PRP Records

Probable Primes Top 10000

(172213 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 ?
70012^203642+3961303Lelio R Paula08/2011
7002floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
700311^58849-604061285Enzo Doria02/2013
700443694!3-361264Robert Price10/2014
700558*(10^(3*20420)-1)/111-161260Robert Price10/2014
70062^203490+1290961257Lelio R Paula10/2011
7007(16*10^61251-31)/361252Robert Price03/2016
700820^47077-570361249Enzo Doria03/2013
70092^203434-11308161240Enzo Doria07/2014
70115^87606+461234Wojciech Florek11/2005
70102^203412-16761234Lelio R Paula08/2011
70122^203402+108961231Lelio R Paula10/2011
7013(8*10^61230+67)/361231Robert Price01/2017
7014(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
70151265^19732+19732^126561211Serge Batalov05/2014
70162^203330+14561209Lelio R Paula08/2011
70176^78647-13761200Lelio R Paula04/2013
701885^31718+8461198Norbert Schneider10/2015
701911^58763-27061196Enzo Doria07/2012
70202^203285-11232161195Enzo Doria06/2014
70212^203253-99514361186Paul Bourdelais11/2012
702215319^9862+9862^1531961184Hans Havermann07/2016
70237^72395-4461181Lelio R Paula04/2013
70245*2^203176-761163Lelio R Paula04/2014
70267^72358+5461150Lelio R Paula04/2013
70252^203133-11177561150Enzo Doria05/2014
7027(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
70282^203112-1800961143Enzo Doria05/2013
702943607!3+72961129Robert Price09/2014
70302^203065-11485361129Enzo Doria05/2015
70313^128111+19661125Lelio R Paula04/2013
7032128^29007+29007^12861124Serge Batalov05/2014
703322355*2^203009-361117Donovan Johnson03/2004
70342^203018+3361115Lelio R Paula08/2011
70352^203017-161561115Lelio R Paula10/2011
703616697^4570+4570^1669761110Hans Havermann12/2016
70372^202998-1724161109Enzo Doria05/2013
703820^46964+9361102Lelio R Paula06/2013
7039(55*10^61097-1)/961098Ray Chandler02/2012
704020^46960-546361097Enzo Doria03/2013
7041(11*10^61095+49)/361096Robert Price05/2016
70422^202934-595561090Lelio R Paula10/2011
704319^47772-6861089Lelio R Paula05/2013
70442^202877-49942361073Paul Bourdelais03/2013
70452^202763-1712561038Enzo Doria05/2013
7046(23*2^202756+1)/961037Lelio R Paula03/2012
704714788^13355+13355^1478861011Hans Havermann12/2016
704816069^6258+6258^1606961005Hans Havermann12/2016
70495^87276-1433661004Enzo Doria02/2013
705050^35899-49^3589960992Robert Price12/2012
70512^202599-304960989Yves Minet10/2014
70522^202535-11157160970Enzo Doria05/2014
705310^60959+5760960Patrick De Geest12/2008
705510^60959-6095960959Henri Lifchitz08/2002
705410^60959-2917760959Patrick De Geest08/2008
70565^87206+4^(87206+1)60955Robert Price07/2016
70572^202476-1590960952Enzo Doria04/2013
70582^202472-1751360951Enzo Doria05/2013
705914858^12651+12651^1485860950Hans Havermann12/2016
70602^202389-5869560926Lelio R Paula09/2011
70613^127597-3460880Lelio R Paula04/2013
706215088^10831+10831^1508860876Hans Havermann12/2016
70632^202198-11326160868Enzo Doria07/2014
70642^202182+13560863Lelio R Paula08/2011
70652^202176+8560862Lelio R Paula08/2011
70665183^16384+5182^1638460860Henri Lifchitz01/2007
7067(31*2^202163+1)/360859Lelio R Paula03/2012
706814708^13707+13707^1470860847Hans Havermann12/2016
70692^202112+202112^2-160842Robert Price04/2014
7070(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
707164743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7072(19*2^202098-1)/679560836Lelio R Paula01/2014
7073(6^78175-11)/560832Paul Bourdelais11/2011
70742^202063+160560828Lelio R Paula09/2011
70752^202058+85960826Lelio R Paula09/2011
70761576^19021+19021^157660821Serge Batalov05/2014
7077(2^202009+3)/600560807Lelio R Paula03/2012
707810^60776+360777Robert Price01/2011
707910^60776-1481960776Patrick De Geest12/2012
7080(6883*2^201869-1)/3560771Lelio R Paula04/2015
