PRP Records

Probable Primes Top 10000

(212140 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 ?
77512^204767-1586561642Enzo Doria04/2013
77527*2^204751-961638Lelio R Paula04/2014
77534*10^61625+2161626Robert Price08/2016
775415369^10226+10226^1536961626Hans Havermann02/2017
77552^204702-1812561622Enzo Doria05/2013
77565*3^129146+861620Lelio R Paula04/2014
77572^204673+12961613Lelio R Paula08/2011
775818^49079+9761608Lelio R Paula05/2013
7759106^30416+10561602Norbert Schneider12/2016
77602^204590-3361588Lelio R Paula08/2011
77612^204586-11197561587Enzo Doria06/2014
77622^204580-1607761585Enzo Doria04/2013
77632^204574-1604161583Enzo Doria04/2013
776415^52358+5661578Lelio R Paula05/2013
7765(28*10^61574+11)/361575Robert Price11/2015
77662^204516-1749361566Enzo Doria05/2013
77674*5^88076-361564Lelio R Paula09/2014
776811^59110-252061557Enzo Doria12/2012
77692^204477-5869561554Lelio R Paula09/2011
777012^57026-7361542Lelio R Paula05/2013
7771(257^25537+1)/25861541Richard Fischer04/2018
777217^50013+9061539Lelio R Paula05/2013
777356^35201-55^3520161538Robert Price10/2013
77748*7^72810+561533Lelio R Paula09/2014
7776204^26641-203^2664161531Jean-Louis Charton08/2009
777543867!3-656161531Robert Price11/2015
777710^61525+9^(61525-1)61526Robert Price03/2016
777810^61525+6225761526Patrick De Geest12/2016
777914821^14166+14166^1482161526Hans Havermann01/2017
778112^57010-8561525Lelio R Paula05/2013
778010^61525-21357961525Patrick De Geest12/2016
77822^204332-9961511Lelio R Paula08/2011
77832^204323-222161508Yves Minet08/2013
77852^204317-19561506Lelio R Paula08/2011
77843^128910-8661506Lelio R Paula04/2013
77862^204318+7453961506Enzo Doria04/2016
7787(2^204334-3)/114133361505Lelio R Paula03/2012
77882^204297-103609361500Paul Bourdelais11/2012
77893^128880+5861492Lelio R Paula04/2013
77902^204216-11167761476Enzo Doria05/2014
7791(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
77922^204129+20412961449Henri Lifchitz04/2002
77933^128787+2^(128787-1)61448Robert Price05/2016
779411^58999-7861442Lelio R Paula05/2013
77952^204083-11196761436Enzo Doria05/2014
7796(45^37159+1)/4661431Robert Price11/2013
7797677^21702+21702^67761430Norbert Schneider06/2016
779814837^13810+13810^1483761429Hans Havermann02/2017
7799(7*2^204043+1)/3961423Lelio R Paula03/2012
780011^58976-174061418Enzo Doria11/2012
78012^204016-1608561415Enzo Doria04/2013
7802V(379967)61393Serge Batalov03/2015
780343777!3-3^4377761392Robert Price08/2015
78047^72642+8861390Lelio R Paula04/2013
78053^128656+3261385Lelio R Paula04/2013
78062^203916-1749361385Enzo Doria05/2013
78076^78880+2361381Lelio R Paula04/2013
7808(388*10^61374-1)/961376Robert Price11/2017
78092^203877-11179961374Enzo Doria05/2014
78102^203867-161561371Lelio R Paula10/2011
78114*10^61367+1961368Robert Price04/2016
7812(19*2^203854+1)/4231961363Lelio R Paula08/2012
7813L(293659)/7652812271961361Serge Batalov07/2017
78142^203825-1580561358Enzo Doria04/2013
78152^203816-1582561355Enzo Doria04/2013
78165*10^61348+5961349Robert Price09/2016
781721^46395-261345Lelio R Paula08/2013
7818(809*29^41946-165)/2861344Curtis Bright05/2015
78197*6^78826+561340Lelio R Paula09/2014
7820(3^128558+7)/8377316642969661324Lelio R Paula04/2012
78212^203706-11161322Lelio R Paula08/2011
782217567^3094+3094^1756761318Hans Havermann02/2017
78232^203689-3161317Thomas Masser10/2005
7824(11*2^203678-1)/5368961310Lelio R Paula01/2014
78262^203642+3961303Lelio R Paula08/2011
7825floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
782711^58849-604061285Enzo Doria02/2013
782843694!3-361264Robert Price10/2014
782958*(10^(3*20420)-1)/111-161260Robert Price10/2014
78302^203490+1290961257Lelio R Paula10/2011
7831(16*10^61251-31)/361252Robert Price03/2016
783220^47077-570361249Enzo Doria03/2013
78332^203434-11308161240Enzo Doria07/2014
