PRP Records

Probable Primes Top 10000

(205869 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 (> 30000) Who ? When ?
327010^100000+342909100001Milton L. Brown12/2007
325110^100000+346579100001Robert Price04/2012
325210^100000+829767100001Robert Price05/2012
325310^100000+871899100001Robert Price05/2012
325410^100000+1475997100001Robert Price07/2012
326310^100000+1751769100001Robert Price08/2012
326410^100000+2155489100001Robert Price10/2012
326510^100000+2483527100001Robert Price12/2012
326610^100000+2503087100001Robert Price12/2012
326710^100000+2686179100001Robert Price12/2012
326810^100000+2688933100001Robert Price12/2012
326910^100000+3667159100001Robert Price08/2013
325510^100000+5354043100001Robert Price05/2016
325610^100000+5717979100001Robert Price05/2016
325710^100000+6080631100001Robert Price07/2016
325810^100000+6308469100001Robert Price07/2016
325910^100000+6512023100001Robert Price08/2016
326010^100000+6596557100001Robert Price08/2016
326110^100000+7115409100001Robert Price10/2016
326210^100000+7235803100001Robert Price10/2016
327110^100000+7867333100001Robert Price12/2016
327210^100000+8743093100001Robert Price02/2017
327310^100000+8955391100001Robert Price03/2017
327410^100000+9180019100001Robert Price03/2017
327510^100000+9225987100001Robert Price04/2017
327610^100000+9265587100001Robert Price04/2017
327710^100000+9287049100001Robert Price04/2017
327810^100000+9425053100001Robert Price05/2017
327910^100000+9450769100001Robert Price05/2017
328010^100000+9528747100001Robert Smith05/2017
328110^100000+9548071100001Robert Price06/2017
328210^100000+10064287100001Robert Price08/2017
328310^100000+10229569100001Robert Price10/2017
328510^99999+309403100000Daniel Heuer01/2004
328410^100000-260199100000Patrick De Geest01/2010
328610^99999-5951199999Patrick De Geest07/2009
32872^332141-11307399985Enzo Doria07/2014
3288(3^209561+2)/72810125599978Lelio R Paula09/2013
32892^332085+186589799968Enzo Doria03/2016
3290(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
32912^332023+19199949Lelio R Paula02/2011
32922^331938+7114999924Enzo Doria04/2016
32932^331932-7879599922Lelio R Paula09/2016
32942^331921+77199919Lelio R Paula01/2013
3295(3^209419-2)/513275599912Lelio R Paula09/2013
32962^331860-11498999900Enzo Doria05/2015
32972^331746-1165599866Lelio R Paula09/2016
329811^95891-2899861Lelio R Paula08/2016
3299(2^331694-5)/1199849Lelio R Paula10/2013
3300(3^209246+7)/6499834Lelio R Paula09/2013
330125062^9617+9617^2506299823Hans Havermann04/2018
330215^84866-5299811Lelio R Paula08/2016
330313^89600+3099810Lelio R Paula08/2016
330422950^22309+22309^2295099798Hans Havermann03/2018
33055^142772-3899794Lelio R Paula08/2016
3306(23*2^331459+1)/47599778Lelio R Paula11/2013
33072^331416-331416+199767Robert Price10/2014
33082^331256-5799718Lelio R Paula12/2012
330928192^3443+3443^2819299714Hans Havermann03/2018
33102^331185+73799697Lelio R Paula01/2013
3311(4*10^99693+149)/999693Robert Price03/2017
33122^331154+188052799688Enzo Doria10/2016
3313(19^77951+1)/2099679Paul Bourdelais03/2010
331424354^12385+12385^2435499679Hans Havermann03/2018
33152^331110+187045999675Enzo Doria05/2016
33165*2^331075+799665Lelio R Paula08/2014
331725776^7351+7351^2577699659Hans Havermann02/2018
3318(16*10^99656-31)/399657Robert Price03/2016
33192^330968+34599632Lelio R Paula09/2016
33212*5^142528-799624Lelio R Paula11/2014
33202^330942+7732999624Enzo Doria05/2016
332214^86914-9999615Lelio R Paula08/2016
3323(19*2^330902+1)/7799611Lelio R Paula11/2013
332422971^21692+21692^2297199610Hans Havermann03/2018
33252^330845+7168799595Enzo Doria04/2016
3326(23*2^330770+1)/399573Lelio R Paula11/2013
332724494^11613+11613^2449499567Hans Havermann03/2018
33282^330735+841599562Lelio R Paula09/2016
33292^330720+7407199557Enzo Doria04/2016
