PRP Records

Probable Primes Top 10000

(252932 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 ?
8751(85*10^60026+23)/960027Robert Price11/2015
875265^33107+6260021Lelio R Paula01/2016
87542^199362-121560014Lelio R Paula06/2011
87532^199362-11163360014Enzo Doria05/2014
87551537^18832+18832^153760012Serge Batalov05/2014
87562^199324-1743360003Enzo Doria05/2013
875810^60000+20433160001Milton L. Brown04/2006
875910^60000+8712960001Milton L. Brown04/2006
8757143^27838-260001Lelio R Paula10/2017
876010^59999+6519760000Patrick De Geest04/2005
877810^60000-3252960000Patrick De Geest08/2009
8774(10^60000+2249)/960000Makoto Morimoto09/2016
8775((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
8776(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
8777(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
8761(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
8762(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
8763(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
8764(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
8765(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
8766(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
8767(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
8768(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
8769(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
8770(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
8771(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
8772(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
8773(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
87792^199313-22567560000Stefano Morozzi05/2019
87802^199313-32690160000Stefano Morozzi05/2019
87812^199313-53217160000Stefano Morozzi05/2019
87822^199313-63285160000Stefano Morozzi05/2019
87832^199313-82528960000Stefano Morozzi05/2019
87842^199313-85769160000Stefano Morozzi05/2019
87852^199313+8370560000Stefano Morozzi05/2019
87862^199313+17543960000Stefano Morozzi05/2019
87872^199313+40171560000Stefano Morozzi05/2019
87882^199313+41836760000Stefano Morozzi05/2019
87892^199313+52051760000Stefano Morozzi05/2019
87902^199313+58297560000Stefano Morozzi05/2019
87912^199313+60032960000Stefano Morozzi05/2019
87922^199313+60116160000Stefano Morozzi05/2019
87932^199313+60146760000Stefano Morozzi05/2019
87942^199313+92970560000Stefano Morozzi05/2019
880310^59999-51626759999Patrick De Geest06/2009
880120^46116-4159999Lelio R Paula03/2013
8802(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
8804(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
8795(2^199313+804446)/259999Stefano Morozzi06/2019
8796(2^199313+885410)/259999Stefano Morozzi06/2019
8797(2^199313+916374)/259999Stefano Morozzi06/2019
8798(2^199313+501865)/359999Stefano Morozzi06/2019
8799(2^199313+979327)/359999Stefano Morozzi06/2019
8800(2^199313+870498)/1059999Stefano Morozzi06/2019
8805(2^199313+911951)/5359998Stefano Morozzi06/2019
8806(2^199313+622557)/5959998Stefano Morozzi06/2019
8807(2^199313+548359)/11159998Stefano Morozzi06/2019
8808(2^199313+881010)/14259998Stefano Morozzi06/2019
8809(2^199313+20613)/41559997Stefano Morozzi06/2019
8810(2^199313+846966)/15859997Stefano Morozzi06/2019
8811(2^199313+689239)/21359997Stefano Morozzi06/2019
8812(2^199313+792637)/30359997Stefano Morozzi06/2019
8813(2^199313+979299)/73359997Stefano Morozzi06/2019
8814(2^199313+760551)/148159997Stefano Morozzi06/2019
88176^77100-5559996Lelio R Paula10/2012
8815(2^199313+8825)/773359996Stefano Morozzi06/2019
8816(2^199313+621926)/159859996Stefano Morozzi06/2019
8818(2^199313+17227)/146774187977159988Stefano Morozzi06/2019
8821(19*2^199274+1)/16159987Lelio R Paula07/2012
8820(23^44053+1)/2459987Robert Price06/2013
8819(2^199313+30419)/195223029100759987Stefano Morozzi06/2019
8822(2^199313+4605)/776935587940608759984Stefano Morozzi06/2019
8823(2^199313+47559)/783044506792936959984Stefano Morozzi06/2019
8824(2^199313+16238)/70962375306317203059982Stefano Morozzi06/2019
88259^62848+6^62848-2^6284859973Mike Oakes08/2010
