PRP Records

Probable Primes Top 10000

(301723 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 ?
72512^360706-458903108584Enzo Doria04/2015
725231112^3087+3087^31112108567Hans Havermann11/2020
72532^360641-113185108564Enzo Doria07/2014
7254(29*10^108559-71)/3108560Robert Price07/2021
72562^360618+75019108557Enzo Doria04/2016
72552^360618+2025108557Henri Lifchitz01/2025
72572^360607-216367108554Harrison Mesh06/2022
725829^74228+556108551Eric Chen06/2025
7259(14*10^108545-221)/9108546Robert Price04/2018
7260(44*10^108544-233)/9108545Robert Price01/2019
72613*5^155286+2108541Lelio R Paula11/2014
72627^128422+4108530Lelio R Paula11/2014
72637^128421-80108529Lelio R Paula03/2017
72642^360497+53807108521Yves Minet07/2010
72652^360468-4559108512Yves Minet03/2019
7266(2^360451+578)/2108507Stefano Morozzi09/2020
72672^360366+1459108481Lelio R Paula09/2011
72682^360364-1499108481Yves Minet05/2013
726925662^16871+16871^25662108477Hans Havermann10/2020
727025009^21748+21748^25009108475Hans Havermann10/2020
727114^94642-23108472Lelio R Paula05/2017
7272(197*10^108446-11)/3108448Robert Price03/2020
7273(2^360229+1290)/2108440Stefano Morozzi01/2021
72744*10^108412+9108413Robert Price05/2015
7275(259*10^108409-1)/3108411Robert Price12/2020
7276(2^360122+1194)/2108408Stefano Morozzi09/2020
7277133^51042-132108406Norbert Schneider02/2019
72782^360093-351103108399Enzo Doria06/2015
72792^360042+723108384Lelio R Paula01/2012
728085^56164-2108364Lelio R Paula10/2013
72812^359937-29323108352Enzo Doria07/2015
728222^80712-23108350Anonymous09/2024
7283(2^359922+1762)/2108348Stefano Morozzi09/2020
7284(2^359903+758)/2108342Stefano Morozzi09/2020
72852^359898-19997108341Enzo Doria06/2013
7286(2^359886+2122)/2108337Stefano Morozzi09/2020
72872*5^154948-7108305Lelio R Paula11/2014
728810^108303+13108304Lelio R Paula02/2017
728910^108303-207959108303Patrick De Geest03/2017
72907*10^108300+69108301Robert Price07/2019
7291198^47155-47155^198108300Norman Luhn09/2024
72922^359730+753108290Lelio R Paula12/2011
7293(8*10^108273+13)/3108274Robert Price06/2018
72942^359650-19797108266Enzo Doria06/2013
7295(47*10^108261+259)/9108262Robert Price03/2022
729691^55259-90^55259108255Robert Price07/2015
729710^108251+85749108252Patrick De Geest02/2021
729810^108251-50000000001108251Robert Price12/2020
729910^108251-252081108251Patrick De Geest02/2021
73004*10^108238-71108239Robert Price12/2018
73013^226845+68108233Lelio R Paula03/2017
730231836^2509+2509^31836108227Hans Havermann10/2020
73035^154822-12866108216Enzo Doria05/2014
7304(9*2^359480+1)/5108215Lelio R Paula03/2014
73052^359454-177108207Lelio R Paula12/2011
7306(19*10^108184+191)/3108185Robert Price05/2019
73076^139022-59108181Lelio R Paula02/2017
7308(19*10^108176-43)/3108177Robert Price05/2019
73092^359352-179108176Lelio R Paula12/2011
73102^359338-1858781108172Enzo Doria04/2016
731112^100230-97108167Lelio R Paula03/2017
731227028^10043+10043^27028108163Hans Havermann11/2020
7313(25*2^359297-1)/137108159Lelio R Paula03/2014
7314(2^359262-509203)/9108148Lelio R Paula12/2013
731526583^11702+11702^26583108147Hans Havermann11/2020
7316(3^226648-8)/352715633108131Lelio R Paula12/2013
73176^138956-59108129Lelio R Paula02/2017
73182^359184+30285108126Lelio R Paula04/2017
731913^97059+10108119Lelio R Paula03/2017
73202^359137-81108112Lelio R Paula12/2011
7322(15185*2^359105-1)/567108103Lelio R Paula05/2015
73212^359110-11655108103Lelio R Paula04/2017
73232^359069-933075108091Paul Bourdelais06/2021
732426227^13222+13222^26227108090Hans Havermann10/2020
73258*6^138875+5108067Lelio R Paula11/2014
73262^358987-216919108066Enzo Doria05/2014
7327(2^358977+2714)/2108063Stefano Morozzi09/2020
732839^67918-67918^39108062Norbert Schneider02/2017
732924^78283-1*78283^24108048Dylan Delgado12/2019
733025282^18767+18767^25282108040Hans Havermann11/2020
73312^358785-16933108006Enzo Doria05/2013
7332(2^358783+5)/33383108000Lelio R Paula12/2013
73336^138770-77107985Lelio R Paula02/2017
