PRP Records

Probable Primes Top 10000

(259919 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 ?
72512^257636-11023577557Enzo Doria05/2014
7253(23*10^77556+97)/377557Robert Price02/2017
7252(2^257639+2630)/277557Stefano Morozzi01/2020
7254(2^257625+3354)/277553Stefano Morozzi01/2020
72552^257621-11007177552Enzo Doria04/2014
725619580^9129+9129^1958077546Hans Havermann03/2020
72572^257567-6487577536Lelio R Paula06/2013
7258(2^257429+2394)/277494Stefano Morozzi01/2020
7259(2^257373+1206)/277477Stefano Morozzi01/2020
72602*7^91674+977474Lelio R Paula10/2014
7261(2^257248+2442)/277440Stefano Morozzi01/2020
7262(17*10^77427-47)/377428Robert Price05/2017
726310^77418+84168377419Patrick De Geest06/2013
726410^77418-3377418Robert Price05/2011
726519^60539-3677415Lelio R Paula03/2015
726637401!!-102477397Robert Price11/2015
7267(2^257095+1410)/277394Stefano Morozzi01/2020
726811^74313-1875077390Enzo Doria12/2012
72702^257044-11288377378Enzo Doria06/2014
72698*10^77377+5177378Robert Price05/2017
72712*7^91553+977372Lelio R Paula10/2014
7272713^27118+27118^71377371Norbert Schneider12/2016
727318652^14043+14043^1865277359Hans Havermann03/2020
72742^256920-11115577341Enzo Doria05/2014
72752^256896-655577334Lelio R Paula06/2013
7276(52*10^77322-7)/977323Robert Price12/2014
72772^256849-11293977320Enzo Doria06/2014
727817275^18246+18246^1727577316Norbert Schneider01/2020
7279(4*10^77309-31)/977309Erik Branger05/2011
7280(3^161988+7)/4186477284Lelio R Paula10/2012
7281(14^67421-1)/1377272Paul Bourdelais09/2008
7282(2^256679+3554)/277268Stefano Morozzi01/2020
72845*3^161923-477258Lelio R Paula06/2014
728320465^5958+5958^2046577258Hans Havermann02/2020
7285(2^256591+954)/277242Stefano Morozzi01/2020
72862^256552-149977230Yves Minet05/2013
7287(2^256493+3126)/277212Stefano Morozzi01/2020
72882^256460-11275777203Enzo Doria06/2014
7289(2^256444+2578)/277198Stefano Morozzi01/2020
72902^256398+2329977184Yves Minet02/2011
72912^256391-1155*25639177182Henri Lifchitz03/2005
7292(2^256391-9)/5659377177Lelio R Paula10/2012
7293(2^256338+3834)/277166Stefano Morozzi01/2020
7294(2^256339+546)/277166Stefano Morozzi01/2020
7295(2^256308+9)/1058577153Lelio R Paula10/2012
729621^58348-277149Lelio R Paula08/2013
7297(17*2^256291-1)/478577149Lelio R Paula02/2014
7298(5*2^256274-1)/214177144Lelio R Paula02/2014
7299(2^256244+2326)/277137Stefano Morozzi01/2020
730019^60321+8277136Lelio R Paula03/2015
73015*2^256233-377135Lelio R Paula06/2014
7302(2^256155+1566)/277111Stefano Morozzi01/2020
73033*2^256149+777110Lelio R Paula06/2014
7304(2^256128+1890)/277102Stefano Morozzi01/2020
73053^161594-10677100Lelio R Paula02/2015
73062^256114-18577098Lelio R Paula03/2012
73078^85349-85349^877078Norbert Schneider05/2017
73082^256043-278637777077Enzo Doria03/2016
73092^255973+186994777056Enzo Doria05/2016
731012^71393-4377046Lelio R Paula02/2015
7311(2^255882+3630)/277028Stefano Morozzi01/2020
731215^65490+4477023Lelio R Paula02/2015
7313(3^161411-7)/94077010Lelio R Paula10/2012
7314lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
7315(570^27943-1)/56977005Serge Batalov12/2016
73162^255750-7576989Lelio R Paula03/2012
73173*6^98926-576980Lelio R Paula10/2014
7318(2^255708+478)/276976Stefano Morozzi01/2020
731918^61320-143376974Enzo Doria03/2013
73206^98916-1709376972Enzo Doria02/2013
7321(2^255691+806)/276971Stefano Morozzi01/2020
73222^255659-11013176962Enzo Doria04/2014
732369805!4-12876956Robert Price11/2019
732412^71303+9176949Lelio R Paula02/2015
732518^61298+5976946Lelio R Paula02/2015
7326(223^32768+1)/13107476945Lelio R Paula02/2009
7327(2^255613-5)/28151776942Lelio R Paula10/2012
732818^61290-1176936Lelio R Paula02/2015
7329(2^255567+1286)/276934Stefano Morozzi01/2020
733163^42752-276926Lelio R Paula08/2013
7330(11*2^255545-1)/11776926Lelio R Paula02/2014
73322^255517+5638776919Yves Minet02/2011
733318376^15329+15329^1837676914Hans Havermann03/2020
73342^255499-11256776913Enzo Doria06/2014
