PRP Records

Probable Primes Top 10000

(271000 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 ?
350139^67918-67918^39108062Norbert Schneider02/2017
350224^78283-1*78283^24108048Dylan Delgado12/2019
35032^358785-16933108006Enzo Doria05/2013
3504(2^358783+5)/33383108000Lelio R Paula12/2013
35056^138770-77107985Lelio R Paula02/2017
3506(2^358727-1017)/94178479107980Lelio R Paula12/2013
350710^107976+19107977Lelio R Paula02/2017
350810^107976-202103107976Patrick De Geest03/2017
35092^358684+75781107975Enzo Doria04/2016
351099^54094+2107952Lelio R Paula06/2013
3511(2^358583-9)/391107942Lelio R Paula12/2013
35122^358538+55107931Lelio R Paula12/2011
35132^358517-109009107925Enzo Doria03/2014
35143^226159+104107906Lelio R Paula03/2017
35152^358310-11655107863Lelio R Paula03/2017
35162^358275-112987107852Enzo Doria07/2014
35172^358233-20005107839Enzo Doria06/2013
35182^358194+175107828Lelio R Paula12/2011
3519107^53125-106107812Norbert Schneider12/2016
3520(25*10^107804+161)/3107805Robert Price09/2019
35213^225922-2107793Lelio R Paula10/2013
352212^99874-95107783Lelio R Paula03/2017
3523(2^358042+3042)/2107782Stefano Morozzi09/2020
35242^358030-171107778Lelio R Paula12/2011
352511^103488-4170107772Enzo Doria12/2012
35262^357930-4547107748Yves Minet03/2019
35272^357911-20089107742Enzo Doria06/2013
35282^357885+12857107735Yves Minet07/2010
3529(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
35307^127473+40107728Lelio R Paula03/2017
35315*2^357850+9107725Lelio R Paula09/2014
35322^357786-291191107705Enzo Doria06/2015
353318^85798-23107700Lelio R Paula04/2017
35343*10^107697+61107698Robert Price09/2020
3535(14*10^107694-83)/3107695Robert Price12/2018
35362^357688-1854269107675Enzo Doria09/2015
35372^357671-112225107670Enzo Doria06/2014
35382^357618-21005107654Enzo Doria06/2013
35392^357615-17505107653Enzo Doria05/2013
3540(30^72871-1)/29107638Robert Price12/2011
35412^357521+1870217107625Enzo Doria05/2016
35422^357477-1203107612Lelio R Paula03/2017
3543(2^357371+3726)/2107580Stefano Morozzi09/2020
35445^153894-18107568Lelio R Paula02/2017
35452^357324-69059107566Enzo Doria11/2015
3546467^40296+40296^467107563Norbert Schneider03/2019
35472^357283-869688105107553Lelio R Paula01/2017
35482^357280-16805107552Enzo Doria05/2013
354910^107547+481719107548Patrick De Geest03/2017
355010^107547-47107547Lelio R Paula02/2017
355117^87396-32107537Lelio R Paula04/2017
3552(746*10^107505+1)/9107507Robert Price03/2020
3553(2^357125+1730)/2107506Stefano Morozzi09/2020
35542^357081+107107493Lelio R Paula12/2011
35552^357058-3911107486Yves Minet04/2017
35563^225274+64107484Lelio R Paula03/2017
355718^85619-95107476Lelio R Paula04/2017
3558(2^357013+2526)/2107472Stefano Morozzi09/2020
35593^225248-130107471Lelio R Paula03/2017
3560(5*2^356961+1)/143107455Lelio R Paula03/2014
35612^356935-18085107449Enzo Doria05/2013
356210^107409+37107410Lelio R Paula02/2017
356310^107409-329633107409Patrick De Geest03/2017
3564(2^356799+3134)/2107407Stefano Morozzi09/2020
35652^356787-109027107404Enzo Doria04/2014
3566(2^356767+78557)/5107397Lelio R Paula12/2013
35673*10^107389+77107390Robert Price09/2018
35685^153622-42107378Lelio R Paula02/2017
35692^356699-97305107378Lelio R Paula03/2017
35702^356654+85107364Lelio R Paula11/2011
35712^356641-19921107360Enzo Doria06/2013
35725*10^107355+11107356Robert Price08/2019
35732^356623-465107355Lelio R Paula03/2017
357419^83945-92107345Lelio R Paula02/2017
357510^107334+28149107335Patrick De Geest03/2017
357610^107334-83107334Lelio R Paula02/2017
35772^356518+885107323Lelio R Paula03/2017
3578(3*2^356506-1)/467107317Lelio R Paula03/2014
3579(2^356468+1162)/2107308Stefano Morozzi09/2020
35802^356442-114713107300Enzo Doria04/2015
35812^356425+72257107295Enzo Doria04/2016
35822^356351-112237107273Enzo Doria06/2014
3584(6^137845-11)/5107264Paul Bourdelais11/2011
35832^356322+74539107264Enzo Doria04/2016
