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) !!!


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 (> 50000) Who ? When ?
2751(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
2752(11*2^416691+1)/43125436Lelio R Paula05/2014
2753(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
27542^416641-2*416641+1125422Robert Price05/2018
2755(21*2^416566-1)/17125399Lelio R Paula05/2014
27562^416530+1870429125389Enzo Doria05/2016
2757(56*10^125385+691)/9125386Robert Price05/2019
27582^416490+1875109125376Enzo Doria09/2016
27592^416416-114929125354Enzo Doria05/2015
2760(77*10^125330-293)/9125331Robert Price09/2019
2761(172*10^125292-1)/9125294Serge Batalov12/2014
27622^416134+1865899125269Enzo Doria03/2016
2763153^57337-152125264Norbert Schneider12/2018
2764(9*2^415992+1)/13560845125220Lelio R Paula05/2014
2765(23^91943-1)/22125201Robert Price01/2012
276643125^27010-106125185Enzo Doria08/2012
2767(38*10^125166+349)/9125167Robert Price10/2018
27682^415765-112603125158Enzo Doria06/2014
27698*10^125088-13125089Robert Price08/2019
2770(25*10^125076-13)/3125077Robert Price09/2019
2771(29*10^125021-113)/3125022Robert Price10/2019
27722^415290-113591125015Enzo Doria08/2014
27732^415276-460919125011Enzo Doria06/2015
27742^415259+77243125006Enzo Doria05/2016
27752^415144-3683124971Yves Minet10/2011
27762^414874+79124890Lelio R Paula01/2015
2777(2^414765+7)/1389124854Lelio R Paula05/2014
27782^414618+79459124813Enzo Doria06/2016
2779(61*10^124809-1)/3124811Robert Price01/2020
27802^414432-1846709124757Enzo Doria07/2015
27812*10^124751-51124752Robert Price04/2018
2782(56*10^124735+367)/9124736Robert Price06/2019
2783(13*2^414274-1)/153124708Lelio R Paula05/2014
278456*10^124656-3124658Robert Price03/2020
2785(7*10^124648+197)/3124649Robert Price07/2018
27872^414032-5124637Henri Lifchitz07/2006
27862^414032+1872331124637Enzo Doria05/2016
278814120^30009-30009^14120124533Norbert Schneider02/2015
2789(85*10^124485-49)/9124486Robert Price12/2020
279064^68909-63^68909124463Robert Price07/2013
27912^413387+76253124442Enzo Doria04/2016
27922^413352+524287124432Paul Underwood09/2018
2793287117#+391613124424Nicolas PALAU01/2017
2794(4*10^124420+83)/3124421Robert Price02/2018
2795(27*2^413207-1)/108335124385Lelio R Paula05/2014
2796(41*10^124335-383)/9124336Robert Price11/2018
2797(304*10^124329-43)/9124331Robert Price02/2020
27982^412868-120599124286Paul Bourdelais02/2012
279910^124248-1000001124248Robert Price08/2020
280045^75145-2124231Lelio R Paula08/2015
28012^412645-112213124219Enzo Doria06/2014
28022^412248+74611124100Enzo Doria04/2016
2803(22*10^124096-13)/9124097Robert Price06/2018
28042^412192-3329124083Yves Minet12/2014
2805(25*2^412191-1)/23124082Lelio R Paula05/2014
2806(25*10^124076-67)/3124077Robert Price06/2019
2807F(593689)124074Henri Lifchitz01/2005
2808(11*2^412161+1)/19124073Lelio R Paula05/2014
2809(266*10^124022-11)/3124024Robert Price04/2020
28102^411884-113279123990Enzo Doria07/2014
2811(2^411832+1)/257123972Lelio R Paula05/2014
2812(2^411833+2)/514123972Stefano Morozzi03/2020
2813(26*10^123970-89)/9123971Robert Price06/2018
28142^411790-1853531123962Enzo Doria08/2015
2815(5^177337+1)/6123953Paul Bourdelais11/2008
28162^411711-113257123938Enzo Doria07/2014
2817(23*2^411675-1)/3123928Lelio R Paula05/2014
2818(11*10^123899-179)/3123900Robert Price09/2018
28192^411325-351103123822Enzo Doria06/2015
28202^411052+1872481123739Enzo Doria05/2016
28212^410997+39123723Lelio R Paula05/2014
2822(649^43987-1)/648123700Michael Stocker05/2020
2823(148*10^123688-1)/3123690Robert Price03/2020
28248*10^123657+87123658Robert Price10/2019
2825155^56438+154123618Norbert Schneider01/2019
28262^410596-39123602Lelio R Paula05/2014
28272^410540-115079123585Enzo Doria06/2015
2828(7*10^123563+107)/3123564Robert Price02/2018
28299*10^123549+89123550Robert Price11/2019
2830(197*10^123545+7)/3123547Robert Price12/2020
2831(3*2^410392-1)/9229123537Lelio R Paula05/2014
28322^410206-113081123485Enzo Doria07/2014