333031^66738-299531Lelio R Paula09/2013
33317*3^208567+499513Lelio R Paula08/2014
3332(13*10^99508+47)/399509Robert Price01/2017
33332^330553+77999507Lelio R Paula01/2013
333415^84606-9499505Lelio R Paula08/2016
33356^127858+4799493Lelio R Paula08/2016
33365^142337+4899490Lelio R Paula08/2016
33377^117724-2099489Lelio R Paula08/2016
3338(29*10^99474-17)/399475Erik Branger09/2014
3339(9*2^330407-1)/799463Lelio R Paula03/2014
3340(68*10^99441+7)/399443Robert Price03/2016
334146^59791-45^5979199418Jean-Louis Charton01/2013
334223839^14802+14802^2383999417Hans Havermann02/2018
3343(2*10^99408+529)/999408Robert Price01/2017
334453^57646-299398Lelio R Paula09/2013
33452^330165+187002599390Enzo Doria05/2016
33462^330142-15599383Lelio R Paula12/2012
33472^330088-11525999367Enzo Doria06/2015
334824216^12671+12671^2421699354Hans Havermann01/2018
3349(746*10^99303+1)/999305Robert Price02/2017
33503^208107+4099293Lelio R Paula08/2016
3351(5*2^329833-1)/36999288Lelio R Paula02/2014
33528*3^208093+599287Lelio R Paula08/2014
33535^142043+5699284Lelio R Paula08/2016
335422*10^99275+799277Robert Price04/2016
33552^329778+187618999274Enzo Doria07/2016
3356(10^99239-13)/399239Robert Price02/2017
33573^207987+6299236Lelio R Paula08/2016
33582^329638+4999231Lelio R Paula12/2012
33597^117413-1899226Lelio R Paula08/2016
33602^329586-45890399216Enzo Doria04/2015
33612^329553+10199206Lelio R Paula12/2012
33622^329551-11289799205Enzo Doria06/2014
3363(3^207925+7)/5099204Lelio R Paula09/2013
33646^127458-1799399182Enzo Doria03/2013
336527197^4428+4428^2719799166Hans Havermann10/2017
3366(46*10^99143-1)/999144Robert Price12/2014
33677*10^99133+6999134Robert Price10/2017
336818^78968-306599127Enzo Doria03/2013
336925927^6654+6654^2592799122Hans Havermann10/2017
33702^329259+18999117Lelio R Paula12/2012
33718*10^99113+3999114Robert Price01/2017
33726^127364+7799109Lelio R Paula08/2016
33736^127285+1399047Lelio R Paula08/2016
3374(228581#+235862)/(2^3*11*71*151)99044Makoto Morimoto10/2017
33752^329007+7328399041Enzo Doria04/2016
33765*3^207543-899024Lelio R Paula08/2014
33772^328885+14999005Lelio R Paula12/2012
337823392^17075+17075^2339299004Hans Havermann09/2017
3379(2^328879-9)/11999001Lelio R Paula10/2013
33805^141618+5498987Lelio R Paula08/2016
33818*10^98982+5198983Robert Price05/2017
3382(21*2^328809-1)/770998979Lelio R Paula03/2014
33832^328794-279760198977Enzo Doria04/2016
33846^127176+598963Lelio R Paula11/2014
338524262^11989+11989^2426298960Hans Havermann09/2017
33862^328700-10970998949Enzo Doria04/2014
338746711!2-2^4671198916Robert Price09/2015
33889*7^117037+498909Lelio R Paula11/2014
3389(10^98890+149)/398890Serge Batalov12/2014
339022775^21978+21978^2277598889Hans Havermann08/2017
33912^328497-21693398888Enzo Doria05/2014
33922^328487+3276998885Lelio R Paula08/2016
33933^207250-11235898884Enzo Doria06/2014
339413^88754-9098867Lelio R Paula08/2016
33952^328406+70998861Lelio R Paula02/2013
3396(17*2^328413-1)/1617398860Lelio R Paula03/2014
33977^116976+7698857Lelio R Paula08/2016
33982^328335+115598839Lelio R Paula08/2016
3400(3*2^328311+1)/598832Lelio R Paula11/2013
3399287^40210+40210^28798832Norbert Schneider11/2014
3401(2^328284+9)/132598821Lelio R Paula10/2013
3402(21*2^328258+1)/212598814Lelio R Paula11/2013
340365^54491+4898788Lelio R Paula04/2016
34043^207042+9898785Lelio R Paula08/2016
34053^206977-11275698754Enzo Doria07/2014
34067^116846-5098747Lelio R Paula08/2016
34072^327967-2863598728Lelio R Paula08/2016
3408707^34642+34642^70798710Norbert Schneider12/2017
34096^126850-4798709Lelio R Paula08/2016
34108*6^126830-798694Lelio R Paula11/2014
341111^94770-27098693Enzo Doria08/2012
34122^327832+4398688Lelio R Paula12/2012
34132^327795+76198677Lelio R Paula02/2013
341410^98669+14741198670Patrick De Geest11/2016
