PRP Records

Probable Primes Top 10000

(255244 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 ?
40012^331416-331416+199767Robert Price10/2014
40022^331256-5799718Lelio R Paula12/2012
400328192^3443+3443^2819299714Hans Havermann03/2018
40042^331185+73799697Lelio R Paula01/2013
4005(4*10^99693+149)/999693Robert Price03/2017
40062^331154+188052799688Enzo Doria10/2016
4008(19^77951+1)/2099679Paul Bourdelais03/2010
400724354^12385+12385^2435499679Hans Havermann03/2018
40092^331110+187045999675Enzo Doria05/2016
40105*2^331075+799665Lelio R Paula08/2014
401125776^7351+7351^2577699659Hans Havermann02/2018
4012(16*10^99656-31)/399657Robert Price03/2016
40132^330968+34599632Lelio R Paula09/2016
40152*5^142528-799624Lelio R Paula11/2014
40142^330942+7732999624Enzo Doria05/2016
401614^86914-9999615Lelio R Paula08/2016
4017(19*2^330902+1)/7799611Lelio R Paula11/2013
401822971^21692+21692^2297199610Hans Havermann03/2018
40192^330845+7168799595Enzo Doria04/2016
4020(23*2^330770+1)/399573Lelio R Paula11/2013
402124494^11613+11613^2449499567Hans Havermann03/2018
40222^330735+841599562Lelio R Paula09/2016
40232^330720+7407199557Enzo Doria04/2016
402431^66738-299531Lelio R Paula09/2013
40257*3^208567+499513Lelio R Paula08/2014
4026(13*10^99508+47)/399509Robert Price01/2017
40272^330553+77999507Lelio R Paula01/2013
402815^84606-9499505Lelio R Paula08/2016
40296^127858+4799493Lelio R Paula08/2016
40305^142337+4899490Lelio R Paula08/2016
40317^117724-2099489Lelio R Paula08/2016
4032(29*10^99474-17)/399475Erik Branger09/2014
4033(9*2^330407-1)/799463Lelio R Paula03/2014
4034(68*10^99441+7)/399443Robert Price03/2016
403546^59791-45^5979199418Jean-Louis Charton01/2013
403623839^14802+14802^2383999417Hans Havermann02/2018
4037(2*10^99408+529)/999408Robert Price01/2017
403853^57646-299398Lelio R Paula09/2013
40392^330165+187002599390Enzo Doria05/2016
40402^330142-15599383Lelio R Paula12/2012
40412^330088-11525999367Enzo Doria06/2015
404324216^12671+12671^2421699354Hans Havermann01/2018
4042Phi(200548,10)/320876999354Makoto Kamada04/2019
4044(746*10^99303+1)/999305Robert Price02/2017
40453^208107+4099293Lelio R Paula08/2016
4046(5*2^329833-1)/36999288Lelio R Paula02/2014
40478*3^208093+599287Lelio R Paula08/2014
40485^142043+5699284Lelio R Paula08/2016
404922*10^99275+799277Robert Price04/2016
40502^329778+187618999274Enzo Doria07/2016
4051(10^99239-13)/399239Robert Price02/2017
40523^207987+6299236Lelio R Paula08/2016
40532^329638+4999231Lelio R Paula12/2012
40547^117413-1899226Lelio R Paula08/2016
40552^329586-45890399216Enzo Doria04/2015
40562^329553+10199206Lelio R Paula12/2012
40572^329551-11289799205Enzo Doria06/2014
4058(3^207925+7)/5099204Lelio R Paula09/2013
40596^127458-1799399182Enzo Doria03/2013
406027197^4428+4428^2719799166Hans Havermann10/2017
4061(46*10^99143-1)/999144Robert Price12/2014
40627*10^99133+6999134Robert Price10/2017
406318^78968-306599127Enzo Doria03/2013
406425927^6654+6654^2592799122Hans Havermann10/2017
406587915!4+1699122Robert Price09/2019
40662^329259+18999117Lelio R Paula12/2012
40678*10^99113+3999114Robert Price01/2017
40686^127364+7799109Lelio R Paula08/2016
40696^127285+1399047Lelio R Paula08/2016
4070(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
40712^329007+7328399041Enzo Doria04/2016
40725*3^207543-899024Lelio R Paula08/2014
40732^328885+14999005Lelio R Paula12/2012
407423392^17075+17075^2339299004Hans Havermann09/2017
4075(2^328879-9)/11999001Lelio R Paula10/2013
40765^141618+5498987Lelio R Paula08/2016
40778*10^98982+5198983Robert Price05/2017
4078(21*2^328809-1)/770998979Lelio R Paula03/2014
40792^328794-279760198977Enzo Doria04/2016
40806^127176+598963Lelio R Paula11/2014
408124262^11989+11989^2426298960Hans Havermann09/2017
40822^328700-10970998949Enzo Doria04/2014
