PRP Records

Probable Primes Top 10000

(172742 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 (> 30000) Who ? When ?
70022^204767-1586561642Enzo Doria04/2013
7001(lucasV(1,2,409560)+2)/307961642Mike Oakes01/2017
70037*2^204751-961638Lelio R Paula04/2014
70054*10^61625+2161626Robert Price08/2016
700415369^10226+10226^1536961626Hans Havermann02/2017
70062^204702-1812561622Enzo Doria05/2013
70075*3^129146+861620Lelio R Paula04/2014
70082^204673+12961613Lelio R Paula08/2011
700918^49079+9761608Lelio R Paula05/2013
7010106^30416+10561602Norbert Schneider12/2016
70112^204590-3361588Lelio R Paula08/2011
70122^204586-11197561587Enzo Doria06/2014
70132^204580-1607761585Enzo Doria04/2013
70142^204574-1604161583Enzo Doria04/2013
701515^52358+5661578Lelio R Paula05/2013
7016(28*10^61574+11)/361575Robert Price11/2015
70172^204516-1749361566Enzo Doria05/2013
70184*5^88076-361564Lelio R Paula09/2014
701911^59110-252061557Enzo Doria12/2012
70202^204477-5869561554Lelio R Paula09/2011
702112^57026-7361542Lelio R Paula05/2013
702217^50013+9061539Lelio R Paula05/2013
702356^35201-55^3520161538Robert Price10/2013
70248*7^72810+561533Lelio R Paula09/2014
7026204^26641-203^2664161531Jean-Louis Charton08/2009
702543867!3-656161531Robert Price11/2015
702710^61525+9^(61525-1)61526Robert Price03/2016
702810^61525+6225761526Patrick De Geest12/2016
702914821^14166+14166^1482161526Hans Havermann01/2017
703112^57010-8561525Lelio R Paula05/2013
703010^61525-21357961525Patrick De Geest12/2016
70322^204332-9961511Lelio R Paula08/2011
70332^204323-222161508Yves Minet08/2013
70362^204317-19561506Lelio R Paula08/2011
70343^128910-8661506Lelio R Paula04/2013
70352^204318+7453961506Enzo Doria04/2016
7037(2^204334-3)/114133361505Lelio R Paula03/2012
70382^204297-103609361500Paul Bourdelais11/2012
70393^128880+5861492Lelio R Paula04/2013
70402^204216-11167761476Enzo Doria05/2014
7041(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
70422^204129+20412961449Henri Lifchitz04/2002
70433^128787+2^(128787-1)61448Robert Price05/2016
704411^58999-7861442Lelio R Paula05/2013
70452^204083-11196761436Enzo Doria05/2014
7046(45^37159+1)/4661431Robert Price11/2013
7047677^21702+21702^67761430Norbert Schneider06/2016
704814837^13810+13810^1483761429Hans Havermann02/2017
7049(7*2^204043+1)/3961423Lelio R Paula03/2012
705011^58976-174061418Enzo Doria11/2012
70512^204016-1608561415Enzo Doria04/2013
7052V(379967)61393Serge Batalov03/2015
705343777!3-3^4377761392Robert Price08/2015
70547^72642+8861390Lelio R Paula04/2013
70553^128656+3261385Lelio R Paula04/2013
70562^203916-1749361385Enzo Doria05/2013
70576^78880+2361381Lelio R Paula04/2013
70582^203877-11179961374Enzo Doria05/2014
70592^203867-161561371Lelio R Paula10/2011
70604*10^61367+1961368Robert Price04/2016
7061(19*2^203854+1)/4231961363Lelio R Paula08/2012
70622^203825-1580561358Enzo Doria04/2013
70632^203816-1582561355Enzo Doria04/2013
70645*10^61348+5961349Robert Price09/2016
706521^46395-261345Lelio R Paula08/2013
7066(809*29^41946-165)/2861344Curtis Bright05/2015
70677*6^78826+561340Lelio R Paula09/2014
7068(3^128558+7)/8377316642969661324Lelio R Paula04/2012
70692^203706-11161322Lelio R Paula08/2011
707017567^3094+3094^1756761318Hans Havermann02/2017
70712^203689-3161317Thomas Masser10/2005
7072(11*2^203678-1)/5368961310Lelio R Paula01/2014
70732^203642+3961303Lelio R Paula08/2011
7074floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
707511^58849-604061285Enzo Doria02/2013
707643694!3-361264Robert Price10/2014
707758*(10^(3*20420)-1)/111-161260Robert Price10/2014
70782^203490+1290961257Lelio R Paula10/2011
7079(16*10^61251-31)/361252Robert Price03/2016
708020^47077-570361249Enzo Doria03/2013
70812^203434-11308161240Enzo Doria07/2014
70835^87606+461234Wojciech Florek11/2005
70822^203412-16761234Lelio R Paula08/2011
