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 ?
2751(2^400693+2634)/2120621Stefano Morozzi09/2020
27522^400571-15120584Lelio R Paula10/2013
2753(10^120574+359)/9120574Serge Batalov12/2014
27542^400424-216413120540Enzo Doria04/2013
2755(2^400346+1722)/2120516Stefano Morozzi09/2020
2756(17*2^400200-1)/587120471Lelio R Paula05/2014
27582^400166+1874899120462Enzo Doria06/2016
2757(2^400165+1602)/2120462Stefano Morozzi09/2020
2759(2^400084+1638)/2120437Stefano Morozzi09/2020
2760(3*2^400045-1)/865120424Lelio R Paula04/2014
27612^399966+73759120402Enzo Doria04/2016
2762(112*10^120395-1)/3120397Serge Batalov12/2014
27632^399918-95120388Lelio R Paula04/2013
2764(49*10^120380-139)/9120381Robert Price03/2019
2765(2^399874+2194)/2120374Stefano Morozzi09/2020
27662^399792-1849259120350Enzo Doria08/2015
27679*10^120342-7120343Robert Price09/2015
2768(2^399751+786)/2120337Stefano Morozzi09/2020
2769(13*10^120306-37)/3120307Robert Price01/2019
2770(2^399604+3070)/2120293Stefano Morozzi09/2020
2771(2^399549+1062)/2120276Stefano Morozzi09/2020
27722^399526-1861721120270Enzo Doria11/2015
2773(10^(2*60126+1)+36*10^60126-1)/9120253Robert Price10/2015
27742^399322-2798111120208Enzo Doria04/2016
277572^64693-71^64693120157Robert Price03/2014
27762^399111-28489120145Enzo Doria08/2015
27782^398877+105120074Donovan Johnson01/2006
2777(101*10^120072-87)/7120074Hans Havermann02/2015
2779(88^61751+1)/89120072Paul Bourdelais09/2017
27802^398710+57120024Lelio R Paula04/2013
2781(2^398698+1138)/2120020Stefano Morozzi09/2020
27822^398691-115057120018Enzo Doria06/2015
2783L(574219)120005Renaud Lifchitz03/2004
27842^398571+60413119982Yves Minet03/2011
2785p(24179)#/2-64119949Robert Price04/2017
27862^398448+1872001119945Enzo Doria05/2016
2787634^42803+42803^634119938Norbert Schneider07/2019
2788(68*10^119931-11)/3119933Robert Price01/2020
27898*10^119930-3119931Ray Chandler04/2011
2790(2^398398+774)/2119930Stefano Morozzi09/2020
2791(10^119880+179)/9119880Serge Batalov12/2014
2792(9*2^398145+1)/73119853Lelio R Paula04/2014
2793(10^119836+77)/3119836Robert Price01/2018
27942^398029+1872527119819Enzo Doria05/2016
27952^397897-113541119779Enzo Doria08/2014
2796(2^397696+1042)/2119719Stefano Morozzi09/2020
2797(19*10^119716+101)/3119717Robert Price09/2019
2798(21*2^397661-1)/27593119705Lelio R Paula04/2014
279977*10^119688+3119690Robert Price06/2020
2800(2^397504+1698)/2119661Stefano Morozzi09/2020
2801(58^67853-1)/57119653Paul Bourdelais09/2017
28022^397426+73849119638Enzo Doria04/2016
28032^396933-112723119489Enzo Doria06/2014
280411^114738-150119488Enzo Doria10/2012
2805(4*10^119474+149)/9119474Robert Price04/2018
28062^396790-21119446Lelio R Paula04/2013
2807(2^396633-7)/5119398Lelio R Paula04/2014
2808(2^396577+2522)/2119382Stefano Morozzi09/2020
2809105^59050+104119352Norbert Schneider11/2016
2810126^56824-125119352Norbert Schneider12/2018
2811139^55690-138119345Norbert Schneider04/2019
2812790^41179+41179^790119322Norbert Schneider04/2019
28132^396374+73729119321Enzo Doria04/2016