408387771!4-12898944Robert Price11/2019
408446711!2-2^4671198916Robert Price09/2015
40859*7^117037+498909Lelio R Paula11/2014
4086127^47012+12698905Norbert Schneider01/2019
4087(10^98890+149)/398890Serge Batalov12/2014
408822775^21978+21978^2277598889Hans Havermann08/2017
40892^328497-21693398888Enzo Doria05/2014
40902^328487+3276998885Lelio R Paula08/2016
40913^207250-11235898884Enzo Doria06/2014
409213^88754-9098867Lelio R Paula08/2016
40932^328406+70998861Lelio R Paula02/2013
4094(17*2^328413-1)/1617398860Lelio R Paula03/2014
40957^116976+7698857Lelio R Paula08/2016
40962^328335+115598839Lelio R Paula08/2016
4098(3*2^328311+1)/598832Lelio R Paula11/2013
4097287^40210+40210^28798832Norbert Schneider11/2014
4099(2^328284+9)/132598821Lelio R Paula10/2013
4100(21*2^328258+1)/212598814Lelio R Paula11/2013
410165^54491+4898788Lelio R Paula04/2016
41023^207042+9898785Lelio R Paula08/2016
41033^206977-11275698754Enzo Doria07/2014
41047^116846-5098747Lelio R Paula08/2016
41052^327967-2863598728Lelio R Paula08/2016
4106707^34642+34642^70798710Norbert Schneider12/2017
41076^126850-4798709Lelio R Paula08/2016
41088*6^126830-798694Lelio R Paula11/2014
410911^94770-27098693Enzo Doria08/2012
41102^327832+4398688Lelio R Paula12/2012
41112^327795+76198677Lelio R Paula02/2013
411210^98669+14741198670Patrick De Geest11/2016
411410^98669-9^(98669-1)98669Robert Price05/2016
411310^98669-10524998669Patrick De Geest11/2016
41152^327671-10980198639Enzo Doria04/2014
411624398^11037+11037^2439898638Hans Havermann10/2019
41175^141090-1498618Lelio R Paula08/2016
411820^75799+4798617Lelio R Paula08/2016
41192^327515-101798592Lelio R Paula08/2016
41206^126692+9768198586Mike Oakes04/2011
41212^327467-74198578Lelio R Paula08/2016
4122(2^327329+9)/1998535Lelio R Paula10/2013
41237^116577-6698519Lelio R Paula08/2016
4124(3*2^327250+1)/798512Lelio R Paula11/2013
4125(19*2^327192+1)/27598494Lelio R Paula11/2013
41262^327162-6694598486Lelio R Paula08/2016
41274*10^98472-398473Erik Branger11/2013
4128(6883*2^327047-1)/7798453Lelio R Paula05/2015
4129(71*10^98446+1)/998447Serge Batalov11/2010
413013^88363+9498432Lelio R Paula08/2016
413148^58543-47^5854398425Jean-Louis Charton11/2005
41326^126481+4198422Lelio R Paula08/2016
413378*10^98413-798415Robert Price05/2017
41347^116416+4698383Lelio R Paula08/2016
41357^116407-2498376Lelio R Paula07/2016
4136439^37228+37228^43998374Norbert Schneider08/2018
41382^326782-186067198372Enzo Doria03/2016
413717^79948+5898372Lelio R Paula08/2016
41393^206143-9898356Lelio R Paula08/2016
41408*5^140705+798350Lelio R Paula11/2014
41412^326585+1198312Lelio R Paula12/2012
41422^326582-45916198311Enzo Doria05/2015
4143(2^326548+9)/598301Lelio R Paula10/2013
41442^326538+7165998298Enzo Doria04/2016
414515^83575-5898292Lelio R Paula08/2016
414610^98288+398289Robert Price03/2011
414710^98288-11701798288Patrick De Geest11/2011
4148(44*10^98284-719)/998285Robert Price12/2017
41492^326421-279757398263Enzo Doria04/2016
41502^326401+1609598257Lelio R Paula07/2016
41517^116240-116240^798235Norbert Schneider05/2017
415217^79826-7898222Lelio R Paula08/2016
41532^326268-80998217Yves Minet04/2011
415422659^21590+21590^2265998210Hans Havermann10/2019
4155(418*10^98199+23)/998201Robert Price08/2017
415612*10^98198-798200Robert Price11/2017
415715^83496-7698199Lelio R Paula08/2016
4158(10223*2^326179+1)/612598190Lelio R Paula07/2014
41599*5^140471-498186Lelio R Paula11/2014
41602^326069-238398157Yves Minet10/2013
41612^325973+118598128Lelio R Paula07/2016
4162(25*2^325949-1)/1798121Lelio R Paula02/2014
41632^325945-184726998120Enzo Doria07/2015
41648*10^98111-6798112Robert Price10/2017
41652^325866+1598096Lelio R Paula12/2012
41662^325765+197430598066Enzo Doria06/2016
41672^325733-5869598056Lelio R Paula07/2016
