PRP Records

Probable Primes Top 10000

(277054 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 ?
375113^97745-24108883Lelio R Paula03/2017
3752(2^361696+2562)/2108882Stefano Morozzi09/2020
375317^88475+8108864Lelio R Paula04/2017
37542^361567+51108843Lelio R Paula01/2012
37552^361563-109501108842Enzo Doria04/2014
375612^100852+83108838Lelio R Paula03/2017
37572^361497+767108822Lelio R Paula01/2012
375828019^7630+7630^28019108785Hans Havermann10/2020
375924723^24758-24758^24723108765Norbert Schneider11/2020
37602^361280-112349108757Enzo Doria06/2014
37612^361271-5955108754Lelio R Paula04/2017
376212^100757+19108736Lelio R Paula03/2017
376325368^19333+19333^25368108735Hans Havermann11/2020
3764(2^361195+3618)/2108731Stefano Morozzi09/2020
376514^94849-61108710Lelio R Paula05/2017
376627267^9700+9700^27267108708Hans Havermann11/2020
3767(19^85009-5^85009)/14108705Robert Price07/2013
376824832^23853+23853^24832108704Hans Havermann11/2020
376927502^8963+8963^27502108701Hans Havermann11/2020
377025807^16278+16278^25807108689Hans Havermann11/2020
3771(11*2^361027+1)/40463108677Lelio R Paula03/2014
37722^360973+1299108664Lelio R Paula04/2017
37732^360959-109101108660Enzo Doria04/2014
37746*5^155454+7108659Lelio R Paula11/2014
377510^108656+79108657Lelio R Paula02/2017
377610^108656-50001108656Patrick De Geest03/2017
37772^360918-35108648Lelio R Paula01/2012
3778(11*2^360886-1)/7108638Lelio R Paula03/2014
37793*10^108624-49108625Robert Price07/2018
3780(2^360831+666)/2108621Stefano Morozzi09/2020
3781(134*10^108610+7)/3108612Robert Price02/2020
3782(2^360742+3222)/2108594Stefano Morozzi09/2020
37832^360706-458903108584Enzo Doria04/2015
378431112^3087+3087^31112108567Hans Havermann11/2020
37852^360641-113185108564Enzo Doria07/2014
37862^360618+75019108557Enzo Doria04/2016
3787(14*10^108545-221)/9108546Robert Price04/2018
3788(44*10^108544-233)/9108545Robert Price01/2019
37893*5^155286+2108541Lelio R Paula11/2014
37907^128422+4108530Lelio R Paula11/2014
37917^128421-80108529Lelio R Paula03/2017
37922^360497+53807108521Yves Minet07/2010
37932^360468-4559108512Yves Minet03/2019
3794(2^360451+578)/2108507Stefano Morozzi09/2020
37952^360366+1459108481Lelio R Paula09/2011
37962^360364-1499108481Yves Minet05/2013
379725662^16871+16871^25662108477Hans Havermann10/2020
379825009^21748+21748^25009108475Hans Havermann10/2020
379914^94642-23108472Lelio R Paula05/2017
3800(197*10^108446-11)/3108448Robert Price03/2020
3801(2^360229+1290)/2108440Stefano Morozzi01/2021
38024*10^108412+9108413Robert Price05/2015
3803(259*10^108409-1)/3108411Robert Price12/2020
3804(2^360122+1194)/2108408Stefano Morozzi09/2020
3805133^51042-132108406Norbert Schneider02/2019
38062^360093-351103108399Enzo Doria06/2015
38072^360042+723108384Lelio R Paula01/2012
380885^56164-2108364Lelio R Paula10/2013
38092^359937-29323108352Enzo Doria07/2015
3810(2^359922+1762)/2108348Stefano Morozzi09/2020
3811(2^359903+758)/2108342Stefano Morozzi09/2020
38122^359898-19997108341Enzo Doria06/2013
3813(2^359886+2122)/2108337Stefano Morozzi09/2020
38142*5^154948-7108305Lelio R Paula11/2014
381510^108303+13108304Lelio R Paula02/2017
381610^108303-207959108303Patrick De Geest03/2017
38177*10^108300+69108301Robert Price07/2019
38182^359730+753108290Lelio R Paula12/2011
3819(8*10^108273+13)/3108274Robert Price06/2018
38202^359650-19797108266Enzo Doria06/2013
382191^55259-90^55259108255Robert Price07/2015
382210^108251-50000000001108251Robert Price12/2020
38234*10^108238-71108239Robert Price12/2018
38243^226845+68108233Lelio R Paula03/2017
382531836^2509+2509^31836108227Hans Havermann10/2020
38265^154822-12866108216Enzo Doria05/2014
3827(9*2^359480+1)/5108215Lelio R Paula03/2014
38282^359454-177108207Lelio R Paula12/2011
3829(19*10^108184+191)/3108185Robert Price05/2019
38306^139022-59108181Lelio R Paula02/2017
3831(19*10^108176-43)/3108177Robert Price05/2019
38322^359352-179108176Lelio R Paula12/2011
38332^359338-1858781108172Enzo Doria04/2016