7081(27*2^201841-1)/4360760Lelio R Paula01/2014
70822^201822-17760755Lelio R Paula08/2011
7083(13*10^60744+17)/360745Robert Price06/2015
7084(31*2^201754-1)/9960734Lelio R Paula01/2014
7085(26*10^60717-71)/960718Robert Price03/2015
708637^38712-260709Lelio R Paula08/2013
70872^201657-11200360705Enzo Doria05/2014
7088(10^60703+3^60703)/1360702Robert Price01/2013
70892^201622-11281760695Enzo Doria06/2014
70902^201620-1717760694Enzo Doria05/2013
7091(2^201615-3)*6-760693Gilbert Mozzo05/2016
70922^201609-4978960691Henri Lifchitz03/2005
70932^201582-1906160683Enzo Doria05/2013
709443316!3+2760679Robert Price09/2014
7095(509203*2^201564-1)/506760679Lelio R Paula04/2015
70962^201560+10560676Lelio R Paula08/2011
7097(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
70982^201545-1802160672Enzo Doria05/2013
70992^201543+1171560671Lelio R Paula09/2011
71002^201512-11175560662Enzo Doria05/2014
710111^58248+1660660Lelio R Paula05/2013
71022^201496-2760657Lelio R Paula08/2011
71032^201426-1609760636Enzo Doria04/2013
7104(17*10^60631-11)/360632Robert Price07/2015
71056^77916-7760631Lelio R Paula04/2013
7106(27*2^201410-1)/49160630Lelio R Paula01/2014
71075^86727+9860620Lelio R Paula04/2013
710817^49266-2660620Lelio R Paula05/2013
710920^46589-3360614Lelio R Paula05/2013
71106^77889+6560610Lelio R Paula04/2013
7111139901#+14838760595Nicolas PALAU09/2016
71122^201285-11172360593Enzo Doria05/2014
711346199*2^201268+12964760593Paul Vanderveen11/2016
71153^126991-10060591Lelio R Paula04/2013
71142^201278-11162360591Enzo Doria05/2014
71165^86682-1600460589Enzo Doria05/2014
7117(58*10^60579+221)/960580Robert Price02/2017
71189*2^201231-560578Lelio R Paula04/2014
7119(78557*2^201207+1)/1306760571Lelio R Paula06/2014
71202^201186-6694560564Lelio R Paula09/2011
71212^201186-9439560564Lelio R Paula09/2011
712265^33403+3260557Lelio R Paula01/2016
7123103^30079+10260545Norbert Schneider10/2016
7124(1000159^10091+1)/100016060541Faysal YAtim08/2008
71252^201098-1771760537Enzo Doria05/2013
7126(3^126881+8)/482960534Lelio R Paula03/2012
71272^201074+7504960530Enzo Doria04/2016
712811^58111-129060517Enzo Doria11/2012
7129(509203*2^201012-1)/960516Lelio R Paula04/2015
71302^200911+571160481Lelio R Paula10/2011
7131(2^200912-3)/2360480Lelio R Paula03/2012
713218^48179-17^4817960478Jean-Louis Charton12/2010
713438^38281-37^3828160476Robert Price09/2012
71334*7^71560-360476Lelio R Paula09/2014
7135(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
7136lucasV(1,2,401712)+260464Mike Oakes01/2017
71372^200833-1849360457Enzo Doria05/2013
713820^46465-504360453Enzo Doria03/2013
71392^200810-1825760450Enzo Doria05/2013
71405^86466-1433660438Enzo Doria02/2013
7141Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
7142(29*2^200703-1)/23160417Lelio R Paula01/2014
71432^200682-101683160412Paul Bourdelais11/2012
71442^200617-1788160392Enzo Doria05/2013
7145(25^43201+1)/2660391Robert Price06/2013
71472^200609-13360390Lelio R Paula08/2011
71462^200608-1283760390Enzo Doria10/2012
71482^200607-1712160389Enzo Doria05/2013
714911^57975-162060375Enzo Doria11/2012
7150(9913*2^200538-1)/380160369Lelio R Paula04/2015
71515^86342+6460351Lelio R Paula04/2013
7152(14*10^60346-23)/960347Robert Price04/2015
71532^200457-829560344Lelio R Paula09/2011
71546^77546+11360343Lelio R Paula04/2013
715637^38461-36^3846160315Robert Price06/2012
71552^200361-1759360315Enzo Doria05/2013
715710103^15059-10660304Enzo Doria07/2012
71582^200301-1740160297Enzo Doria05/2013
7159(37*10^60290+71)/960291Robert Price04/2015
71602^200266-9439560287Lelio R Paula09/2011
71612^200261-11161360285Enzo Doria05/2014
716246^36238-4560256Norbert Schneider07/2014
716313^54091+9460255Lelio R Paula05/2013
7164311^24171-15460253Enzo Doria07/2012