41682^325717-364598051Lelio R Paula07/2016
416923968^12293+12293^2396898021Hans Havermann11/2019
4170(23*2^325583-1)/2198011Lelio R Paula02/2014
4171(7*10^98007-13)/398008Robert Price06/2016
41722^325512-45995997989Enzo Doria05/2015
4173(3^205354-8)/1797978Lelio R Paula09/2013
41742^325433+7681797966Enzo Doria05/2016
41755*10^97963+8197964Robert Price08/2017
41762^325390-10906197953Enzo Doria04/2014
417713^87921+2497940Lelio R Paula08/2016
4178961^32831-960^3283197926Jean-Louis Charton02/2011
41792^325215+1290997900Lelio R Paula07/2016
41807*10^97874-6997875Robert Price01/2017
4182(17^79537+5^79537)/2297865Robert Price06/2013
418115^83212+2297865Lelio R Paula08/2016
41832^325087-10905797861Enzo Doria04/2014
41842^325074+187065797858Enzo Doria05/2016
41862^325066-211197855Yves Minet08/2013
4185CopelandErdos(97855)97855Eric W. Weisstein10/2015
418718^77944-8997841Lelio R Paula07/2016
4188119^47136+11897833Norbert Schneider09/2018
41896^125720-1766397830Enzo Doria02/2013
41902^324972-206997827Yves Minet05/2013
41912^324958-469197823Yves Minet05/2019
41922^324944-278831997818Enzo Doria03/2016
419322845^19112+19112^2284597807Hans Havermann10/2019
41954*10^97799-997800Erik Branger11/2013
41942^324882+57729457597800Lelio R Paula09/2016
41962^324863-186792197794Enzo Doria04/2016
41976^125662-1847397785Enzo Doria03/2013
419812^90604+1197779Lelio R Paula07/2016
41995^139830+2497737Lelio R Paula04/2016
42002^324612+115597718Lelio R Paula07/2016
420119^76404-4497702Lelio R Paula07/2016
42022^324505-298397686Yves Minet04/2011
4203(144^45259+1)/14597684Paul Bourdelais08/2019
4204(31*2^324496-1)/4597683Lelio R Paula02/2014
42056^125488-1784397649Enzo Doria02/2013
42067^115515-297622Lelio R Paula09/2013
4207(89^50069-1)/8897603Paul Bourdelais08/2017
42086^125418-597595Lelio R Paula11/2014
42092^324076+115597557Lelio R Paula07/2016
4210(2^324074+9)/1397555Lelio R Paula10/2013
4211(55459*2^323993+1)/2197536Lelio R Paula07/2014
421213^87557-12^8755797534Jean-Louis Charton12/2008
42132^323946+7393997518Enzo Doria04/2016
42142^323937+186694797515Enzo Doria03/2016
42156^125290-1853397495Enzo Doria03/2013
42162^323845+10197488Lelio R Paula12/2012
421718^77662+6597487Lelio R Paula07/2016
42182^323772+7677197466Enzo Doria05/2016
42192^323765-11221397463Enzo Doria06/2014
42202^323720-655597450Lelio R Paula07/2016
42212^323694-186040197442Enzo Doria03/2016
422220^74886+397429Lelio R Paula06/2016
42243*10^97399+7397400Robert Price04/2016
42237^115252-5097400Lelio R Paula07/2016
4225224737#+39358197389Nicolas PALAU12/2016
4226(26*10^97353+31)/397354Robert Price07/2016
422761^54517-60^5451797331Jean-Louis Charton09/2005
4228(38*10^97329+187)/997330Robert Price11/2017
422986455!4+897319Robert Price09/2019
4230p(19982)#/2-102497293Robert Price09/2017
42316^125021-8597286Lelio R Paula08/2016
42322^323164-4735597283Lelio R Paula07/2016
4233(3^203902+4)/3605101515797276Lelio R Paula09/2013
42342^323054-655597249Lelio R Paula07/2016
42359*10^97247-2997248Robert Price05/2017
4236(31*10^97242+41)/997243Robert Price04/2015
4237GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
423812^90098-4197233Lelio R Paula07/2016
42392^322928-21692997212Enzo Doria05/2014
4240(7*2^322896-1)/5797201Lelio R Paula02/2014
4241(2^322897+5)/314610748997193Lelio R Paula10/2013
42422^322725+7576197150Enzo Doria04/2016
4243(13*2^322686+1)/11997138Lelio R Paula11/2013
4244(41*10^97085+373)/997086Robert Price04/2017
42452^322413+7797056Lelio R Paula12/2012
42462^322406+17797054Lelio R Paula12/2012
4247(14*10^97044+31)/997045Robert Price02/2015
42482^322302+25525597023Lelio R Paula07/2016
42492^322196-11309396991Enzo Doria07/2014
42502^322000-186146996932Enzo Doria03/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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