383412^100230-97108167Lelio R Paula03/2017
383527028^10043+10043^27028108163Hans Havermann11/2020
3836(25*2^359297-1)/137108159Lelio R Paula03/2014
3837(2^359262-509203)/9108148Lelio R Paula12/2013
383826583^11702+11702^26583108147Hans Havermann11/2020
3839(3^226648-8)/352715633108131Lelio R Paula12/2013
38406^138956-59108129Lelio R Paula02/2017
38412^359184+30285108126Lelio R Paula04/2017
384213^97059+10108119Lelio R Paula03/2017
38432^359137-81108112Lelio R Paula12/2011
3845(15185*2^359105-1)/567108103Lelio R Paula05/2015
38442^359110-11655108103Lelio R Paula04/2017
384626227^13222+13222^26227108090Hans Havermann10/2020
38478*6^138875+5108067Lelio R Paula11/2014
38482^358987-216919108066Enzo Doria05/2014
3849(2^358977+2714)/2108063Stefano Morozzi09/2020
385039^67918-67918^39108062Norbert Schneider02/2017
385124^78283-1*78283^24108048Dylan Delgado12/2019
385225282^18767+18767^25282108040Hans Havermann11/2020
38532^358785-16933108006Enzo Doria05/2013
3854(2^358783+5)/33383108000Lelio R Paula12/2013
38556^138770-77107985Lelio R Paula02/2017
3856(2^358727-1017)/94178479107980Lelio R Paula12/2013
385710^107976+19107977Lelio R Paula02/2017
385810^107976-202103107976Patrick De Geest03/2017
38592^358684+75781107975Enzo Doria04/2016
386024928^21411+21411^24928107955Hans Havermann10/2020
386199^54094+2107952Lelio R Paula06/2013
3862(2^358583-9)/391107942Lelio R Paula12/2013
38632^358538+55107931Lelio R Paula12/2011
38642^358517-109009107925Enzo Doria03/2014
386526395^12258+12258^26395107914Hans Havermann10/2020
38663^226159+104107906Lelio R Paula03/2017
38672^358310-11655107863Lelio R Paula03/2017
38682^358275-112987107852Enzo Doria07/2014
38693^226038+4107848Tyler NeSmith01/2021
38702^358233-20005107839Enzo Doria06/2013
38712^358194+175107828Lelio R Paula12/2011
3872107^53125-106107812Norbert Schneider12/2016
3873(25*10^107804+161)/3107805Robert Price09/2019
38743^225922-2107793Lelio R Paula10/2013
387512^99874-95107783Lelio R Paula03/2017
3876(2^358042+3042)/2107782Stefano Morozzi09/2020
38772^358030-171107778Lelio R Paula12/2011
387811^103488-4170107772Enzo Doria12/2012
38792^357930-4547107748Yves Minet03/2019
38802^357911-20089107742Enzo Doria06/2013
38812^357885+12857107735Yves Minet07/2010
3882(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
38837^127473+40107728Lelio R Paula03/2017
38845*2^357850+9107725Lelio R Paula09/2014
38852^357786-291191107705Enzo Doria06/2015
388628907^5320+5320^28907107705Hans Havermann10/2020
388718^85798-23107700Lelio R Paula04/2017
38883*10^107697+61107698Robert Price09/2020
3889(14*10^107694-83)/3107695Robert Price12/2018
38902^357688-1854269107675Enzo Doria09/2015
38912^357671-112225107670Enzo Doria06/2014
389234323^1370+1370^34323107662Hans Havermann11/2020
38932^357618-21005107654Enzo Doria06/2013
38942^357615-17505107653Enzo Doria05/2013
389526350^12171+12171^26350107649Hans Havermann11/2020
3896(30^72871-1)/29107638Robert Price12/2011
389725021^20026+20026^25021107631Hans Havermann11/2020
38982^357521+1870217107625Enzo Doria05/2016
38992^357477-1203107612Lelio R Paula03/2017
390026008^13693+13693^26008107583Hans Havermann10/2020
390125432^16991+16991^25432107583Hans Havermann10/2020
3902(2^357371+3726)/2107580Stefano Morozzi09/2020
39035^153894-18107568Lelio R Paula02/2017
39042^357324-69059107566Enzo Doria11/2015
3905467^40296+40296^467107563Norbert Schneider03/2019
390629446^4495+4495^29446107559Hans Havermann10/2020
39072^357283-869688105107553Lelio R Paula01/2017
39082^357280-16805107552Enzo Doria05/2013
390910^107547+481719107548Patrick De Geest03/2017
391010^107547-47107547Lelio R Paula02/2017
391117^87396-32107537Lelio R Paula04/2017
3912(746*10^107505+1)/9107507Robert Price03/2020
3913(2^357125+1730)/2107506Stefano Morozzi09/2020
39142^357081+107107493Lelio R Paula12/2011
39152^357058-3911107486Yves Minet04/2017
39163^225274+64107484Lelio R Paula03/2017
391718^85619-95107476Lelio R Paula04/2017
3918(2^357013+2526)/2107472Stefano Morozzi09/2020