341610^98669-9^(98669-1)98669Robert Price05/2016
341510^98669-10524998669Patrick De Geest11/2016
34172^327671-10980198639Enzo Doria04/2014
34185^141090-1498618Lelio R Paula08/2016
341920^75799+4798617Lelio R Paula08/2016
34202^327515-101798592Lelio R Paula08/2016
34216^126692+9768198586Mike Oakes04/2011
34222^327467-74198578Lelio R Paula08/2016
3423(2^327329+9)/1998535Lelio R Paula10/2013
34247^116577-6698519Lelio R Paula08/2016
3425(3*2^327250+1)/798512Lelio R Paula11/2013
3426(19*2^327192+1)/27598494Lelio R Paula11/2013
34272^327162-6694598486Lelio R Paula08/2016
34284*10^98472-398473Erik Branger11/2013
3429(6883*2^327047-1)/7798453Lelio R Paula05/2015
3430(71*10^98446+1)/998447Serge Batalov11/2010
343113^88363+9498432Lelio R Paula08/2016
343248^58543-47^5854398425Jean-Louis Charton11/2005
34336^126481+4198422Lelio R Paula08/2016
343478*10^98413-798415Robert Price05/2017
34357^116416+4698383Lelio R Paula08/2016
34367^116407-2498376Lelio R Paula07/2016
34382^326782-186067198372Enzo Doria03/2016
343717^79948+5898372Lelio R Paula08/2016
34393^206143-9898356Lelio R Paula08/2016
34408*5^140705+798350Lelio R Paula11/2014
34412^326585+1198312Lelio R Paula12/2012
34422^326582-45916198311Enzo Doria05/2015
3443(2^326548+9)/598301Lelio R Paula10/2013
34442^326538+7165998298Enzo Doria04/2016
344515^83575-5898292Lelio R Paula08/2016
344610^98288+398289Robert Price03/2011
344710^98288-11701798288Patrick De Geest11/2011
3448(44*10^98284-719)/998285Robert Price12/2017
34492^326421-279757398263Enzo Doria04/2016
34502^326401+1609598257Lelio R Paula07/2016
34517^116240-116240^798235Norbert Schneider05/2017
345217^79826-7898222Lelio R Paula08/2016
34532^326268-80998217Yves Minet04/2011
3454(418*10^98199+23)/998201Robert Price08/2017
345512*10^98198-798200Robert Price11/2017
345615^83496-7698199Lelio R Paula08/2016
3457(10223*2^326179+1)/612598190Lelio R Paula07/2014
34589*5^140471-498186Lelio R Paula11/2014
34592^326069-238398157Yves Minet10/2013
34602^325973+118598128Lelio R Paula07/2016
3461(25*2^325949-1)/1798121Lelio R Paula02/2014
34622^325945-184726998120Enzo Doria07/2015
34638*10^98111-6798112Robert Price10/2017
34642^325866+1598096Lelio R Paula12/2012
34652^325765+197430598066Enzo Doria06/2016
34662^325733-5869598056Lelio R Paula07/2016
34672^325717-364598051Lelio R Paula07/2016
3468(23*2^325583-1)/2198011Lelio R Paula02/2014
3469(7*10^98007-13)/398008Robert Price06/2016
34702^325512-45995997989Enzo Doria05/2015
3471(3^205354-8)/1797978Lelio R Paula09/2013
34722^325433+7681797966Enzo Doria05/2016
34735*10^97963+8197964Robert Price08/2017
34742^325390-10906197953Enzo Doria04/2014
347513^87921+2497940Lelio R Paula08/2016
3476961^32831-960^3283197926Jean-Louis Charton02/2011
34772^325215+1290997900Lelio R Paula07/2016
34787*10^97874-6997875Robert Price01/2017
3479(17^79537+5^79537)/2297865Robert Price06/2013
348015^83212+2297865Lelio R Paula08/2016
34812^325087-10905797861Enzo Doria04/2014
34822^325074+187065797858Enzo Doria05/2016
34842^325066-211197855Yves Minet08/2013
3483CopelandErdos(97855)97855Eric W. Weisstein10/2015
348518^77944-8997841Lelio R Paula07/2016
34866^125720-1766397830Enzo Doria02/2013
34872^324972-206997827Yves Minet05/2013
34882^324944-278831997818Enzo Doria03/2016
34904*10^97799-997800Erik Branger11/2013
34892^324882+57729457597800Lelio R Paula09/2016
34912^324863-186792197794Enzo Doria04/2016
34926^125662-1847397785Enzo Doria03/2013
349312^90604+1197779Lelio R Paula07/2016
34945^139830+2497737Lelio R Paula04/2016
34952^324612+115597718Lelio R Paula07/2016
349619^76404-4497702Lelio R Paula07/2016
34972^324505-298397686Yves Minet04/2011
3498(31*2^324496-1)/4597683Lelio R Paula02/2014
34996^125488-1784397649Enzo Doria02/2013
35007^115515-297622Lelio R Paula09/2013


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!