281488*10^119295+3119297Robert Price05/2020
28152^396258-459491119286Enzo Doria05/2015
2816(2^396248+3126)/2119283Stefano Morozzi09/2020
28172^396128-396128-1119247Karsten Bonath06/2018
2818(2^395986+5)/76881119199Lelio R Paula04/2014
2819(23*2^395942-1)/91119190Lelio R Paula04/2014
2820(2^395902+202)/2119179Stefano Morozzi09/2020
2821(2^395825+582)/2119155Stefano Morozzi09/2020
2822(2^395733+1130)/2119128Stefano Morozzi09/2020
2823(11*2^395548+1)/3119073Lelio R Paula04/2014
2824(30^80599+1)/31119054Robert Price07/2013
2825(43*10^119024-403)/9119025Robert Price01/2019
28266*10^118964+43118965Robert Price07/2020
2827(8*10^118960+49)/3118961Robert Price05/2020
2828(194*10^118925-17)/3118927Robert Price09/2020
28292^395062-109121118926Enzo Doria04/2014
28302^395055-4627118924Yves Minet05/2019
2831(2^395054+702)/2118923Stefano Morozzi09/2020
2832(2^395011+2526)/2118910Stefano Morozzi09/2020
2833(2^394918+78557)/3118882Lelio R Paula01/2015
2834(2^394858+1018)/2118864Stefano Morozzi09/2020
2835(16*10^118852+77)/3118853Robert Price03/2019
2836(2^394739+3)/1883118826Lelio R Paula04/2014
283710^118772-40000000001118772Robert Price09/2020
2838(2^394513+2034)/2118760Stefano Morozzi09/2020
28392^394266+71389118686Enzo Doria04/2016
28402^394215-51261118671Tony Prest / Never Odd Or Even04/2018
2841(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
2842(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
2843(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
2844(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
2845(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
2846(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
2847(2^394131+2214)/2118645Stefano Morozzi09/2020
2848(17*10^118635+13)/3118636Robert Price01/2019
28495^169727+2118635Lelio R Paula08/2013
28502^394034-3118617M. Frind & P. Underwood09/2002
2851(7*10^118607+179)/3118608Robert Price09/2018
28523^248572-6242118599Enzo Doria05/2014
2853(3*2^393964-1)/181118594Lelio R Paula04/2014
28547^140303-6118570Robert Price11/2014
2855(2^393864+2686)/2118565Stefano Morozzi09/2020
2856(2^393862+3150)/2118564Stefano Morozzi09/2020
2857(2^393661+2666)/2118504Stefano Morozzi09/2020
2858(2^393650+1614)/2118501Stefano Morozzi09/2020
285910^118485-50001118485Robert Price08/2020
2860(2^393528+1030)/2118464Stefano Morozzi09/2020
28612^393427+75683118434Enzo Doria04/2016
28622^393376-114749118418Enzo Doria04/2015
2863(2^393234+2010)/2118375Stefano Morozzi09/2020
2864(2^393205+3030)/2118367Stefano Morozzi09/2020
2865(2^393191+2174)/2118362Stefano Morozzi09/2020
28662^393180+73118359Lelio R Paula04/2013
2867p(23881)#/2+256118328Robert Price05/2017
2868(10^118324+359)/9118324Serge Batalov12/2014
2869(2^393048+570)/2118319Stefano Morozzi09/2020
2870p(23879)#/2+64118317Robert Price03/2017
2871(238*10^118265-1)/3118267Robert Price04/2020
2873(53*10^118216+1)/9118217Serge Batalov11/2010
2872(2^392707+1710)/2118217Stefano Morozzi09/2020
2874(7*2^392697+1)/15118214Renaud Lifchitz03/2011
2875(157^53819-1)/156118179Alexander Zhirkov06/2016
