PRP Records

Probable Primes Top 10000

(280932 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 ?
9251(25*2^257853+1)/377623Lelio R Paula07/2012
9252(2^257832+1362)/277615Stefano Morozzi01/2020
9253(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
92546^99728+7177604Lelio R Paula01/2015
92552^257778-11276777599Enzo Doria06/2014
9256(31*2^257771+1)/53777596Lelio R Paula07/2012
9257(2^257762+2214)/277594Stefano Morozzi01/2020
92582^257729-7377585Lelio R Paula03/2012
9259(2^257728+1890)/277584Stefano Morozzi01/2020
92612^257689-6377573Lelio R Paula03/2012
9260(47*10^77572+493)/977573Robert Price11/2017
9262(78557*2^257665+1)/610872577564Lelio R Paula06/2014
9263(5570^20707-1)/556977562Serge Batalov08/2020
9264(3^162563+8)/288577559Lelio R Paula10/2012
92672^257636-11023577557Enzo Doria05/2014
9266(23*10^77556+97)/377557Robert Price02/2017
9265(2^257639+2630)/277557Stefano Morozzi01/2020
9268(2^257625+3354)/277553Stefano Morozzi01/2020
92692^257621-11007177552Enzo Doria04/2014
927019580^9129+9129^1958077546Hans Havermann03/2020
92712^257567-6487577536Lelio R Paula06/2013
9272(18098^18211-1)/1809777532Serge Batalov08/2020
9273(2^257429+2394)/277494Stefano Morozzi01/2020
9274(2^257373+1206)/277477Stefano Morozzi01/2020
92752*7^91674+977474Lelio R Paula10/2014
9276(2^257248+2442)/277440Stefano Morozzi01/2020
9277(17*10^77427-47)/377428Robert Price05/2017
927810^77418+84168377419Patrick De Geest06/2013
927910^77418-3377418Robert Price05/2011
928019^60539-3677415Lelio R Paula03/2015
9281(9562^19447-1)/956177406Serge Batalov08/2020
928237401!!-102477397Robert Price11/2015
9283(2^257095+1410)/277394Stefano Morozzi01/2020
928411^74313-1875077390Enzo Doria12/2012
92862^257044-11288377378Enzo Doria06/2014
92858*10^77377+5177378Robert Price05/2017
9287Phi(258121,2)/71977375Jeppe Stig Nielsen09/2020
92882*7^91553+977372Lelio R Paula10/2014
9289713^27118+27118^71377371Norbert Schneider12/2016
9290(22711^17761-1)/2271077367Serge Batalov08/2020
929118652^14043+14043^1865277359Hans Havermann03/2020
9292(11391^19069-1)/1139077351Serge Batalov08/2020
92936*10^77346-2977347Robert Price08/2020
92942^256920-11115577341Enzo Doria05/2014
92952^256896-655577334Lelio R Paula06/2013
9296(52*10^77322-7)/977323Robert Price12/2014
92972^256849-11293977320Enzo Doria06/2014
929817275^18246+18246^1727577316Norbert Schneider01/2020
9299(4*10^77309-31)/977309Erik Branger05/2011
930020936^4923+4923^2093677301Hans Havermann04/2020
9301(25376^17551-1)/2537577298Serge Batalov08/2020
9302(3^161988+7)/4186477284Lelio R Paula10/2012
9303(14^67421-1)/1377272Paul Bourdelais09/2008
9304(2^256679+3554)/277268Stefano Morozzi01/2020
93065*3^161923-477258Lelio R Paula06/2014
930520465^5958+5958^2046577258Hans Havermann02/2020
9307(2^256591+954)/277242Stefano Morozzi01/2020
930824806^1299+1299^2480677237Hans Havermann05/2020
93092^256552-149977230Yves Minet05/2013
931018339^16258+16258^1833977227Hans Havermann04/2020
931121243^4316+4316^2124377221Hans Havermann04/2020
9312(2^256493+3126)/277212Stefano Morozzi01/2020
93132^256460-11275777203Enzo Doria06/2014
9314(2^256444+2578)/277198Stefano Morozzi01/2020
93152^256398+2329977184Yves Minet02/2011
93162^256391-1155*25639177182Henri Lifchitz03/2005
9317(2^256391-9)/5659377177Lelio R Paula10/2012
9318(7665^19867-1)/766477170Serge Batalov08/2020
9319(2^256338+3834)/277166Stefano Morozzi01/2020
9320(2^256339+546)/277166Stefano Morozzi01/2020
9321(2^256308+9)/1058577153Lelio R Paula10/2012
932221^58348-277149Lelio R Paula08/2013
9323(17*2^256291-1)/478577149Lelio R Paula02/2014
9324(5*2^256274-1)/214177144Lelio R Paula02/2014
9325(2^256244+2326)/277137Stefano Morozzi01/2020
932619^60321+8277136Lelio R Paula03/2015
93275*2^256233-377135Lelio R Paula06/2014
9328(2^256155+1566)/277111Stefano Morozzi01/2020
93293*2^256149+777110Lelio R Paula06/2014
9330(2^256128+1890)/277102Stefano Morozzi01/2020
93313^161594-10677100Lelio R Paula02/2015
93322^256114-18577098Lelio R Paula03/2012