73352^255492+34576911Lelio R Paula06/2013
7336(2^255488+1678)/276910Stefano Morozzi01/2020
733710^76875+21759176876Patrick De Geest05/2013
733910^76875-5376875Robert Price05/2011
733811^73819-588076875Enzo Doria01/2013
73402^255313+1891576857Lelio R Paula06/2013
7341(2^255320-1017)/144666776853Lelio R Paula10/2012
73422^255296+577576852Lelio R Paula06/2013
734314^67052-2976851Lelio R Paula02/2015
7344(8*10^76840+43)/376841Robert Price10/2017
7345(2^255246+1642)/276837Stefano Morozzi01/2020
7346(2^255243+2250)/276836Stefano Morozzi01/2020
7347(2^255240+1218)/276835Stefano Morozzi01/2020
7348(7*10^76818-313)/976818Robert Price11/2016
734910^76801+6976802Robert Price03/2011
735010^76801-8094376801Patrick De Geest06/2013
73512^255105+5776795Lelio R Paula03/2012
7352(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
7353(2^255097-7)/2002005576785Lelio R Paula10/2012
7354(2^255063+3098)/276782Stefano Morozzi01/2020
73552^255055+186935376780Enzo Doria05/2016
735617^62396-9076776Lelio R Paula03/2015
735718797^12130+12130^1879776765Hans Havermann03/2020
73587^90833-6076763Lelio R Paula02/2015
735913^68901-5676752Lelio R Paula03/2015
73602^254961+186991776751Enzo Doria05/2016
7361(2^254950+594)/276748Stefano Morozzi01/2020
736220734^5027+5027^2073476743Hans Havermann03/2020
73639*5^109791-876742Lelio R Paula10/2014
7364(2^254908+982)/276735Stefano Morozzi01/2020
7365(2^254903+2766)/276734Stefano Morozzi01/2020
736682^40089+40089^8276723Serge Batalov02/2012
73672^254861-279001376721Enzo Doria03/2016
7368(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/2045977974176718Makoto Kamada03/2019
736910^76705+1376706Robert Price01/2011
737010^76705-9407776705Patrick De Geest06/2013
7371(5*2^254785-1)/99976696Lelio R Paula02/2014
73722^254758-11040576690Enzo Doria05/2014
7373(2^254721+470)/276679Stefano Morozzi01/2020
73742^254716-377976678Yves Minet04/2017
73752^254708-11050776675Enzo Doria05/2014
7376(47*10^76672+133)/976673Robert Price04/2017
73772^254670-11290176664Enzo Doria06/2014
7378(3^160665+7)/98135076651Lelio R Paula10/2012
73792^254598-11318376642Enzo Doria07/2014
738019^59932+2276639Lelio R Paula01/2015
73812^254569-11221376633Enzo Doria06/2014
73822*5^109626+976626Lelio R Paula10/2014
73832^254521+187252776619Enzo Doria05/2016
7384(2^254515+2570)/276617Stefano Morozzi01/2020
7385(76*10^76615+167)/976616Robert Price08/2016
7386(2^254495+918)/276611Stefano Morozzi01/2020
738725^54799-24^5479976606Robert Price07/2012
7388(24737*2^254464+1)/976605Lelio R Paula06/2014
738925863^916+916^2586376604Hans Havermann01/2020
7390(2^254458+2398)/276600Stefano Morozzi01/2020
7391(2^254434+1354)/276592Stefano Morozzi01/2020
7392(2^254410+2842)/276585Stefano Morozzi01/2020
739319878^7121+7121^1987876581Hans Havermann01/2020
739412^70961-8576580Lelio R Paula02/2015
739518867^11452+11452^1886776579Hans Havermann01/2020
7396(2^254333+1806)/276562Stefano Morozzi01/2020
73977^90590-3876558Lelio R Paula02/2015
73982^254304+522776554Lelio R Paula06/2013
7399(76*10^76547-211)/976548Robert Price10/2017
740118^60979-536376546Enzo Doria03/2013
7400(2^254278+3250)/276546Stefano Morozzi01/2020
7402(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
7404(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
7403(7*10^76536-313)/976536Robert Price11/2016
74062^254239-2776534Lelio R Paula03/2012
74052^254238-184176534Yves Minet03/2013
7407(2^254235+3978)/276533Stefano Morozzi01/2020
7409(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
7408(2^254223+3938)/276529Stefano Morozzi01/2020
74102^254189-11222576519Enzo Doria06/2014
741118^60938-139776494Enzo Doria03/2013
74132^254075-278841776485Enzo Doria03/2016
741218239^15612+15612^1823976485Hans Havermann01/2020
74147*10^76483-2376484Robert Price04/2016
741518471^13822+13822^1847176481Hans Havermann01/2020
741618850^11407+11407^1885076478Hans Havermann01/2020
74172^254042-11291376475Enzo Doria06/2014
741814^66723-3776474Lelio R Paula02/2015