2833(25*2^410192+1)/10397123478Lelio R Paula04/2014
28342^409909-189123395Enzo Doria05/2014
28352^409896-109043123391Enzo Doria04/2014
28362^409890+75409123390Enzo Doria04/2016
2837133^58076-2123345Lelio R Paula10/2017
2838F(590041)123311Henri Lifchitz01/2005
28392^409566-113501123292Enzo Doria08/2014
28402^409533+77747123282Enzo Doria05/2016
28412^409436-112799123253Enzo Doria06/2014
28422^409225+1873787123189Enzo Doria06/2016
28432^409174+73009123174Enzo Doria04/2016
28442^409058-112685123139Enzo Doria06/2014
2845(13*10^123137-61)/3123138Robert Price11/2018
28464*10^123113+21123114Robert Price12/2018
28472^408778+77689123055Enzo Doria05/2016
28482^408690-75123028Lelio R Paula11/2013
2849(29*10^122996+673)/9122997Robert Price12/2018
28502^408574-2787341122994Enzo Doria03/2016
28513*10^122977+37122978Robert Price08/2018
2852Phi(157825,10)122961Maksym Voznyy06/2015
2853(68*10^122933-419)/9122934Robert Price07/2019
2854(13*2^408283+1)/1665122904Lelio R Paula05/2014
2855(266*10^122872-17)/3122874Robert Price07/2020
2856(16*10^122871+77)/3122872Robert Price03/2019
2857(11*2^408100-1)/35122850Lelio R Paula04/2014
2858(19*10^122836-43)/3122837Robert Price05/2019
2859(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
2860(32*10^122733-77)/9122734Robert Price06/2018
2861(21*2^407604-1)/215122701Lelio R Paula04/2014
2862(22*10^122681+161)/3122682Robert Price05/2019
2863(21*2^407433-1)/13122650Lelio R Paula04/2014
2864(26*10^122625-131)/3122626Robert Price10/2019
2865(73*10^122592-1)/9122593Robert Price01/2015
2866(5*10^122592+91)/3122593Robert Price04/2018
2867(85*10^122585-1)/3122587Robert Price02/2020
28682^407179-112075122574Enzo Doria06/2014
2869(21*2^407131+1)/207517523122552Lelio R Paula04/2014
2870(66^67349+1)/67122543Paul Bourdelais09/2017
28712^407008-1867919122522Enzo Doria04/2016
287211^117642-300122512Enzo Doria10/2012
2873(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
28742^406949+72197122504Enzo Doria04/2016
2875(19*10^122501+149)/3122502Robert Price05/2019
28762^406826-65122467Lelio R Paula11/2013
28772^406821-2797363122466Enzo Doria04/2016
28782^406758-17122447Lelio R Paula11/2013
2879(30^82883-1)/29122427Robert Price12/2011
288027496^27577+27577^27496122422Norbert Schneider12/2020
2881(2^406583-1)/813167122388Jens K. Andersen02/2009
28824*10^122377+19122378Robert Price10/2018
2883Phi(246362,10)122365Makoto Kamada09/2019
28843*10^122345-97122346Robert Price07/2018
288597^61575-2122336Lelio R Paula12/2014
2886208^52765+52765^208122313Norbert Schneider11/2020
28872^406298+2799109122308Enzo Doria04/2016
28887*10^122294+57122295Robert Price06/2019
2889(27*2^406241-1)/10277122289Lelio R Paula04/2014
28902^406229-1849993122288Enzo Doria08/2015
28913*10^122274+7122275Robert Price07/2015
28922^406117+1876577122254Enzo Doria07/2016
28933^256199-2^256199122238Mike Oakes06/2005
28942^405992-78557122216Jorge Menendez03/2018
2895(8*10^122203+43)/3122204Robert Price06/2018
2896(58*10^122170+329)/9122171Robert Price05/2019
28972^405774+179149122151Enzo Doria06/2016
289834*10^122082-9122084Robert Price06/2020
28995*10^122082+41122083Robert Price03/2019
29002^405514-3311122072Yves Minet12/2014
29012^405514-115511122072Enzo Doria07/2015
290223*10^122070-7122072Robert Price02/2020
29032^405422-113261122045Enzo Doria07/2014
29042^405173+71237121970Enzo Doria04/2016
2905(2^405016+1)/257121920Lelio R Paula04/2014
29062^404858+71329121875Enzo Doria04/2016
29072^404813-114703121861Enzo Doria04/2015
29082^404764+77791121847Enzo Doria05/2016
2909317^48694+48694^317121787Norbert Schneider08/2015
29102^404536-115259121778Enzo Doria06/2015
29112^404501-631121767Yves Minet07/2012
291263^67620+2121672Lelio R Paula08/2015
2913(16*10^121633+167)/3121634Robert Price06/2019
2914(17*10^121621+1)/9121622Serge Batalov05/2010
2915(15*2^403912+1)/271121589Lelio R Paula05/2014
2916(10^121543-79)/3121543Robert Price01/2018
29172^403676+76831121519Enzo Doria05/2016
2918(7*10^121487+143)/3121488Robert Price03/2018