70842^203402+108961231Lelio R Paula10/2011
7085(8*10^61230+67)/361231Robert Price01/2017
7086(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
70871265^19732+19732^126561211Serge Batalov05/2014
70882^203330+14561209Lelio R Paula08/2011
70896^78647-13761200Lelio R Paula04/2013
709085^31718+8461198Norbert Schneider10/2015
709111^58763-27061196Enzo Doria07/2012
70922^203285-11232161195Enzo Doria06/2014
70932^203253-99514361186Paul Bourdelais11/2012
709415319^9862+9862^1531961184Hans Havermann07/2016
70957^72395-4461181Lelio R Paula04/2013
70965*2^203176-761163Lelio R Paula04/2014
70987^72358+5461150Lelio R Paula04/2013
70972^203133-11177561150Enzo Doria05/2014
7099(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
71002^203112-1800961143Enzo Doria05/2013
710143607!3+72961129Robert Price09/2014
71022^203065-11485361129Enzo Doria05/2015
71033^128111+19661125Lelio R Paula04/2013
7104128^29007+29007^12861124Serge Batalov05/2014
710522355*2^203009-361117Donovan Johnson03/2004
71062^203018+3361115Lelio R Paula08/2011
71072^203017-161561115Lelio R Paula10/2011
710816697^4570+4570^1669761110Hans Havermann12/2016
71092^202998-1724161109Enzo Doria05/2013
711020^46964+9361102Lelio R Paula06/2013
7111(55*10^61097-1)/961098Ray Chandler02/2012
711220^46960-546361097Enzo Doria03/2013
7113(11*10^61095+49)/361096Robert Price05/2016
71142^202934-595561090Lelio R Paula10/2011
711519^47772-6861089Lelio R Paula05/2013
71162^202877-49942361073Paul Bourdelais03/2013
71172^202763-1712561038Enzo Doria05/2013
7118(23*2^202756+1)/961037Lelio R Paula03/2012
711914788^13355+13355^1478861011Hans Havermann12/2016
712016069^6258+6258^1606961005Hans Havermann12/2016
71215^87276-1433661004Enzo Doria02/2013
712250^35899-49^3589960992Robert Price12/2012
71232^202599-304960989Yves Minet10/2014
71242^202535-11157160970Enzo Doria05/2014
712510^60959+5760960Patrick De Geest12/2008
712710^60959-6095960959Henri Lifchitz08/2002
712610^60959-2917760959Patrick De Geest08/2008
71285^87206+4^(87206+1)60955Robert Price07/2016
71292^202476-1590960952Enzo Doria04/2013
71302^202472-1751360951Enzo Doria05/2013
713114858^12651+12651^1485860950Hans Havermann12/2016
71322^202389-5869560926Lelio R Paula09/2011
71333^127597-3460880Lelio R Paula04/2013
713415088^10831+10831^1508860876Hans Havermann12/2016
71352^202198-11326160868Enzo Doria07/2014
71362^202182+13560863Lelio R Paula08/2011
71372^202176+8560862Lelio R Paula08/2011
71385183^16384+5182^1638460860Henri Lifchitz01/2007
7139(31*2^202163+1)/360859Lelio R Paula03/2012
714014708^13707+13707^1470860847Hans Havermann12/2016
71412^202112+202112^2-160842Robert Price04/2014
7142(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
714364743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7144(19*2^202098-1)/679560836Lelio R Paula01/2014
7145(6^78175-11)/560832Paul Bourdelais11/2011
71462^202063+160560828Lelio R Paula09/2011
71472^202058+85960826Lelio R Paula09/2011
71481576^19021+19021^157660821Serge Batalov05/2014
7149(2^202009+3)/600560807Lelio R Paula03/2012
715010^60776+360777Robert Price01/2011
715110^60776-1481960776Patrick De Geest12/2012
7152(6883*2^201869-1)/3560771Lelio R Paula04/2015
7153(27*2^201841-1)/4360760Lelio R Paula01/2014
71542^201822-17760755Lelio R Paula08/2011
7155(13*10^60744+17)/360745Robert Price06/2015
7156(31*2^201754-1)/9960734Lelio R Paula01/2014
7157(26*10^60717-71)/960718Robert Price03/2015
715837^38712-260709Lelio R Paula08/2013
71592^201657-11200360705Enzo Doria05/2014
7160(10^60703+3^60703)/1360702Robert Price01/2013
71612^201622-11281760695Enzo Doria06/2014
71622^201620-1717760694Enzo Doria05/2013
7163(2^201615-3)*6-760693Gilbert Mozzo05/2016
71642^201609-4978960691Henri Lifchitz03/2005
71652^201582-1906160683Enzo Doria05/2013
716643316!3+2760679Robert Price09/2014
7167(509203*2^201564-1)/506760679Lelio R Paula04/2015