78355^87606+461234Wojciech Florek11/2005
78342^203412-16761234Lelio R Paula08/2011
78372^203402+108961231Lelio R Paula10/2011
7836(8*10^61230+67)/361231Robert Price01/2017
7838(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
78391265^19732+19732^126561211Serge Batalov05/2014
78402^203330+14561209Lelio R Paula08/2011
78416^78647-13761200Lelio R Paula04/2013
784285^31718+8461198Norbert Schneider10/2015
784311^58763-27061196Enzo Doria07/2012
78442^203285-11232161195Enzo Doria06/2014
78452^203253-99514361186Paul Bourdelais11/2012
784615319^9862+9862^1531961184Hans Havermann07/2016
78477^72395-4461181Lelio R Paula04/2013
7848(49*10^61167-67)/961168Robert Price08/2017
78495*2^203176-761163Lelio R Paula04/2014
7850(26*10^61156-413)/961157Robert Price10/2017
78517^72358+5461150Lelio R Paula04/2013
78522^203133-11177561150Enzo Doria05/2014
7853(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
78542^203112-1800961143Enzo Doria05/2013
785543607!3+72961129Robert Price09/2014
78562^203065-11485361129Enzo Doria05/2015
78573^128111+19661125Lelio R Paula04/2013
7858128^29007+29007^12861124Serge Batalov05/2014
78594*10^61119+4961120Robert Price08/2017
786022355*2^203009-361117Donovan Johnson03/2004
78612^203018+3361115Lelio R Paula08/2011
78622^203017-161561115Lelio R Paula10/2011
786316697^4570+4570^1669761110Hans Havermann12/2016
78642^202998-1724161109Enzo Doria05/2013
786520^46964+9361102Lelio R Paula06/2013
7866(55*10^61097-1)/961098Ray Chandler02/2012
786720^46960-546361097Enzo Doria03/2013
7868(11*10^61095+49)/361096Robert Price05/2016
78692^202934-595561090Lelio R Paula10/2011
787019^47772-6861089Lelio R Paula05/2013
78712^202877-49942361073Paul Bourdelais03/2013
78722^202763-1712561038Enzo Doria05/2013
7873(23*2^202756+1)/961037Lelio R Paula03/2012
787414788^13355+13355^1478861011Hans Havermann12/2016
787516069^6258+6258^1606961005Hans Havermann12/2016
78765^87276-1433661004Enzo Doria02/2013
787750^35899-49^3589960992Robert Price12/2012
78782^202599-304960989Yves Minet10/2014
78792^202535-11157160970Enzo Doria05/2014
7880(13*10^60966+107)/360967Robert Price11/2017
788210^60959+5760960Patrick De Geest12/2008
78816*10^60959-9160960Robert Price11/2017
788410^60959-6095960959Henri Lifchitz08/2002
788310^60959-2917760959Patrick De Geest08/2008
78855^87206+4^(87206+1)60955Robert Price07/2016
78862^202476-1590960952Enzo Doria04/2013
78872^202472-1751360951Enzo Doria05/2013
788814858^12651+12651^1485860950Hans Havermann12/2016
78892^202389-5869560926Lelio R Paula09/2011
78903^127597-3460880Lelio R Paula04/2013
789115088^10831+10831^1508860876Hans Havermann12/2016
78922^202198-11326160868Enzo Doria07/2014
78932^202182+13560863Lelio R Paula08/2011
78942^202176+8560862Lelio R Paula08/2011
78955183^16384+5182^1638460860Henri Lifchitz01/2007
7896(31*2^202163+1)/360859Lelio R Paula03/2012
789714708^13707+13707^1470860847Hans Havermann12/2016
78982^202112+202112^2-160842Robert Price04/2014
7899(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
790064743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7901(19*2^202098-1)/679560836Lelio R Paula01/2014
7902(6^78175-11)/560832Paul Bourdelais11/2011
79032^202063+160560828Lelio R Paula09/2011
79042^202058+85960826Lelio R Paula09/2011
79051576^19021+19021^157660821Serge Batalov05/2014
7906(2^202009+3)/600560807Lelio R Paula03/2012
790710^60776+360777Robert Price01/2011
790810^60776-1481960776Patrick De Geest12/2012
790955*10^60772+760774Robert Price10/2017
7910(6883*2^201869-1)/3560771Lelio R Paula04/2015
7911(27*2^201841-1)/4360760Lelio R Paula01/2014
79122^201822-17760755Lelio R Paula08/2011
7913(13*10^60744+17)/360745Robert Price06/2015
7914(31*2^201754-1)/9960734Lelio R Paula01/2014
7915(26*10^60717-71)/960718Robert Price03/2015
791637^38712-260709Lelio R Paula08/2013
79172^201657-11200360705Enzo Doria05/2014