29192^403363-113635121425Enzo Doria08/2014
29202^403336-1861469121417Enzo Doria03/2016
2921p(24442)#/2-64121381Robert Price04/2017
292211^116555-720121380Enzo Doria11/2012
29232^403100-461267121346Enzo Doria07/2015
29242^403093-112213121344Enzo Doria06/2014
2925(316^48539+1)/317121330Eric Chen10/2017
2926(23*10^121320-71)/3121321Robert Price07/2020
29272^403004+1866361121317Enzo Doria03/2016
29282^402953+89121301Lelio R Paula10/2013
29292^402944-2788319121299Enzo Doria03/2016
2930(44*10^121297-719)/9121298Robert Price12/2018
2931(27*2^402865+1)/5121276Lelio R Paula04/2014
29322^402828-113183121264Enzo Doria07/2014
2933(17*10^121242+1)/9121243Serge Batalov05/2010
2934(15*2^402757+1)/101121242Lelio R Paula05/2014
29352^402715+1874223121230Enzo Doria06/2016
2936(35*10^121229-593)/9121230Robert Price07/2018
2937(91^61879+1)/92121222Paul Bourdelais09/2017
29387*10^121144+9121145Robert Price09/2015
29392^401725-113251120932Enzo Doria07/2014
2940(15*2^401677-1)/19120917Lelio R Paula05/2014
29412^401652+73711120910Enzo Doria04/2016
2942(2^401632+3)/79120902Lelio R Paula04/2014
294340450^973+973^40450120870Hans Havermann01/2021
294410^120841+88417120842Patrick De Geest04/2020
294510^120841-123456789120841Robert Price02/2020
294610^120841-176853120841Patrick De Geest04/2020
29472^401406-2791331120836Enzo Doria03/2016
2948(28^83497+1)/29120832Robert Price07/2013
2949(22*10^120828+161)/3120829Robert Price05/2019
29502^401369+1867367120825Enzo Doria03/2016
2951(10^120782+29)/3120782Serge Batalov12/2014
29522^401215-1657120778Yves Minet07/2014
29532^401159+53120761Lelio R Paula10/2013
295427782^22179+22179^27782120739Hans Havermann01/2021
29552^401031-113047120723Enzo Doria07/2014
2956(71*10^120703-287)/9120704Robert Price09/2019
2957(29*2^400909-1)/303120685Lelio R Paula04/2014
2958(2^400846+538)/2120667Stefano Morozzi09/2020
2959(2^400709+3546)/2120626Stefano Morozzi09/2020
2960(2^400700+3126)/2120623Stefano Morozzi09/2020
2961(2^400693+2634)/2120621Stefano Morozzi09/2020
29622^400571-15120584Lelio R Paula10/2013
2963(10^120574+359)/9120574Serge Batalov12/2014
29642^400424-216413120540Enzo Doria04/2013
2965(2^400346+1722)/2120516Stefano Morozzi09/2020
2966(17*2^400200-1)/587120471Lelio R Paula05/2014
29682^400166+1874899120462Enzo Doria06/2016
2967(2^400165+1602)/2120462Stefano Morozzi09/2020
2969(2^400084+1638)/2120437Stefano Morozzi09/2020
2970(3*2^400045-1)/865120424Lelio R Paula04/2014
29712^399966+73759120402Enzo Doria04/2016
2972(112*10^120395-1)/3120397Serge Batalov12/2014
29732^399918-95120388Lelio R Paula04/2013
2974(28*10^120381-67)/3120382Robert Price10/2020
2975(49*10^120380-139)/9120381Robert Price03/2019
2976(2^399874+2194)/2120374Stefano Morozzi09/2020
29772^399792-1849259120350Enzo Doria08/2015
29789*10^120342-7120343Robert Price09/2015
2979(2^399751+786)/2120337Stefano Morozzi09/2020
2980(13*10^120306-37)/3120307Robert Price01/2019
2981(2^399604+3070)/2120293Stefano Morozzi09/2020
2982(2^399549+1062)/2120276Stefano Morozzi09/2020
29832^399526-1861721120270Enzo Doria11/2015
2984(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
29852^399322-2798111120208Enzo Doria04/2016
298672^64693-71^64693120157Robert Price03/2014
29872^399111-28489120145Enzo Doria08/2015
29892^398877+105120074Donovan Johnson01/2006
2988(101*10^120072-87)/7120074Hans Havermann02/2015
2990(88^61751+1)/89120072Paul Bourdelais09/2017
29912^398710+57120024Lelio R Paula04/2013
2992(2^398698+1138)/2120020Stefano Morozzi09/2020
29932^398691-115057120018Enzo Doria06/2015
2994L(574219)120005Renaud Lifchitz03/2004
29952^398571+60413119982Yves Minet03/2011
2996p(24179)#/2-64119949Robert Price04/2017
29972^398448+1872001119945Enzo Doria05/2016
2998634^42803+42803^634119938Norbert Schneider07/2019
2999(68*10^119931-11)/3119933Robert Price01/2020
30008*10^119930-3119931Ray Chandler04/2011


Find by discoverer :


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

Go back
Valid XHTML 1.0!    Valid CSS!