7334(2^358727-1017)/94178479107980Lelio R Paula12/2013
733510^107976+19107977Lelio R Paula02/2017
733610^107976-202103107976Patrick De Geest03/2017
73372^358684+75781107975Enzo Doria04/2016
733824928^21411+21411^24928107955Hans Havermann10/2020
733999^54094+2107952Lelio R Paula06/2013
7340(2^358583-9)/391107942Lelio R Paula12/2013
7341(2^358562+838)/2107938Stefano Morozzi02/2021
73422^358538+55107931Lelio R Paula12/2011
73432^358517-109009107925Enzo Doria03/2014
734426395^12258+12258^26395107914Hans Havermann10/2020
73453^226159+104107906Lelio R Paula03/2017
73467*10^107870+39107871Robert Price01/2023
73472^358310-11655107863Lelio R Paula03/2017
7348(68*10^107852-329)/9107853Robert Price03/2021
73492^358275-112987107852Enzo Doria07/2014
73503^226038+4107848Tyler NeSmith01/2021
73512^358233-20005107839Enzo Doria06/2013
73522^358194+175107828Lelio R Paula12/2011
7353107^53125-106107812Norbert Schneider12/2016
7354(25*10^107804+161)/3107805Robert Price09/2019
73553^225922-2107793Lelio R Paula10/2013
735612^99874-95107783Lelio R Paula03/2017
7357(2^358042+3042)/2107782Stefano Morozzi09/2020
73582^358030-171107778Lelio R Paula12/2011
735911^103488-4170107772Enzo Doria12/2012
73602^357930-4547107748Yves Minet03/2019
73612^357911-20089107742Enzo Doria06/2013
73622^357885+12857107735Yves Minet07/2010
7363(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
73647^127473+40107728Lelio R Paula03/2017
73655*2^357850+9107725Lelio R Paula09/2014
73662^357786-291191107705Enzo Doria06/2015
736728907^5320+5320^28907107705Hans Havermann10/2020
736818^85798-23107700Lelio R Paula04/2017
73693*10^107697+61107698Robert Price09/2020
7370(14*10^107694-83)/3107695Robert Price12/2018
73712^357688-1854269107675Enzo Doria09/2015
73722^357671-112225107670Enzo Doria06/2014
737334323^1370+1370^34323107662Hans Havermann11/2020
73742^357618-21005107654Enzo Doria06/2013
73752^357615-17505107653Enzo Doria05/2013
737626350^12171+12171^26350107649Hans Havermann11/2020
7377(30^72871-1)/29107638Robert Price12/2011
737825021^20026+20026^25021107631Hans Havermann11/2020
73792^357521+1870217107625Enzo Doria05/2016
73802^357477-1203107612Lelio R Paula03/2017
738126008^13693+13693^26008107583Hans Havermann10/2020
738225432^16991+16991^25432107583Hans Havermann10/2020
7383(2^357371+3726)/2107580Stefano Morozzi09/2020
73845^153894-18107568Lelio R Paula02/2017
73852^357324-69059107566Enzo Doria11/2015
7386467^40296+40296^467107563Norbert Schneider03/2019
738729446^4495+4495^29446107559Hans Havermann10/2020
7388(8*10^107556-149)/3107557Robert Price12/2021
73892^357283-869688105107553Lelio R Paula01/2017
73902^357280-16805107552Enzo Doria05/2013
739110^107547+481719107548Patrick De Geest03/2017
739210^107547-47107547Lelio R Paula02/2017
7393(23*10^107540+37)/3107541Robert Price02/2022
739417^87396-32107537Lelio R Paula04/2017
7395(746*10^107505+1)/9107507Robert Price03/2020
7396(2^357125+1730)/2107506Stefano Morozzi09/2020
73972^357081+107107493Lelio R Paula12/2011
73982^357058-3911107486Yves Minet04/2017
73993^225274+64107484Lelio R Paula03/2017
74005*10^107482-57107483Robert Price03/2021
740118^85619-95107476Lelio R Paula04/2017
7402(2^357013+2526)/2107472Stefano Morozzi09/2020
74033^225248-130107471Lelio R Paula03/2017
7404(5*2^356961+1)/143107455Lelio R Paula03/2014
740527029^9448+9448^27029107450Hans Havermann11/2020
74062^356935-18085107449Enzo Doria05/2013
740755396^87+87^55396107442Hans Havermann10/2020
7408(14*10^107439-137)/3107440Robert Price04/2021
7409164^48505-48505^164107432Norman Luhn09/2024
741010^107409+37107410Lelio R Paula02/2017
741110^107409-329633107409Patrick De Geest03/2017
7412(2^356799+3134)/2107407Stefano Morozzi09/2020
74132^356787-109027107404Enzo Doria04/2014
7414(2^356767+78557)/5107397Lelio R Paula12/2013
74153*10^107389+77107390Robert Price09/2018
7416(11*10^107385+61)/9107386Tyler Busby01/2023
74175^153622-42107378Lelio R Paula02/2017
74182^356699-97305107378Lelio R Paula03/2017
741913129^26072-26072^13129107371Norbert Schneider09/2022