93338^85349-85349^877078Norbert Schneider05/2017
93342^256043-278637777077Enzo Doria03/2016
93352^255973+186994777056Enzo Doria05/2016
933612^71393-4377046Lelio R Paula02/2015
9337(2^255882+3630)/277028Stefano Morozzi01/2020
933815^65490+4477023Lelio R Paula02/2015
9339(3^161411-7)/94077010Lelio R Paula10/2012
9340lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
9341(570^27943-1)/56977005Serge Batalov12/2016
9342(570^27943-1)/(570-1)77005Michael Stocker04/2020
93432^255750-7576989Lelio R Paula03/2012
93443*6^98926-576980Lelio R Paula10/2014
9345(2^255708+478)/276976Stefano Morozzi01/2020
934618^61320-143376974Enzo Doria03/2013
93476^98916-1709376972Enzo Doria02/2013
9348(2^255691+806)/276971Stefano Morozzi01/2020
93492^255659-11013176962Enzo Doria04/2014
935069805!4-12876956Robert Price11/2019
935112^71303+9176949Lelio R Paula02/2015
935218^61298+5976946Lelio R Paula02/2015
9353(223^32768+1)/13107476945Lelio R Paula02/2009
9354(2^255613-5)/28151776942Lelio R Paula10/2012
935518^61290-1176936Lelio R Paula02/2015
9356(2^255567+1286)/276934Stefano Morozzi01/2020
935863^42752-276926Lelio R Paula08/2013
9357(11*2^255545-1)/11776926Lelio R Paula02/2014
93592^255517+5638776919Yves Minet02/2011
9360(7*10^76916+89)/376917Robert Price08/2020
936118376^15329+15329^1837676914Hans Havermann03/2020
93622^255499-11256776913Enzo Doria06/2014
93632^255492+34576911Lelio R Paula06/2013
9364(2^255488+1678)/276910Stefano Morozzi01/2020
936510^76875+21759176876Patrick De Geest05/2013
936710^76875-5376875Robert Price05/2011
936611^73819-588076875Enzo Doria01/2013
93682^255313+1891576857Lelio R Paula06/2013
9369(2^255320-1017)/144666776853Lelio R Paula10/2012
93702^255296+577576852Lelio R Paula06/2013
937114^67052-2976851Lelio R Paula02/2015
9372(8*10^76840+43)/376841Robert Price10/2017
9373(2^255246+1642)/276837Stefano Morozzi01/2020
9374(2^255243+2250)/276836Stefano Morozzi01/2020
9375(2^255240+1218)/276835Stefano Morozzi01/2020
9376(7*10^76818-313)/976818Robert Price11/2016
937710^76801+6976802Robert Price03/2011
937810^76801-8094376801Patrick De Geest06/2013
93792^255105+5776795Lelio R Paula03/2012
9380(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
9381(2^255097-7)/2002005576785Lelio R Paula10/2012
9382(2^255063+3098)/276782Stefano Morozzi01/2020
93832^255055+186935376780Enzo Doria05/2016
938417^62396-9076776Lelio R Paula03/2015
938518797^12130+12130^1879776765Hans Havermann03/2020
93867^90833-6076763Lelio R Paula02/2015
938713^68901-5676752Lelio R Paula03/2015
93882^254961+186991776751Enzo Doria05/2016
9389(2^254950+594)/276748Stefano Morozzi01/2020
939020734^5027+5027^2073476743Hans Havermann03/2020
93919*5^109791-876742Lelio R Paula10/2014
9392(469^28729-1)/46876738Serge Batalov08/2020
9393(2^254908+982)/276735Stefano Morozzi01/2020
9394(2^254903+2766)/276734Stefano Morozzi01/2020
9395(4143^21211-1)/414276724Serge Batalov08/2020
939682^40089+40089^8276723Serge Batalov02/2012
93972^254861-279001376721Enzo Doria03/2016
9398(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/2045977974176718Makoto Kamada03/2019
939910^76705+1376706Robert Price01/2011
940010^76705-9407776705Patrick De Geest06/2013
9401(13709^18541-1)/1370876701Serge Batalov08/2020
9402(5*2^254785-1)/99976696Lelio R Paula02/2014
94032^254758-11040576690Enzo Doria05/2014
9404(2^254721+470)/276679Stefano Morozzi01/2020
94052^254716-377976678Yves Minet04/2017
94062^254708-11050776675Enzo Doria05/2014
9407(47*10^76672+133)/976673Robert Price04/2017
94082^254670-11290176664Enzo Doria06/2014
9409(3^160665+7)/98135076651Lelio R Paula10/2012
94102^254598-11318376642Enzo Doria07/2014
941119^59932+2276639Lelio R Paula01/2015
941277*10^76635+376637Robert Price06/2020
94132^254569-11221376633Enzo Doria06/2014
94142*5^109626+976626Lelio R Paula10/2014
94152^254521+187252776619Enzo Doria05/2016
9416(2^254515+2570)/276617Stefano Morozzi01/2020
9417(76*10^76615+167)/976616Robert Price08/2016
9418(2^254495+918)/276611Stefano Morozzi01/2020