35852^356274+1874479107250Enzo Doria06/2016
3586(2^356243+3686)/2107240Stefano Morozzi09/2020
358720^82422-93107234Lelio R Paula02/2017
35882^356157-20365107214Enzo Doria06/2013
35892^356129-18949107206Enzo Doria05/2013
35902^356100-109587107197Enzo Doria04/2014
3591(31*2^355970+1)/5107159Lelio R Paula03/2014
35922^355968-64875107158Lelio R Paula01/2017
35932^355952+1870321107153Enzo Doria05/2016
35942^355915-117107142Lelio R Paula11/2011
3595(16*10^107140+77)/3107141Robert Price03/2019
3596(19*2^355838-1)/15107119Lelio R Paula03/2014
35973^224495-8107112Lelio R Paula12/2013
35987^126691-44107067Lelio R Paula03/2017
35994^177830-8243107065Mike Oakes02/2011
3600(2^355562+1702)/2107035Stefano Morozzi09/2020
36012^355524-21237107024Enzo Doria06/2013
3602(10223*2^355515+1)/4855107022Lelio R Paula07/2014
36032^355494-19901107015Enzo Doria06/2013
36042^355454-869688105107003Lelio R Paula01/2017
36052^355366+54615106976Lelio R Paula01/2017
3606(31*2^355346-1)/1563106969Lelio R Paula03/2014
36072^355275-19861106949Enzo Doria06/2013
3608(9179*2^355234-1)/1915106937Lelio R Paula05/2015
36094*10^106914-93106915Robert Price07/2020
36104*10^106892-3106893Robert Price10/2015
3611(66^58741+1)/67106881Paul Bourdelais08/2017
36122^354946-3106850M. Frind & P. Underwood08/2002
3613(2^354945+3134)/2106849Stefano Morozzi09/2020
36142^354873-18693106828Enzo Doria05/2013
3615(2^354831+3186)/2106815Stefano Morozzi09/2020
36162^354828+4257106814Lelio R Paula01/2017
3617(2^354799+1218)/2106805Stefano Morozzi09/2020
3618436^40459+40459^436106791Norbert Schneider03/2019
3619(21^80761+1)/22106783Paul Bourdelais03/2010
3620(115*10^106772-7)/9106774Robert Price02/2020
36212^354640-354640+1106758Robert Price10/2014
3622(2^354603+2606)/2106746Stefano Morozzi09/2020
36232^354585+95106741Lelio R Paula10/2011
36242^354553+189106732Lelio R Paula10/2011
36252^354514-109031106720Enzo Doria04/2014
36262^354509-109465106718Enzo Doria04/2014
3627(15*2^354478-1)/26983106706Lelio R Paula03/2014
3628Phi(217618,10)/899798636917106693Makoto Kamada06/2019
362915^90710+28106684Lelio R Paula04/2017
36307^126237+34106683Lelio R Paula03/2017
36312^354385-115315106681Enzo Doria06/2015
36322^354327-19305106664Enzo Doria06/2013
3633(35*10^106649+1)/9106650Serge Batalov11/2010
363410^106636+97106637Lelio R Paula02/2017
363510^106636-22923106636Patrick De Geest03/2017
36362^354220-57106631Lelio R Paula10/2011
3637(29*10^106620-77)/3106621Robert Price02/2020
3638(746*10^106618+1)/9106620Robert Price03/2020
36392^354157-17041106612Enzo Doria05/2013
364012^98778+73106600Lelio R Paula02/2017
36412^354064+1870651106584Enzo Doria05/2016
36422^353992-57106563Lelio R Paula10/2011
36439*10^106559+59106560Robert Price01/2020
3644NSW(139160)106535Robert Price12/2018
3645(7*10^106516+113)/3106517Robert Price02/2018
36462^353832-1853849106515Enzo Doria09/2015
3647(7^126037-1)/6106513Paul Bourdelais09/2008
36482^353794-18453106503Enzo Doria05/2013
3649(2^353761+2094)/2106493Stefano Morozzi09/2020
36502^353728+7695106483Lelio R Paula01/2017
36512^353672-303106466Yves Minet02/2012
36526^136811+101106460Lelio R Paula02/2017
36532^353641+1871981106457Enzo Doria05/2016
3654(8*10^106454-29)/3106455Robert Price07/2018
36552^353553+54615106431Lelio R Paula01/2017
36562^353544-18897106428Enzo Doria05/2013
36576^136729-133106396Lelio R Paula02/2017
36582^353418+1605106390Lelio R Paula01/2017
36592^353387+65106381Lelio R Paula10/2011
36602^353372+74311106376Enzo Doria04/2016
36612^353344-3693106368Yves Minet03/2017
36632^353277-20089106347Enzo Doria06/2013
36622^353275+72173106347Enzo Doria04/2016
36642^353268-17705106345Enzo Doria05/2013
36652^353267-19857106344Enzo Doria06/2013
3666(46*10^106343+143)/9106344Robert Price01/2019
3667(2^353189+3054)/2106321Stefano Morozzi09/2020
3668(2^353051+606)/2106279Stefano Morozzi09/2020
3669222748^3+3^222748106278Anatoly F. Selevich12/2010