74202^356654+85107364Lelio R Paula11/2011
74212^356641-19921107360Enzo Doria06/2013
74225*10^107355+11107356Robert Price08/2019
74232^356623-465107355Lelio R Paula03/2017
742419^83945-92107345Lelio R Paula02/2017
742525491^16246+16246^25491107337Hans Havermann11/2020
742610^107334+28149107335Patrick De Geest03/2017
742710^107334-83107334Lelio R Paula02/2017
74282^356518+885107323Lelio R Paula03/2017
7429(59*10^107322+391)/9107323Robert Price03/2021
7430(3*2^356506-1)/467107317Lelio R Paula03/2014
7431(2^356468+1162)/2107308Stefano Morozzi09/2020
74322^356442-114713107300Enzo Doria04/2015
74332^356425+72257107295Enzo Doria04/2016
74342^356351-112237107273Enzo Doria06/2014
7436(6^137845-11)/5107264Paul Bourdelais11/2011
74352^356322+74539107264Enzo Doria04/2016
74372^356274+1874479107250Enzo Doria06/2016
743824606^22819+22819^24606107241Hans Havermann10/2020
7439(2^356243+3686)/2107240Stefano Morozzi09/2020
744020^82422-93107234Lelio R Paula02/2017
74412^356157-20365107214Enzo Doria06/2013
74428*10^107209+99107210Robert Price03/2021
74432^356129-18949107206Enzo Doria05/2013
7444(15^91163-1)/13873078234414574107200Paul Vanderveen06/2025
74452^356100-109587107197Enzo Doria04/2014
74462*10^107173-37107174Robert Price11/2021
7447(2^355978+3262)/2107160Stefano Morozzi02/2021
7448(31*2^355970+1)/5107159Lelio R Paula03/2014
74492^355968-64875107158Lelio R Paula01/2017
74502^355952+1870321107153Enzo Doria05/2016
745127069^9088+9088^27069107152Hans Havermann11/2020
74522^355915-117107142Lelio R Paula11/2011
7453(16*10^107140+77)/3107141Robert Price03/2019
745424628^22369+22369^24628107124Hans Havermann11/2020
7455(19*2^355838-1)/15107119Lelio R Paula03/2014
74563^224495-8107112Lelio R Paula12/2013
74573*10^107096+23107097Robert Price03/2022
745825077^18632+18632^25077107086Hans Havermann10/2020
74597^126691-44107067Lelio R Paula03/2017
74604^177830-8243107065Mike Oakes02/2011
7461(509*10^107057+13)/9107059Robert Price05/2022
74622^355604+214051107048Enzo Doria10/2023
7463(2^355562+1702)/2107035Stefano Morozzi09/2020
746410^107028+3593037107029Paul Bourdelais10/2021
746510^107028-43301107028Alfred Reich08/2024
74662^355524-21237107024Enzo Doria06/2013
7468(10223*2^355515+1)/4855107022Lelio R Paula07/2014
746724843^20320+20320^24843107022Hans Havermann10/2020
74692^355494-19901107015Enzo Doria06/2013
74702^355454-869688105107003Lelio R Paula01/2017
74714*10^106997+13106998Robert Price02/2021
7472(8*10^106985-629)/9106985Robert Price01/2022
74732^355366+54615106976Lelio R Paula01/2017
7474(31*2^355346-1)/1563106969Lelio R Paula03/2014
74752^355275-19861106949Enzo Doria06/2013
747627503^7738+7738^27503106949Hans Havermann11/2020
7477(85*10^106943+77)/9106944Robert Price07/2022
7478(9179*2^355234-1)/1915106937Lelio R Paula05/2015
74794*10^106914-93106915Robert Price07/2020
7480(151^49069-1)/90910031243271150106904Paul Vanderveen06/2025
74814*10^106892-3106893Robert Price10/2015
7482(66^58741+1)/67106881Paul Bourdelais08/2017
74832^355001+335931106866Enzo Doria08/2024
74842^354946-3106850M. Frind & P. Underwood08/2002
7485(2^354945+3134)/2106849Stefano Morozzi09/2020
7486(46^64384+1)/(46^128+1)106843Martin Hopf12/2023
74872^354873-18693106828Enzo Doria05/2013
7488(2^354831+3186)/2106815Stefano Morozzi09/2020
74902^354828+4257106814Lelio R Paula01/2017
748925216^17217+17217^25216106814Hans Havermann10/2020
7491(2^354799+1218)/2106805Stefano Morozzi09/2020
7492436^40459+40459^436106791Norbert Schneider03/2019
7493(21^80761+1)/22106783Paul Bourdelais03/2010
7494(115*10^106772-7)/9106774Robert Price02/2020
74952^354640-354640+1106758Robert Price10/2014
7496(2^354603+2606)/2106746Stefano Morozzi09/2020
74972^354585+95106741Lelio R Paula10/2011
7498(206*10^106737+1)/9106739Robert Price04/2022
74992^354553+189106732Lelio R Paula10/2011
7500(8*10^106729-71)/9106729Serge Batalov11/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 10 2025 14:11 (Time in France)

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