2876(19*2^392551+1)/3118171Lelio R Paula04/2014
28772^392516-29219118160Enzo Doria07/2015
287866*10^118155+7118157Robert Price07/2020
2879Phi(177231,10)118152Maksym Voznyy09/2015
28802^392413-112123118129Enzo Doria06/2014
2881(2^392342+5)/27118106Lelio R Paula04/2014
28822^392300-1841429118095Enzo Doria06/2015
28832^392220+75241118070Enzo Doria04/2016
288410^118009+664447118010Patrick De Geest07/2018
288510^118009-20001118009Robert Price01/2018
2886(14*10^117991+61)/3117992Robert Price12/2018
28872^391933+5897117984Yves Minet02/2011
28882^391912-1849259117978Enzo Doria08/2015
2889(2^391812+5)/14181117944Lelio R Paula04/2014
2890(46*10^117902+683)/9117903Robert Price03/2019
2891(7*2^391521+1)/285117858Lelio R Paula04/2014
28922^391324+90901117801Yves Minet02/2011
28932^391301-1859923117794Enzo Doria03/2016
28942^391261-4131117782Yves Minet02/2018
2895(2^391211+554)/2117766Stefano Morozzi09/2020
2896(2^391115-7)/11791117734Lelio R Paula04/2014
2897(85*10^117719+473)/9117720Robert Price01/2020
2898(2^391049+582)/2117718Stefano Morozzi09/2020
28992^390960+1880881117691Enzo Doria11/2016
29002^390897-1860553117672Enzo Doria11/2015
29012^390889-115003117670Enzo Doria06/2015
29022^390779-30337117637Paul Bourdelais02/2012
290311^112916-780117590Enzo Doria12/2012
2904(2^390473+1002)/2117544Stefano Morozzi09/2020
2905(16^97613-5^97613)/11117537Robert Price07/2013
2906(2^390418+1722)/2117528Stefano Morozzi09/2020
2907(2^390403+654)/2117523Stefano Morozzi09/2020
2908(17*2^390272+1)/1983117482Lelio R Paula04/2014
290931^78759-30117459Theodore Burton02/2007
2910(2^390176+1222)/2117455Stefano Morozzi09/2020
2911(2^390133+1242)/2117442Stefano Morozzi09/2020
2912(2^390013+2634)/2117406Stefano Morozzi09/2020
29133*10^117402+61117403Robert Price09/2020
29142^389998+37117402Lelio R Paula03/2013
2915(2^389977+314)/2117395Stefano Morozzi09/2020
2916(2^389768+1582)/2117332Stefano Morozzi09/2020
291729^80192-1*80192^29117273Dylan Delgado12/2019
2918(13*10^117249+161)/3117250Robert Price11/2018
29192^389478+43117245Lelio R Paula03/2013
2920(298*10^117229-7)/3117231Robert Price06/2020
2921(29*2^389351-1)/9117207Lelio R Paula04/2014
29225*10^117205+23117206Robert Price03/2019
2923(2^389341-7)/3865117200Lelio R Paula03/2014
2924(2^389276+2650)/2117184Stefano Morozzi09/2020
292510^117142+209223117143Patrick De Geest04/2018
292710^117142-1000000001117142Robert Price03/2018
292610^117142-966057117142Patrick De Geest04/2018
292810^117135+360577117136Patrick De Geest07/2018
292910^117135-401117135Robert Price01/2018
29304*10^117123+79117124Robert Price08/2018
29312^389033-12797413117111Enzo Doria04/2016
2932(2^388987+2634)/2117097Stefano Morozzi09/2020
29332^388960-109505117089Enzo Doria04/2014
29347*10^117082-57117083Robert Price06/2020
2935(2^388928-5)/569117077Lelio R Paula03/2014
29362^388888-1529117067Yves Minet01/2013
293710^117059+28879117060Patrick De Geest05/2016
2938(10^117059-71)/1117059Serge Batalov12/2014
2939(2^388854+3630)/2117057Stefano Morozzi09/2020