3670(9179*2^353019-1)/9106273Lelio R Paula05/2015
36712^353025+72257106272Enzo Doria04/2016
36732^352932-20345106244Enzo Doria06/2013
3672(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
36742^352883-187106229Lelio R Paula10/2011
367520^81649-19^81649106228Jean-Louis Charton03/2011
3676(55*10^106222+377)/9106223Robert Price02/2019
36772^352814-131106208Lelio R Paula10/2011
36782^352752+73951106189Enzo Doria04/2016
36796^136434+5106167Lelio R Paula11/2014
368025296^15737+15737^25296106166Hans Havermann09/2020
36818*10^106157-13106158Robert Price08/2019
36827*5^151872-8106155Lelio R Paula11/2014
3683105^52520-2106153Lelio R Paula10/2017
36842^352601-1604809106144Enzo Doria05/2015
368512^98353-43106141Lelio R Paula02/2017
36862^352585-18901106139Enzo Doria05/2013
368726363^10614+10614^26363106135Hans Havermann09/2020
3688(2^352554-3)/193106128Lelio R Paula12/2013
36892^352540+15015106126Lelio R Paula01/2017
369025068^17119+17119^25068106125Hans Havermann09/2020
36912^352524-3149106121Yves Minet10/2014
36922^352486-1858781106109Enzo Doria04/2016
36932^352444+12705106097Lelio R Paula01/2017
3694(182*10^106083+43)/9106085Robert Price02/2020
3695(266*10^106066+1)/3106068Robert Price04/2020
36962^352228-18953106032Enzo Doria05/2013
3697(2^352223+1118)/2106030Stefano Morozzi09/2020
3698(2^352136+2638)/2106004Stefano Morozzi09/2020
36992^352107+1872533105995Enzo Doria05/2016
3700(2^352096+2086)/2105992Stefano Morozzi09/2020
37012^352066-2591105983Yves Minet07/2014
37022^352030+715105972Lelio R Paula10/2011
37039*6^136176-5105967Lelio R Paula11/2014
370417099*2^351991+58329105965Paul Vanderveen12/2017
370528582^5097+5097^28582105963Hans Havermann09/2020
3706155^48377+2105962Lelio R Paula08/2013
37072^351865+1869707105922Enzo Doria05/2016
370824974^17427+17427^24974105921Hans Havermann09/2020
370925163^16194+16194^25163105920Hans Havermann09/2020
37102^351831+23105912Lelio R Paula10/2011
37119*2^351784-5105899Lelio R Paula09/2014
3712(85*10^105881+203)/9105882Robert Price09/2020
37132^351671-112387105864Enzo Doria06/2014
37142^351669-109501105863Enzo Doria04/2014
37152^351644+74731105856Enzo Doria04/2016
371613^95025-42105853Lelio R Paula12/2016
37172^351599+15015105842Lelio R Paula01/2017
371819^82763+90105834Lelio R Paula01/2017
371926050^11551+11551^26050105832Hans Havermann09/2020
3720(9179*2^351540-1)/221105826Lelio R Paula05/2015
372120^81329-51105812Lelio R Paula01/2017
3722(5*10^105811+211)/9105811Robert Price02/2018
37232^351483+28425105807Lelio R Paula01/2017
372425231^15610+15610^25231105804Hans Havermann09/2020
372515^89960+86105802Lelio R Paula02/2017
37262^351460-17289105801Enzo Doria05/2013
372719^82735+22105798Lelio R Paula01/2017
37282^351435-109077105793Enzo Doria04/2014
37292^351393+1089105780Lelio R Paula01/2017
37302^351364+72631105772Enzo Doria04/2016
3731(2^351333+3626)/2105762Stefano Morozzi09/2020
373226818^8783+8783^26818105761Hans Havermann09/2020
37342^351305+1872467105754Enzo Doria05/2016
37353^221649+16105754Lelio R Paula11/2016
373332511^1790+1790^32511105754Hans Havermann09/2020
37368*3^221637-5105749Lelio R Paula09/2014
37372^351279-2780449105746Enzo Doria03/2016
3738(2^351263+3198)/2105741Stefano Morozzi09/2020
373915^89903-26105735Lelio R Paula02/2017
37412^351213-73105726Lelio R Paula10/2011
3740(2^351214+1210)/2105726Stefano Morozzi09/2020
37422^351192-4589105720Yves Minet07/2011
374320^81250-33105709Lelio R Paula12/2016
3744(2^351133+3530)/2105702Stefano Morozzi09/2020
3745(2^351103+534)/2105693Stefano Morozzi09/2020
37462^351076-113159105685Enzo Doria07/2014
374793^53688-2105684Lelio R Paula09/2013
37482^351060-4559105680Yves Minet07/2011
3749((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
375011^101473-750105674Enzo Doria11/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2020 00:24 (Time in France)

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