019
51892^356623-465107355Lelio R Paula03/2017
519019^83945-92107345Lelio R Paula02/2017
519125491^16246+16246^25491107337Hans Havermann11/2020
519210^107334+28149107335Patrick De Geest03/2017
519310^107334-83107334Lelio R Paula02/2017
51942^356518+885107323Lelio R Paula03/2017
5195(59*10^107322+391)/9107323Robert Price03/2021
5196(3*2^356506-1)/467107317Lelio R Paula03/2014
5197(2^356468+1162)/2107308Stefano Morozzi09/2020
51982^356442-114713107300Enzo Doria04/2015
51992^356425+72257107295Enzo Doria04/2016
52002^356351-112237107273Enzo Doria06/2014
5202(6^137845-11)/5107264Paul Bourdelais11/2011
52012^356322+74539107264Enzo Doria04/2016
52032^356274+1874479107250Enzo Doria06/2016
520424606^22819+22819^24606107241Hans Havermann10/2020
5205(2^356243+3686)/2107240Stefano Morozzi09/2020
520620^82422-93107234Lelio R Paula02/2017
52072^356157-20365107214Enzo Doria06/2013
52088*10^107209+99107210Robert Price03/2021
52092^356129-18949107206Enzo Doria05/2013
52102^356100-109587107197Enzo Doria04/2014
52112*10^107173-37107174Robert Price11/2021
5212(2^355978+3262)/2107160Stefano Morozzi02/2021
5213(31*2^355970+1)/5107159Lelio R Paula03/2014
52142^355968-64875107158Lelio R Paula01/2017
52152^355952+1870321107153Enzo Doria05/2016
521627069^9088+9088^27069107152Hans Havermann11/2020
52172^355915-117107142Lelio R Paula11/2011
5218(16*10^107140+77)/3107141Robert Price03/2019
521924628^22369+22369^24628107124Hans Havermann11/2020
5220(19*2^355838-1)/15107119Lelio R Paula03/2014
52213^224495-8107112Lelio R Paula12/2013
52223*10^107096+23107097Robert Price03/2022
522325077^18632+18632^25077107086Hans Havermann10/2020
52247^126691-44107067Lelio R Paula03/2017
52254^177830-8243107065Mike Oakes02/2011
5226(509*10^107057+13)/9107059Robert Price05/2022
5227(2^355562+1702)/2107035Stefano Morozzi09/2020
522810^107028+3593037107029Paul Bourdelais10/2021
52292^355524-21237107024Enzo Doria06/2013
5231(10223*2^355515+1)/4855107022Lelio R Paula07/2014
523024843^20320+20320^24843107022Hans Havermann10/2020
52322^355494-19901107015Enzo Doria06/2013
52332^355454-869688105107003Lelio R Paula01/2017
52344*10^106997+13106998Robert Price02/2021
5235(8*10^106985-629)/9106985Robert Price01/2022
52362^355366+54615106976Lelio R Paula01/2017
5237(31*2^355346-1)/1563106969Lelio R Paula03/2014
52382^355275-19861106949Enzo Doria06/2013
523927503^7738+7738^27503106949Hans Havermann11/2020
5240(9179*2^355234-1)/1915106937Lelio R Paula05/2015
52414*10^106914-93106915Robert Price07/2020
52424*10^106892-3106893Robert Price10/2015
5243(66^58741+1)/67106881Paul Bourdelais08/2017
52442^354946-3106850M. Frind & P. Underwood08/2002
5245(2^354945+3134)/2106849Stefano Morozzi09/2020
52462^354873-18693106828Enzo Doria05/2013
5247(2^354831+3186)/2106815Stefano Morozzi09/2020
52492^354828+4257106814Lelio R Paula01/2017
524825216^17217+17217^25216106814Hans Havermann10/2020
5250(2^354799+1218)/2106805Stefano Morozzi09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

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