7419(2^254040+2970)/276474Stefano Morozzi01/2020
74202^254037-11030576473Enzo Doria05/2014
7421(2^254008+2290)/276464Stefano Morozzi01/2020
742215927^18196+18196^1592776463Norbert Schneider12/2019
7423(2^253979+1110)/276455Stefano Morozzi01/2020
74242^253931-11110976441Enzo Doria05/2014
74252^253926-116776440Lelio R Paula05/2013
7426(49*10^76438-13)/976439Robert Price07/2015
7427(2^253876+1302)/276424Stefano Morozzi01/2020
7428(21*2^253845-1)/14376415Lelio R Paula02/2014
742910^76374+3176375Robert Price03/2011
743010^76374-22215976374Patrick De Geest05/2013
7431(2^253660+490)/276359Stefano Morozzi01/2020
743219227^9352+9352^1922776349Hans Havermann01/2020
7433(2^253617+2874)/276347Stefano Morozzi01/2020
74342^253561-11053376330Enzo Doria05/2014
7435(2^253546+954)/276325Stefano Morozzi01/2020
7436gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
74379*5^109182+276316Lelio R Paula10/2014
743811^73279-369076313Enzo Doria12/2012
7439(598*10^76309-31)/976311Robert Price02/2017
744011^73274-2400076308Enzo Doria12/2012
74417^90291-676305Theodore Burton11/2005
7442(2^253479+3650)/276305Stefano Morozzi01/2020
7443(2^253460+2902)/276299Stefano Morozzi01/2020
7444(21181*2^253432+1)/2143776291Lelio R Paula06/2014
7445(2^253399+3254)/276281Stefano Morozzi01/2020
744669247!4+476280Robert Price09/2019
74476^98025+14576279Lelio R Paula01/2015
7448(2^253382+1978)/276276Stefano Morozzi01/2020
74492^253355+115576268Lelio R Paula05/2013
7450(73*10^76262+413)/976263Robert Price10/2017
74512^253292-7121976249Enzo Doria04/2016
74527^90221-3676246Lelio R Paula02/2015
7453(2^253273+3486)/276243Stefano Morozzi01/2020
7454(2^253238+894)/276232Stefano Morozzi01/2020
745518^60727-347376229Enzo Doria03/2013
7456(2^253210+1170)/276224Stefano Morozzi01/2020
7457(78557*2^253184+1)/376221Lelio R Paula06/2014
7458(8*10^76220-83)/376221Robert Price10/2017
745918568^12717+12717^1856876211Hans Havermann01/2020
7460(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
746119443^8294+8294^1944376193Hans Havermann12/2019
746211^73163-201076192Enzo Doria12/2012
746319006^10201+10201^1900676189Hans Havermann12/2019
74642^253060+5461576179Lelio R Paula05/2013
7465(2^253049+3966)/276176Stefano Morozzi01/2020
74662^253029+186976176170Enzo Doria05/2016
7467(2^253028+1906)/276169Stefano Morozzi01/2020
74682^252955-11100776148Enzo Doria05/2014
74692*5^108931+776140Lelio R Paula10/2014
7470(86*10^76128+121)/976129Robert Price03/2017
747122154*29^52050+976123Curtis Bright05/2015
747218915^10574+10574^1891576119Hans Havermann01/2020
74733^159530-11235876116Enzo Doria06/2014
747411^73089-4876115Lelio R Paula02/2015
747586^39337-8576098Norbert Schneider10/2015
7476(3^159505-7)/31329731676095Lelio R Paula06/2012
74776^97783+7776090Lelio R Paula01/2015
7478(2^252716+1842)/276075Stefano Morozzi01/2020
74792^252712-10576074Lelio R Paula03/2012
7480(10^76069-19)/976069Robert Price10/2017
7482131^35927+276068Lelio R Paula05/2013
7481(41*10^76067+373)/976068Robert Price04/2017
74832^252683-13976066Lelio R Paula03/2012
7484137^35597-13676061Norbert Schneider05/2015
74853^159413+10676060Lelio R Paula01/2015
7486(2^252593+1682)/276038Stefano Morozzi01/2020
74879^79677+3*8^79677-2*4^79677-3*2^7967776032Mike Oakes12/2010
748822235^2626+2626^2223576029Hans Havermann12/2019
7489(2^252557-9)/7176026Lelio R Paula07/2012
7491(85*10^76021-103)/976022Robert Price10/2017
7490(2^252539+2690)/276022Stefano Morozzi01/2020
749211^72989+8076011Lelio R Paula02/2015
749399877!6-3675996Robert Price11/2018
74942^252449-45952375995Enzo Doria05/2015
749520^58408+7375991Lelio R Paula01/2015
74962^252418-142175986Yves Minet01/2013
7497(11*2^252396-1)/575980Lelio R Paula02/2014
749820871^4366+4366^2087175973Hans Havermann01/2020
74992^252365-11068975970Enzo Doria05/2014
750011^72949-102075969Enzo Doria11/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 29 2020 17:41 (Time in France)

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