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) !!!


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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 ?
87522^257636-11023577557Enzo Doria05/2014
8753(23*10^77556+97)/377557Robert Price02/2017
8751(2^257639+2630)/277557Stefano Morozzi01/2020
8754(2^257625+3354)/277553Stefano Morozzi01/2020
87552^257621-11007177552Enzo Doria04/2014
875619580^9129+9129^1958077546Hans Havermann03/2020
87572^257567-6487577536Lelio R Paula06/2013
8758(18098^18211-1)/1809777532Serge Batalov08/2020
8759(2^257429+2394)/277494Stefano Morozzi01/2020
8760(2^257373+1206)/277477Stefano Morozzi01/2020
87612*7^91674+977474Lelio R Paula10/2014
8762(2^257248+2442)/277440Stefano Morozzi01/2020
8763(17*10^77427-47)/377428Robert Price05/2017
876410^77418+84168377419Patrick De Geest06/2013
876510^77418-3377418Robert Price05/2011
876619^60539-3677415Lelio R Paula03/2015
8767(9562^19447-1)/956177406Serge Batalov08/2020
876837401!!-102477397Robert Price11/2015
8769(2^257095+1410)/277394Stefano Morozzi01/2020
877011^74313-1875077390Enzo Doria12/2012
87712^257044-11288377378Enzo Doria06/2014
87728*10^77377+5177378Robert Price05/2017
8773Phi(258121,2)/71977375Jeppe Stig Nielsen09/2020
87742*7^91553+977372Lelio R Paula10/2014
8775713^27118+27118^71377371Norbert Schneider12/2016
8776(22711^17761-1)/2271077367Serge Batalov08/2020
877718652^14043+14043^1865277359Hans Havermann03/2020
8778(11391^19069-1)/1139077351Serge Batalov08/2020
87796*10^77346-2977347Robert Price08/2020
87802^256920-11115577341Enzo Doria05/2014
87812^256896-655577334Lelio R Paula06/2013
8782(52*10^77322-7)/977323Robert Price12/2014
87832^256849-11293977320Enzo Doria06/2014
878417275^18246+18246^1727577316Norbert Schneider01/2020
8785(4*10^77309-31)/977309Erik Branger05/2011
878620936^4923+4923^2093677301Hans Havermann04/2020
8787(25376^17551-1)/2537577298Serge Batalov08/2020
8788(3^161988+7)/4186477284Lelio R Paula10/2012
8789(14^67421-1)/1377272Paul Bourdelais09/2008
8790(2^256679+3554)/277268Stefano Morozzi01/2020
87925*3^161923-477258Lelio R Paula06/2014
879120465^5958+5958^2046577258Hans Havermann02/2020
8793(2^256591+954)/277242Stefano Morozzi01/2020
879424806^1299+1299^2480677237Hans Havermann05/2020
87952^256552-149977230Yves Minet05/2013
879618339^16258+16258^1833977227Hans Havermann04/2020
879721243^4316+4316^2124377221Hans Havermann04/2020
8798(2^256493+3126)/277212Stefano Morozzi01/2020
87992^256460-11275777203Enzo Doria06/2014
8800(2^256444+2578)/277198Stefano Morozzi01/2020
88012^256398+2329977184Yves Minet02/2011
88022^256391-1155*25639177182Henri Lifchitz03/2005
8803(2^256391-9)/5659377177Lelio R Paula10/2012
8804(7665^19867-1)/766477170Serge Batalov08/2020
8805(2^256338+3834)/277166Stefano Morozzi01/2020
8806(2^256339+546)/277166Stefano Morozzi01/2020
8807(2^256308+9)/1058577153Lelio R Paula10/2012
880821^58348-277149Lelio R Paula08/2013
8809(17*2^256291-1)/478577149Lelio R Paula02/2014
8810(5*2^256274-1)/214177144Lelio R Paula02/2014