941925^54799-24^5479976606Robert Price07/2012
9420(24737*2^254464+1)/976605Lelio R Paula06/2014
942125863^916+916^2586376604Hans Havermann01/2020
9422(2^254458+2398)/276600Stefano Morozzi01/2020
9423(2^254434+1354)/276592Stefano Morozzi01/2020
9424(2^254410+2842)/276585Stefano Morozzi01/2020
942519878^7121+7121^1987876581Hans Havermann01/2020
942612^70961-8576580Lelio R Paula02/2015
942718867^11452+11452^1886776579Hans Havermann01/2020
9428(2^254333+1806)/276562Stefano Morozzi01/2020
94297^90590-3876558Lelio R Paula02/2015
94302^254304+522776554Lelio R Paula06/2013
9431(76*10^76547-211)/976548Robert Price10/2017
943318^60979-536376546Enzo Doria03/2013
9432(2^254278+3250)/276546Stefano Morozzi01/2020
9434(19098^17881-1)/1909776545Serge Batalov08/2020
9435(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
9437(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
9436(7*10^76536-313)/976536Robert Price11/2016
94392^254239-2776534Lelio R Paula03/2012
94382^254238-184176534Yves Minet03/2013
9440(2^254235+3978)/276533Stefano Morozzi01/2020
9442(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
9441(2^254223+3938)/276529Stefano Morozzi01/2020
94432^254189-11222576519Enzo Doria06/2014
944418^60938-139776494Enzo Doria03/2013
94462^254075-278841776485Enzo Doria03/2016
944518239^15612+15612^1823976485Hans Havermann01/2020
94477*10^76483-2376484Robert Price04/2016
944818471^13822+13822^1847176481Hans Havermann01/2020
944918850^11407+11407^1885076478Hans Havermann01/2020
94502^254042-11291376475Enzo Doria06/2014
945114^66723-3776474Lelio R Paula02/2015
9452(2^254040+2970)/276474Stefano Morozzi01/2020
94532^254037-11030576473Enzo Doria05/2014
9454(2^254008+2290)/276464Stefano Morozzi01/2020
945515927^18196+18196^1592776463Norbert Schneider12/2019
9456(2^253979+1110)/276455Stefano Morozzi01/2020
9457(1575^23911-1)/157476447Serge Batalov08/2020
94582^253931-11110976441Enzo Doria05/2014
94592^253926-116776440Lelio R Paula05/2013
9460(49*10^76438-13)/976439Robert Price07/2015
9461(2^253876+1302)/276424Stefano Morozzi01/2020
9462(21*2^253845-1)/14376415Lelio R Paula02/2014
946310^76374+3176375Robert Price03/2011
946410^76374-22215976374Patrick De Geest05/2013
9465(6300^20101-1)/629976367Serge Batalov08/2020
9466(2^253660+490)/276359Stefano Morozzi01/2020
946719227^9352+9352^1922776349Hans Havermann01/2020
9468(2^253617+2874)/276347Stefano Morozzi01/2020
94692^253561-11053376330Enzo Doria05/2014
9470(2^253546+954)/276325Stefano Morozzi01/2020
9471gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
94729*5^109182+276316Lelio R Paula10/2014
947311^73279-369076313Enzo Doria12/2012
9474(598*10^76309-31)/976311Robert Price02/2017
947511^73274-2400076308Enzo Doria12/2012
94767^90291-676305Theodore Burton11/2005
9477(2^253479+3650)/276305Stefano Morozzi01/2020
9478(2^253460+2902)/276299Stefano Morozzi01/2020
94796*10^76295-2976296Robert Price08/2020
9480(21181*2^253432+1)/2143776291Lelio R Paula06/2014
9481(2^253399+3254)/276281Stefano Morozzi01/2020
948269247!4+476280Robert Price09/2019
94836^98025+14576279Lelio R Paula01/2015
9484(2^253382+1978)/276276Stefano Morozzi01/2020
94852^253355+115576268Lelio R Paula05/2013
9486(73*10^76262+413)/976263Robert Price10/2017
94872^253292-7121976249Enzo Doria04/2016
94887^90221-3676246Lelio R Paula02/2015
9489(2^253273+3486)/276243Stefano Morozzi01/2020
9490(2^253238+894)/276232Stefano Morozzi01/2020
949118^60727-347376229Enzo Doria03/2013
9492(2^253210+1170)/276224Stefano Morozzi01/2020
9493(78557*2^253184+1)/376221Lelio R Paula06/2014
9494(8*10^76220-83)/376221Robert Price10/2017
949518568^12717+12717^1856876211Hans Havermann01/2020
9496(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
9497(5168^20521-1)/516776198Serge Batalov08/2020
949819443^8294+8294^1944376193Hans Havermann12/2019
949911^73163-201076192Enzo Doria12/2012
950019006^10201+10201^1900676189Hans Havermann12/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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