882611438^14775-14775^1143859963Norbert Schneider05/2019
882715852^6061+6061^1585259961Hans Havermann08/2016
882819^46880-2059948Lelio R Paula03/2013
88292^199107-1773759938Enzo Doria05/2013
8830(13*10^59928+83)/359929Robert Price09/2016
883110^59913+10893143159914Marisa Kirisame02/2015
883210^59913+4861959914Patrick De Geest04/2016
883310^59913-7412359913Patrick De Geest03/2016
8834t(199528)59890Robert Price01/2015
88352^198903-1790159876Enzo Doria05/2013
88369*10^59862-1959863Robert Price10/2017
8837gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
8838(3^125447+7)/259854Lelio R Paula04/2012
88395^85630+4^(85630-1)59853Robert Price03/2016
88402^198824-213559852Yves Minet06/2013
8841(124^28591-1)/12359851Richard Fischer10/2017
88422^198799-1611759845Enzo Doria04/2013
88437^70811+6^(70811+1)59843Robert Price07/2016
88442^198774-1594559837Enzo Doria04/2013
88452^198753-1587359831Enzo Doria04/2013
8846(31*2^198748-1)/4559829Lelio R Paula01/2014
88472^198725+6959823Lelio R Paula04/2011
8848(68*10^59821+31)/959822Robert Price10/2015
8849(37*25^42785+1867)/859812Curtis Bright05/2015
88503^125354+266059810Lelio R Paula10/2012
8851105^29591-10459810Norbert Schneider08/2013
88524*5^85565-359808Lelio R Paula09/2014
885313963842222*Bern(19550)/5572727559803Thomas Ritschel03/2014
8856125330^3+3^12533059798Anatoly F. Selevich06/2010
88542^198643-318959798Yves Minet10/2014
8855(13*10^59797+191)/359798Robert Price08/2017
8857(7*10^59796-1)/359797Erik Branger03/2014
88582^198595+15359784Lelio R Paula04/2011
8859(19*10^59766+161)/959767Robert Price07/2016
88602^198510-196559758Lelio R Paula06/2011
88612^198506-1907759757Enzo Doria05/2013
88622^198484-1600559750Enzo Doria04/2013
88632^198473-1682159747Enzo Doria05/2013
8864(2^198481-5)/2831159745Lelio R Paula02/2012
88652^198400-18959725Lelio R Paula04/2011
88662^198384-1283759720Enzo Doria10/2012
886742694!3-72959719Robert Price09/2014
88682^198320-1871759701Enzo Doria05/2013
886920^45881-118359693Enzo Doria03/2013
88702^198224-685559672Lelio R Paula05/2011
88712^198181-1910159659Enzo Doria05/2013
88725*10^59650+4159651Robert Price08/2017
88732^198149-11221359649Enzo Doria06/2014
88742^198138+7369959646Enzo Doria04/2016
88752^198129-5559643Lelio R Paula04/2011
887616029^5258+5258^1602959642Hans Havermann05/2019
88775^85318-1463659635Enzo Doria02/2013
8878(2^198119+47)/156093559634Lelio R Paula02/2012
88792^198090-1609759632Enzo Doria04/2013
88809*10^59617+8959618Robert Price11/2016
888142625!3+8159612Robert Price09/2014
88825^85277-8459607Lelio R Paula10/2012
8883(871*10^59599-7)/959601Robert Price11/2017
88842^197984-1824559600Enzo Doria05/2013
888512202^14583-14583^1220259593Norbert Schneider01/2019
88862^197951-213759590Yves Minet06/2013
8887(38*10^59589+187)/959590Robert Price11/2017
888866^32749-65^3274959589Robert Price09/2013
88895*10^59586-359587Dmitry Domanov11/2010
8890(35*10^59584-197)/959585Robert Kinser10/2017
88912^197932-395959584Yves Minet04/2017
88922^197909-1896159577Enzo Doria05/2013
8893(3^124871+2)/4503159574Lelio R Paula04/2012
88942^197872+8159566Henri Lifchitz10/2005
88952^197873-1846959566Enzo Doria05/2013
8896(22*10^59558-31)/959559Robert Price04/2015
889712003^14600-14600^1200359558Norbert Schneider02/2019
88982^197840-46559556Lelio R Paula05/2011
8899(31*2^197856-1)/388960559556Lelio R Paula01/2014
89002^197808-1780559547Enzo Doria05/2013
89012^197781-1790559539Enzo Doria05/2013
89022^197777-1747359537Enzo Doria05/2013
89036^76507-14959535Lelio R Paula10/2012
8905Phi(61456,109)59526Enzo Doria05/2012
890418^47420+2359526Lelio R Paula03/2013
8906(59^33613+1)/6059522Paul Bourdelais08/2017
89073^124747+9459520Lelio R Paula10/2012
890817^48370+1859517Lelio R Paula03/2013
890920^45740-152359510Enzo Doria03/2013
8910(47*10^59509+493)/959510Robert Price11/2017
8911(7*2^197642-1)/305159494Lelio R Paula01/2014
891218^47390-185359488Enzo Doria03/2013
8914(2^197581-7)/191559475Lelio R Paula02/2012
891310621^14772-14772^1062159475Norbert Schneider05/2019
8915(24737*2^197559+1)/7759474Lelio R Paula06/2014