8811(2^256244+2326)/277137Stefano Morozzi01/2020
881219^60321+8277136Lelio R Paula03/2015
88135*2^256233-377135Lelio R Paula06/2014
8814(2^256155+1566)/277111Stefano Morozzi01/2020
88153*2^256149+777110Lelio R Paula06/2014
8816(2^256128+1890)/277102Stefano Morozzi01/2020
88173^161594-10677100Lelio R Paula02/2015
88182^256114-18577098Lelio R Paula03/2012
88198^85349-85349^877078Norbert Schneider05/2017
88202^256043-278637777077Enzo Doria03/2016
88212^255973+186994777056Enzo Doria05/2016
882212^71393-4377046Lelio R Paula02/2015
8823(2^255882+3630)/277028Stefano Morozzi01/2020
882415^65490+4477023Lelio R Paula02/2015
8825(3^161411-7)/94077010Lelio R Paula10/2012
8826lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
8828(570^27943-1)/56977005Serge Batalov12/2016
8827(570^27943-1)/(570-1)77005Michael Stocker04/2020
88292^255750-7576989Lelio R Paula03/2012
88303*6^98926-576980Lelio R Paula10/2014
8831(2^255708+478)/276976Stefano Morozzi01/2020
883218^61320-143376974Enzo Doria03/2013
88336^98916-1709376972Enzo Doria02/2013
8834(2^255691+806)/276971Stefano Morozzi01/2020
88352^255659-11013176962Enzo Doria04/2014
883669805!4-12876956Robert Price11/2019
883712^71303+9176949Lelio R Paula02/2015
883818^61298+5976946Lelio R Paula02/2015
8839(223^32768+1)/13107476945Lelio R Paula02/2009
8840(2^255613-5)/28151776942Lelio R Paula10/2012
884118^61290-1176936Lelio R Paula02/2015
8842(2^255567+1286)/276934Stefano Morozzi01/2020
884463^42752-276926Lelio R Paula08/2013
8843(11*2^255545-1)/11776926Lelio R Paula02/2014
88452^255517+5638776919Yves Minet02/2011
8846(7*10^76916+89)/376917Robert Price08/2020
884718376^15329+15329^1837676914Hans Havermann03/2020
88482^255499-11256776913Enzo Doria06/2014
88492^255492+34576911Lelio R Paula06/2013
8850(2^255488+1678)/276910Stefano Morozzi01/2020
885110^76875+21759176876Patrick De Geest05/2013
885310^76875-5376875Robert Price05/2011
885211^73819-588076875Enzo Doria01/2013
88542^255313+1891576857Lelio R Paula06/2013
8855(2^255320-1017)/144666776853Lelio R Paula10/2012
88562^255296+577576852Lelio R Paula06/2013
885714^67052-2976851Lelio R Paula02/2015
8858(8*10^76840+43)/376841Robert Price10/2017
8859(2^255246+1642)/276837Stefano Morozzi01/2020
8860(2^255243+2250)/276836Stefano Morozzi01/2020
8861(2^255240+1218)/276835Stefano Morozzi01/2020
8862(7*10^76818-313)/976818Robert Price11/2016
886310^76801+6976802Robert Price03/2011
886410^76801-8094376801Patrick De Geest06/2013
88652^255105+5776795Lelio R Paula03/2012
8866(lucasV(1,2,510187)+2)/(3*5*11)76789Mike Oakes04/2017
8867(2^255097-7)/2002005576785Lelio R Paula10/2012
8868(2^255063+3098)/276782Stefano Morozzi01/2020
88692^255055+186935376780Enzo Doria05/2016
887017^62396-9076776Lelio R Paula03/2015
887118797^12130+12130^1879776765Hans Havermann03/2020
88727^90833-6076763Lelio R Paula02/2015
887313^68901-5676752Lelio R Paula03/2015
88742^254961+186991776751Enzo Doria05/2016
8875(2^254950+594)/276748Stefano Morozzi01/2020
887620734^5027+5027^2073476743Hans Havermann03/2020