71682^201560+10560676Lelio R Paula08/2011
7169(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
71702^201545-1802160672Enzo Doria05/2013
71712^201543+1171560671Lelio R Paula09/2011
71722^201512-11175560662Enzo Doria05/2014
7173p(13013)#/2+6460662Robert Price03/2017
717411^58248+1660660Lelio R Paula05/2013
71752^201496-2760657Lelio R Paula08/2011
71762^201426-1609760636Enzo Doria04/2013
7177(17*10^60631-11)/360632Robert Price07/2015
71786^77916-7760631Lelio R Paula04/2013
7179(27*2^201410-1)/49160630Lelio R Paula01/2014
71805^86727+9860620Lelio R Paula04/2013
718117^49266-2660620Lelio R Paula05/2013
718220^46589-3360614Lelio R Paula05/2013
71836^77889+6560610Lelio R Paula04/2013
7184139901#+14838760595Nicolas PALAU09/2016
71852^201285-11172360593Enzo Doria05/2014
718646199*2^201268+12964760593Paul Vanderveen11/2016
71883^126991-10060591Lelio R Paula04/2013
71872^201278-11162360591Enzo Doria05/2014
71895^86682-1600460589Enzo Doria05/2014
7190(58*10^60579+221)/960580Robert Price02/2017
71919*2^201231-560578Lelio R Paula04/2014
7192(78557*2^201207+1)/1306760571Lelio R Paula06/2014
71932^201186-6694560564Lelio R Paula09/2011
71942^201186-9439560564Lelio R Paula09/2011
719565^33403+3260557Lelio R Paula01/2016
7196103^30079+10260545Norbert Schneider10/2016
7197(1000159^10091+1)/100016060541Faysal YAtim08/2008
71982^201098-1771760537Enzo Doria05/2013
7199(3^126881+8)/482960534Lelio R Paula03/2012
72002^201074+7504960530Enzo Doria04/2016
720111^58111-129060517Enzo Doria11/2012
7202(509203*2^201012-1)/960516Lelio R Paula04/2015
72032^200911+571160481Lelio R Paula10/2011
7204(2^200912-3)/2360480Lelio R Paula03/2012
720518^48179-17^4817960478Jean-Louis Charton12/2010
720738^38281-37^3828160476Robert Price09/2012
72064*7^71560-360476Lelio R Paula09/2014
7208(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
7209lucasV(1,2,401712)+260464Mike Oakes01/2017
72102^200833-1849360457Enzo Doria05/2013
721120^46465-504360453Enzo Doria03/2013
72122^200810-1825760450Enzo Doria05/2013
72135^86466-1433660438Enzo Doria02/2013
7214Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
7215(29*2^200703-1)/23160417Lelio R Paula01/2014
72162^200682-101683160412Paul Bourdelais11/2012
72172^200617-1788160392Enzo Doria05/2013
7218(25^43201+1)/2660391Robert Price06/2013
72202^200609-13360390Lelio R Paula08/2011
72192^200608-1283760390Enzo Doria10/2012
72212^200607-1712160389Enzo Doria05/2013
722211^57975-162060375Enzo Doria11/2012
7223(9913*2^200538-1)/380160369Lelio R Paula04/2015
72245^86342+6460351Lelio R Paula04/2013
7225(14*10^60346-23)/960347Robert Price04/2015
72262^200457-829560344Lelio R Paula09/2011
72276^77546+11360343Lelio R Paula04/2013
722937^38461-36^3846160315Robert Price06/2012
72282^200361-1759360315Enzo Doria05/2013
723010103^15059-10660304Enzo Doria07/2012
72312^200301-1740160297Enzo Doria05/2013
7232(37*10^60290+71)/960291Robert Price04/2015
72332^200266-9439560287Lelio R Paula09/2011
72342^200261-11161360285Enzo Doria05/2014
723546^36238-4560256Norbert Schneider07/2014
723613^54091+9460255Lelio R Paula05/2013
7237311^24171-15460253Enzo Doria07/2012
72382^200120-8108960243Paul Bourdelais01/2012
72393^126262+868060243Lelio R Paula04/2013
724043031!3-5904960239Robert Price12/2015
72412^200100-11126960237Enzo Doria05/2014
7242(29*2^200069-1)/537360225Lelio R Paula01/2014
724320^46283-192360216Enzo Doria03/2013
72442^200011-11207560210Enzo Doria05/2014
72452^200002+7453960207Enzo Doria04/2016
7246(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
72472^199872+9360168Donovan Johnson06/2008
72486^77321+7760168Lelio R Paula04/2013
7249(86*10^60165-77)/960166Robert Price05/2016
7250(2^199868+78557)/2337360162Lelio R Paula05/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 21 2017 08:01 (Time in France)

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