2940(2^388842+2098)/2117053Stefano Morozzi09/2020
2941(2^388789+3150)/2117037Stefano Morozzi09/2020
2942(693^41189-1)/692117005Michael Stocker05/2020
2943(26*10^116999-503)/9117000Robert Price07/2018
2944(2^388609+1554)/2116983Stefano Morozzi09/2020
29453^245154-6256116969Enzo Doria05/2014
29465*10^116966-43116967Robert Price01/2019
29472^388536-113495116961Enzo Doria08/2014
29482^388469-43116941Lelio R Paula03/2013
2949(7*2^388372-1)/111116911Lelio R Paula04/2014
2950(7*2^388335-1)/25116900Lelio R Paula04/2014
29512^388180+93116854Donovan Johnson07/2008
2952(2^388167+2510)/2116850Stefano Morozzi09/2020
2953(85*10^116842+293)/9116843Robert Price12/2019
2954(2^388081+7)/1179116821Lelio R Paula03/2014
29552^387946-113261116784Enzo Doria07/2014
29562^387745+75557116723Enzo Doria04/2016
2957(206*10^116687-17)/9116689Robert Price01/2020
2958(7*10^116684+179)/3116685Robert Price09/2018
29592^387554+71455116666Enzo Doria04/2016
2960(2^387447+78557)/365116631Lelio R Paula12/2014
2961(145*10^116610-1)/9116612Serge Batalov12/2014
2962(25*10^116601-331)/9116602Robert Price08/2018
2964(17*2^387284-1)/59116584Lelio R Paula04/2014
2963(2^387284+3726)/2116584Stefano Morozzi09/2020
296510^116557+987654321116558Robert Price12/2019
296610^116557+9141116558Patrick De Geest02/2020
296710^116557-609431116557Patrick De Geest02/2020
2968(2^387076+2046)/2116522Stefano Morozzi09/2020
2969(2^387073+2570)/2116521Stefano Morozzi09/2020
2970(31*2^386968+1)/7116490Lelio R Paula03/2014
29712^386947+1869143116483Enzo Doria05/2016
2972(30^78857-1)/29116480Robert Price12/2011
2973(2^386903-3)/5116469Lelio R Paula03/2014
29742^386389-1864783116315Enzo Doria03/2016
2975(31*2^386231-1)/1711116266Lelio R Paula03/2014
2976297^47012+47012^297116250Norbert Schneider07/2018
2977(2^386087-5)/40959116220Lelio R Paula03/2014
2978(2^386054+714)/2116214Stefano Morozzi09/2020
29792^385969-823116189Yves Minet05/2012
298057^66162+2116173Lelio R Paula08/2013
29812^385854+75049116154Enzo Doria04/2016
2982(2^385832+2590)/2116147Stefano Morozzi09/2020
29832^385775-109587116130Enzo Doria04/2014
2984(14*10^116112-101)/3116113Robert Price02/2019
2985Phi(236354,10)/24817171116109Makoto Kamada08/2019
29862^385622+71839116084Enzo Doria04/2016
29882^385564+781116067Lelio R Paula01/2012
2987(2^385565+1562)/2116067Stefano Morozzi09/2020
2989(2^385557+2214)/2116064Stefano Morozzi09/2020
2990(266*10^116024-17)/3116026Robert Price07/2020
29912^385410+71893116020Enzo Doria04/2016
2992(25*2^385091+1)/27115924Lelio R Paula04/2014
2993(11*10^115910-131)/3115911Robert Price09/2018
29942^384953-111943115883Paul Bourdelais02/2012
299543^70942-2115882Lelio R Paula04/2014
2996(94*10^115879-7)/3115881Robert Price03/2020
29977*10^115863+3115864Robert Price08/2015
29982^384834+93115847Donovan Johnson07/2008
29992^384809+71297115840Enzo Doria04/2016
3000(7*2^384759-1)/5115825Lelio R Paula04/2014


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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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