88779*5^109791-876742Lelio R Paula10/2014
8878(469^28729-1)/46876738Serge Batalov08/2020
8879(2^254908+982)/276735Stefano Morozzi01/2020
8880(2^254903+2766)/276734Stefano Morozzi01/2020
8881(4143^21211-1)/414276724Serge Batalov08/2020
888282^40089+40089^8276723Serge Batalov02/2012
88832^254861-279001376721Enzo Doria03/2016
8884(10^278+1)*(10^115926+1)/(10^834+1)/(10^38642+1)/2045977974176718Makoto Kamada03/2019
888510^76705+1376706Robert Price01/2011
888610^76705-9407776705Patrick De Geest06/2013
8887(13709^18541-1)/1370876701Serge Batalov08/2020
8888(5*2^254785-1)/99976696Lelio R Paula02/2014
88892^254758-11040576690Enzo Doria05/2014
8890(2^254721+470)/276679Stefano Morozzi01/2020
88912^254716-377976678Yves Minet04/2017
88922^254708-11050776675Enzo Doria05/2014
8893(47*10^76672+133)/976673Robert Price04/2017
88942^254670-11290176664Enzo Doria06/2014
8895(3^160665+7)/98135076651Lelio R Paula10/2012
88962^254598-11318376642Enzo Doria07/2014
889719^59932+2276639Lelio R Paula01/2015
889877*10^76635+376637Robert Price06/2020
88992^254569-11221376633Enzo Doria06/2014
89002*5^109626+976626Lelio R Paula10/2014
89012^254521+187252776619Enzo Doria05/2016
8902(2^254515+2570)/276617Stefano Morozzi01/2020
8903(76*10^76615+167)/976616Robert Price08/2016
8904(2^254495+918)/276611Stefano Morozzi01/2020
890525^54799-24^5479976606Robert Price07/2012
8906(24737*2^254464+1)/976605Lelio R Paula06/2014
890725863^916+916^2586376604Hans Havermann01/2020
8908(2^254458+2398)/276600Stefano Morozzi01/2020
8909(2^254434+1354)/276592Stefano Morozzi01/2020
8910(2^254410+2842)/276585Stefano Morozzi01/2020
891119878^7121+7121^1987876581Hans Havermann01/2020
891212^70961-8576580Lelio R Paula02/2015
891318867^11452+11452^1886776579Hans Havermann01/2020
8914(2^254333+1806)/276562Stefano Morozzi01/2020
89157^90590-3876558Lelio R Paula02/2015
89162^254304+522776554Lelio R Paula06/2013
8917(76*10^76547-211)/976548Robert Price10/2017
891918^60979-536376546Enzo Doria03/2013
8918(2^254278+3250)/276546Stefano Morozzi01/2020
8920(19098^17881-1)/1909776545Serge Batalov08/2020
8921(21181*2^254264+1)/5531437976538Lelio R Paula06/2014
8923(34*10^76547-7)/9/61/94529/21480776536Makoto Morimoto05/2016
8922(7*10^76536-313)/976536Robert Price11/2016
89252^254239-2776534Lelio R Paula03/2012
89242^254238-184176534Yves Minet03/2013
8926(2^254235+3978)/276533Stefano Morozzi01/2020
8928(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
8927(2^254223+3938)/276529Stefano Morozzi01/2020
89292^254189-11222576519Enzo Doria06/2014
893018^60938-139776494Enzo Doria03/2013
89322^254075-278841776485Enzo Doria03/2016
893118239^15612+15612^1823976485Hans Havermann01/2020
89337*10^76483-2376484Robert Price04/2016
893418471^13822+13822^1847176481Hans Havermann01/2020
893518850^11407+11407^1885076478Hans Havermann01/2020
89362^254042-11291376475Enzo Doria06/2014
893714^66723-3776474Lelio R Paula02/2015
8938(2^254040+2970)/276474Stefano Morozzi01/2020
89392^254037-11030576473Enzo Doria05/2014