39193^225248-130107471Lelio R Paula03/2017
3920(5*2^356961+1)/143107455Lelio R Paula03/2014
392127029^9448+9448^27029107450Hans Havermann11/2020
39222^356935-18085107449Enzo Doria05/2013
392355396^87+87^55396107442Hans Havermann10/2020
392410^107409+37107410Lelio R Paula02/2017
392510^107409-329633107409Patrick De Geest03/2017
3926(2^356799+3134)/2107407Stefano Morozzi09/2020
39272^356787-109027107404Enzo Doria04/2014
3928(2^356767+78557)/5107397Lelio R Paula12/2013
39293*10^107389+77107390Robert Price09/2018
39305^153622-42107378Lelio R Paula02/2017
39312^356699-97305107378Lelio R Paula03/2017
39322^356654+85107364Lelio R Paula11/2011
39332^356641-19921107360Enzo Doria06/2013
39345*10^107355+11107356Robert Price08/2019
39352^356623-465107355Lelio R Paula03/2017
393619^83945-92107345Lelio R Paula02/2017
393725491^16246+16246^25491107337Hans Havermann11/2020
393810^107334+28149107335Patrick De Geest03/2017
393910^107334-83107334Lelio R Paula02/2017
39402^356518+885107323Lelio R Paula03/2017
3941(3*2^356506-1)/467107317Lelio R Paula03/2014
3942(2^356468+1162)/2107308Stefano Morozzi09/2020
39432^356442-114713107300Enzo Doria04/2015
39442^356425+72257107295Enzo Doria04/2016
39452^356351-112237107273Enzo Doria06/2014
3947(6^137845-11)/5107264Paul Bourdelais11/2011
39462^356322+74539107264Enzo Doria04/2016
39482^356274+1874479107250Enzo Doria06/2016
394924606^22819+22819^24606107241Hans Havermann10/2020
3950(2^356243+3686)/2107240Stefano Morozzi09/2020
395120^82422-93107234Lelio R Paula02/2017
39522^356157-20365107214Enzo Doria06/2013
39532^356129-18949107206Enzo Doria05/2013
39542^356100-109587107197Enzo Doria04/2014
3955(31*2^355970+1)/5107159Lelio R Paula03/2014
39562^355968-64875107158Lelio R Paula01/2017
39572^355952+1870321107153Enzo Doria05/2016
395827069^9088+9088^27069107152Hans Havermann11/2020
39592^355915-117107142Lelio R Paula11/2011
3960(16*10^107140+77)/3107141Robert Price03/2019
396124628^22369+22369^24628107124Hans Havermann11/2020
3962(19*2^355838-1)/15107119Lelio R Paula03/2014
39633^224495-8107112Lelio R Paula12/2013
396425077^18632+18632^25077107086Hans Havermann10/2020
39657^126691-44107067Lelio R Paula03/2017
39664^177830-8243107065Mike Oakes02/2011
3967(2^355562+1702)/2107035Stefano Morozzi09/2020
39682^355524-21237107024Enzo Doria06/2013
3969(10223*2^355515+1)/4855107022Lelio R Paula07/2014
397024843^20320+20320^24843107022Hans Havermann10/2020
39712^355494-19901107015Enzo Doria06/2013
39722^355454-869688105107003Lelio R Paula01/2017
39732^355366+54615106976Lelio R Paula01/2017
3974(31*2^355346-1)/1563106969Lelio R Paula03/2014
39762^355275-19861106949Enzo Doria06/2013
397527503^7738+7738^27503106949Hans Havermann11/2020
3977(9179*2^355234-1)/1915106937Lelio R Paula05/2015
39784*10^106914-93106915Robert Price07/2020
39794*10^106892-3106893Robert Price10/2015
3980(66^58741+1)/67106881Paul Bourdelais08/2017
39812^354946-3106850M. Frind & P. Underwood08/2002
3982(2^354945+3134)/2106849Stefano Morozzi09/2020
39832^354873-18693106828Enzo Doria05/2013
3984(2^354831+3186)/2106815Stefano Morozzi09/2020
39852^354828+4257106814Lelio R Paula01/2017
398625216^17217+17217^25216106814Hans Havermann10/2020
3987(2^354799+1218)/2106805Stefano Morozzi09/2020
3988436^40459+40459^436106791Norbert Schneider03/2019
3989(21^80761+1)/22106783Paul Bourdelais03/2010
3990(115*10^106772-7)/9106774Robert Price02/2020
39912^354640-354640+1106758Robert Price10/2014
3992(2^354603+2606)/2106746Stefano Morozzi09/2020
39932^354585+95106741Lelio R Paula10/2011
39942^354553+189106732Lelio R Paula10/2011
39952^354514-109031106720Enzo Doria04/2014
39962^354509-109465106718Enzo Doria04/2014
3997(15*2^354478-1)/26983106706Lelio R Paula03/2014
3998Phi(217618,10)/899798636917106693Makoto Kamada06/2019
399915^90710+28106684Lelio R Paula04/2017
40007^126237+34106683Lelio R Paula03/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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