89162^197540-245959466Yves Minet07/2014
8917(44*10^59454+1)/959455Serge Batalov11/2010
89182^197494-1780559452Enzo Doria05/2013
89192^197482-1682159449Enzo Doria05/2013
89202^197485+7576759449Enzo Doria04/2016
8921(3*2^197483+1)/2559448Lelio R Paula07/2012
89222^197466-186835159444Enzo Doria04/2016
89232^197411-1778159427Enzo Doria05/2013
8924(F(142164)^3-F(142163)^3)/F(142162)59421Wayne Halsdorf03/2012
89252^197392-11462959421Enzo Doria05/2015
892615441^7046+7046^1544159417Hans Havermann05/2019
89272^197355-15759410Lelio R Paula04/2011
89285^84992-8459407Lelio R Paula10/2012
89292*3^124504-559404Lelio R Paula04/2014
89302^197307-1916559396Enzo Doria05/2013
89322^197303+3276959395Lelio R Paula05/2011
89312*10^59394-6959395Robert Price07/2017
8933(53*10^59389+1)/959390Serge Batalov11/2010
89346^76316-3559386Lelio R Paula10/2012
89352^197259-292959381Yves Minet09/2014
893615036^8893+8893^1503659378Hans Havermann05/2019
8937lucasU(46,1,35715)-lucasU(46,1,35714)59377Mike Oakes04/2009
893917^48253-659373Lelio R Paula03/2013
893814678^11091+11091^1467859373Hans Havermann05/2019
89402^197156-1583759350Enzo Doria04/2013
89412^197152-429559349Yves Minet08/2018
89422^197149-1848159348Enzo Doria05/2013
89432^197142-1715759346Enzo Doria05/2013
8945(F(6)^65707-F(5)^65707)/F(4)59339Wayne Halsdorf04/2010
8944(8^65707-5^65707)/359339Robert Price12/2012
8946(2*14283^14283+1)/792549797559334David Broadhurst09/2010
894715267^7682+7682^1526759320Hans Havermann05/2019
89482^197012-11171959307Enzo Doria05/2014
89492^196975+51359296Lelio R Paula05/2011
8950(61*10^59294+119)/959295Robert Price09/2017
89514*10^59292+3959293Robert Price11/2017
89522^196960+9759291Lelio R Paula04/2011
89539^62116+8^(62116-1)59274Robert Price03/2016
89542^196900-9730559273Lelio R Paula09/2011
895513706^14327-14327^1370659270Norbert Schneider05/2019
89565*6^76155+759261Lelio R Paula09/2014
895715^50385-1459258Wojciech Florek06/2006
8958(136777#-1)/882358147759254Donovan Johnson05/2006
8959(2^196744-3)*6-759227Gilbert Mozzo05/2016
896014694^10717+10717^1469459218Hans Havermann05/2019
8961(67607*2^196696+1)/359216Lelio R Paula05/2014
89622^196696-11296759212Enzo Doria06/2014
896320^45508-422359208Enzo Doria03/2013
8964gcd(Phi(325820,10),(10^16291+1)^3*(10^16291+1-10^8146)+(10^32582+10^16291)*(10^8146+1)+10^48873)59201Serge Batalov04/2015
896514^51651-8159199Lelio R Paula03/2013
89662^196650-145159198Yves Minet08/2012
89672^196636-279779959194Enzo Doria04/2016
89681111*2^196610-55559189Henri Lifchitz04/2005
89693^124041+65859183Lelio R Paula10/2012
89702^196590-11179759180Enzo Doria05/2014
8971(10^59174-13)/359174Robert Price02/2017
8972(2*10^59174-113)/359174Robert Price09/2017
8973(9179*2^196533-1)/78359164Lelio R Paula04/2015
897411267^14600-14600^1126759157Norbert Schneider02/2019
8975379*10^59152+959155Arkadiusz Wesolowski10/2011
8976(404*10^59149-53)/959151Robert Price11/2017
897713^53095+4059145Lelio R Paula03/2013
89782*F(282999)-159144Henri Lifchitz12/2009
89794*7^69984+359144Lelio R Paula09/2014
8980(5*10^59142+1)/359143Erik Branger12/2013
89812^196463+571159142Lelio R Paula10/2011
89822^196453-9730559139Lelio R Paula09/2011
8983(28*10^59135+53)/959136Serge Batalov11/2008
8984(28*10^59133+113)/359134Robert Price03/2016
89852^196434+759133Lelio R Paula04/2011
8986(8*10^59127-29)/359128Robert Price05/2016
89872^196414+25559127Lelio R Paula05/2011
89885^84586-9259124Lelio R Paula10/2012
89892^196388-1717759119Enzo Doria05/2013
899079427!6-659119Robert Price08/2018
89913^123890+2059111Lelio R Paula10/2012
89922^196355-102177759109Paul Bourdelais11/2012
899311^56754-141059104Enzo Doria11/2012
899410902^14635-14635^1090259089Norbert Schneider02/2019
8995(7*2^196297-1)/120040759087Lelio R Paula01/2014
8996(16*10^59062-19)/359063Robert Price03/2016
899735^38249-122859060Enzo Doria03/2013
89985^84475-1859046Lelio R Paula10/2012
89992^196123-1770159039Enzo Doria05/2013
900012^54702-3159034Lelio R Paula03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

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