8940(2^254008+2290)/276464Stefano Morozzi01/2020
894115927^18196+18196^1592776463Norbert Schneider12/2019
8942(2^253979+1110)/276455Stefano Morozzi01/2020
8943(1575^23911-1)/157476447Serge Batalov08/2020
89442^253931-11110976441Enzo Doria05/2014
89452^253926-116776440Lelio R Paula05/2013
8946(49*10^76438-13)/976439Robert Price07/2015
8947(2^253876+1302)/276424Stefano Morozzi01/2020
8948(21*2^253845-1)/14376415Lelio R Paula02/2014
894910^76374+3176375Robert Price03/2011
895010^76374-22215976374Patrick De Geest05/2013
8951(6300^20101-1)/629976367Serge Batalov08/2020
8952(2^253660+490)/276359Stefano Morozzi01/2020
895319227^9352+9352^1922776349Hans Havermann01/2020
8954(2^253617+2874)/276347Stefano Morozzi01/2020
89552^253561-11053376330Enzo Doria05/2014
8956(2^253546+954)/276325Stefano Morozzi01/2020
8957gcd(V(917285),5*F(183457)*(F(183457)+1)+1)76321Serge Batalov04/2015
89589*5^109182+276316Lelio R Paula10/2014
895911^73279-369076313Enzo Doria12/2012
8960(598*10^76309-31)/976311Robert Price02/2017
896111^73274-2400076308Enzo Doria12/2012
89627^90291-676305Theodore Burton11/2005
8963(2^253479+3650)/276305Stefano Morozzi01/2020
8964(2^253460+2902)/276299Stefano Morozzi01/2020
89656*10^76295-2976296Robert Price08/2020
8966(21181*2^253432+1)/2143776291Lelio R Paula06/2014
8967(2^253399+3254)/276281Stefano Morozzi01/2020
896869247!4+476280Robert Price09/2019
89696^98025+14576279Lelio R Paula01/2015
8970(2^253382+1978)/276276Stefano Morozzi01/2020
89712^253355+115576268Lelio R Paula05/2013
8972(73*10^76262+413)/976263Robert Price10/2017
89732^253292-7121976249Enzo Doria04/2016
89747^90221-3676246Lelio R Paula02/2015
8975(2^253273+3486)/276243Stefano Morozzi01/2020
8976(2^253238+894)/276232Stefano Morozzi01/2020
897718^60727-347376229Enzo Doria03/2013
8978(2^253210+1170)/276224Stefano Morozzi01/2020
8979(78557*2^253184+1)/376221Lelio R Paula06/2014
8980(8*10^76220-83)/376221Robert Price10/2017
898118568^12717+12717^1856876211Hans Havermann01/2020
8982(44791^20480+1)/(44791^4096+1)76206Serge Batalov01/2017
8983(5168^20521-1)/516776198Serge Batalov08/2020
898419443^8294+8294^1944376193Hans Havermann12/2019
898511^73163-201076192Enzo Doria12/2012
898619006^10201+10201^1900676189Hans Havermann12/2019
89872^253060+5461576179Lelio R Paula05/2013
8988(2^253049+3966)/276176Stefano Morozzi01/2020
89892^253029+186976176170Enzo Doria05/2016
8990(2^253028+1906)/276169Stefano Morozzi01/2020
8991(1078^25111-1)/107776150Serge Batalov08/2020
89922^252955-11100776148Enzo Doria05/2014
89932*5^108931+776140Lelio R Paula10/2014
8994(86*10^76128+121)/976129Robert Price03/2017
899522154*29^52050+976123Curtis Bright05/2015
899618915^10574+10574^1891576119Hans Havermann01/2020
89973^159530-11235876116Enzo Doria06/2014
899811^73089-4876115Lelio R Paula02/2015
899986^39337-8576098Norbert Schneider10/2015
9000(3^159505-7)/31329731676095Lelio R Paula06/2012


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

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