7918(10^60703+3^60703)/1360702Robert Price01/2013
79192^201622-11281760695Enzo Doria06/2014
79202^201620-1717760694Enzo Doria05/2013
7921(2^201615-3)*6-760693Gilbert Mozzo05/2016
79222^201609-4978960691Henri Lifchitz03/2005
79232^201582-1906160683Enzo Doria05/2013
792443316!3+2760679Robert Price09/2014
7925(509203*2^201564-1)/506760679Lelio R Paula04/2015
79262^201560+10560676Lelio R Paula08/2011
7927(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
79282^201545-1802160672Enzo Doria05/2013
79292^201543+1171560671Lelio R Paula09/2011
79312^201512-11175560662Enzo Doria05/2014
7930p(13013)#/2+6460662Robert Price03/2017
793211^58248+1660660Lelio R Paula05/2013
79332^201496-2760657Lelio R Paula08/2011
79345*10^60655+5760656Robert Price11/2017
7935(7*10^60643+197)/360644Robert Price07/2017
79362^201426-1609760636Enzo Doria04/2013
7937(17*10^60631-11)/360632Robert Price07/2015
79386^77916-7760631Lelio R Paula04/2013
7939(27*2^201410-1)/49160630Lelio R Paula01/2014
79405^86727+9860620Lelio R Paula04/2013
794117^49266-2660620Lelio R Paula05/2013
794220^46589-3360614Lelio R Paula05/2013
79436^77889+6560610Lelio R Paula04/2013
7944139901#+14838760595Nicolas PALAU09/2016
79452^201285-11172360593Enzo Doria05/2014
794646199*2^201268+12964760593Paul Vanderveen11/2016
79483^126991-10060591Lelio R Paula04/2013
79472^201278-11162360591Enzo Doria05/2014
79495^86682-1600460589Enzo Doria05/2014
7950(865*10^60583-1)/960585Robert Price11/2017
7951(58*10^60579+221)/960580Robert Price02/2017
79529*2^201231-560578Lelio R Paula04/2014
79534*10^60572-8960573Robert Price08/2017
7954(78557*2^201207+1)/1306760571Lelio R Paula06/2014
79552^201186-6694560564Lelio R Paula09/2011
79562^201186-9439560564Lelio R Paula09/2011
795765^33403+3260557Lelio R Paula01/2016
7958103^30079+10260545Norbert Schneider10/2016
7959(1000159^10091+1)/100016060541Faysal YAtim08/2008
79602^201098-1771760537Enzo Doria05/2013
7961(3^126881+8)/482960534Lelio R Paula03/2012
79622^201074+7504960530Enzo Doria04/2016
796311^58111-129060517Enzo Doria11/2012
7964(509203*2^201012-1)/960516Lelio R Paula04/2015
79652^200911+571160481Lelio R Paula10/2011
7966(2^200912-3)/2360480Lelio R Paula03/2012
796718^48179-17^4817960478Jean-Louis Charton12/2010
796938^38281-37^3828160476Robert Price09/2012
79684*7^71560-360476Lelio R Paula09/2014
7970(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
7971lucasV(1,2,401712)+260464Mike Oakes01/2017
79722^200833-1849360457Enzo Doria05/2013
797320^46465-504360453Enzo Doria03/2013
79742^200810-1825760450Enzo Doria05/2013
7975((2)^(2*100400-1)+(2)^(100400-1)+1)+2667260447Faysal YAtim04/2018
79765^86466-1433660438Enzo Doria02/2013
7977Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
7978(29*2^200703-1)/23160417Lelio R Paula01/2014
79792^200682-101683160412Paul Bourdelais11/2012
79802^200617-1788160392Enzo Doria05/2013
7981(25^43201+1)/2660391Robert Price06/2013
79832^200609-13360390Lelio R Paula08/2011
79822^200608-1283760390Enzo Doria10/2012
79842^200607-1712160389Enzo Doria05/2013
798511^57975-162060375Enzo Doria11/2012
7986(9913*2^200538-1)/380160369Lelio R Paula04/2015
79875^86342+6460351Lelio R Paula04/2013
7988(14*10^60346-23)/960347Robert Price04/2015
79892^200457-829560344Lelio R Paula09/2011
79906^77546+11360343Lelio R Paula04/2013
799237^38461-36^3846160315Robert Price06/2012
79912^200361-1759360315Enzo Doria05/2013
799310103^15059-10660304Enzo Doria07/2012
79942^200301-1740160297Enzo Doria05/2013
7995(37*10^60290+71)/960291Robert Price04/2015
79962^200266-9439560287Lelio R Paula09/2011
79972^200261-11161360285Enzo Doria05/2014
799846^36238-4560256Norbert Schneider07/2014
799913^54091+9460255Lelio R Paula05/2013
8000311^24171-15460253Enzo Doria07/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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