71652^200120-8108960243Paul Bourdelais01/2012
71663^126262+868060243Lelio R Paula04/2013
716743031!3-5904960239Robert Price12/2015
71682^200100-11126960237Enzo Doria05/2014
7169(29*2^200069-1)/537360225Lelio R Paula01/2014
717020^46283-192360216Enzo Doria03/2013
71712^200011-11207560210Enzo Doria05/2014
71722^200002+7453960207Enzo Doria04/2016
7173(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
71742^199872+9360168Donovan Johnson06/2008
71756^77321+7760168Lelio R Paula04/2013
7176(86*10^60165-77)/960166Robert Price05/2016
7177(2^199868+78557)/2337360162Lelio R Paula05/2012
71787^71180+8260155Lelio R Paula04/2013
71792^199814-11229560151Enzo Doria06/2014
718042964!3-8160135Robert Price09/2014
71812^199709-5160119Lelio R Paula05/2011
71822^199700-11162360116Enzo Doria05/2014
7183(15185*2^199681-1)/15960112Lelio R Paula04/2015
71842^199672+253360108Henri Lifchitz09/2004
718520^46198-1160105Lelio R Paula04/2013
71862^199657+9325760103Yves Minet03/2010
71873^125967-11060102Lelio R Paula10/2012
71882^199654-1881360102Enzo Doria05/2013
7189(29*10^60100+19)/360101Robert Price01/2017
7190129^28468+28468^12960085Serge Batalov05/2014
71912^199572-1587360078Enzo Doria04/2013
71929*2^199559+760075Lelio R Paula03/2014
71932^199527-11191960064Enzo Doria05/2014
71942^199522+8287560063Lelio R Paula10/2012
71955^85928-7260062Lelio R Paula10/2012
719639^37749+3860062Norbert Schneider05/2014
71976^77182-14360060Lelio R Paula10/2012
71982^199502-214560057Lelio R Paula06/2011
71992^199493+425760054Lelio R Paula06/2011
72002^199488+4075560052Lelio R Paula06/2011
7201(2^199451+9)/2561960037Lelio R Paula02/2012
72022^199425-6160033Lelio R Paula05/2011
7203(85*10^60026+23)/960027Robert Price11/2015
720465^33107+6260021Lelio R Paula01/2016
72062^199362-121560014Lelio R Paula06/2011
72052^199362-11163360014Enzo Doria05/2014
72071537^18832+18832^153760012Serge Batalov05/2014
72082^199324-1743360003Enzo Doria05/2013
720910^60000+20433160001Milton L. Brown04/2006
721010^60000+8712960001Milton L. Brown04/2006
721110^59999+6519760000Patrick De Geest04/2005
722910^60000-3252960000Patrick De Geest08/2009
7225(10^60000+2249)/960000Makoto Morimoto09/2016
7226((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
7227(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
7228(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
7212(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
7213(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
7214(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
7215(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
7216(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
7217(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
7218(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
7219(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
7220(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
7221(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
7222(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
7223(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
7224(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
723310^59999-51626759999Patrick De Geest06/2009
723120^46116-4159999Lelio R Paula03/2013
7230(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
7232(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
72346^77100-5559996Lelio R Paula10/2012
7236(19*2^199274+1)/16159987Lelio R Paula07/2012
7235(23^44053+1)/2459987Robert Price06/2013
72379^62848+6^62848-2^6284859973Mike Oakes08/2010
723815852^6061+6061^1585259961Hans Havermann08/2016
723919^46880-2059948Lelio R Paula03/2013
72402^199107-1773759938Enzo Doria05/2013
7241(13*10^59928+83)/359929Robert Price09/2016
724210^59913+10893143159914Marisa Kirisame02/2015
724310^59913+4861959914Patrick De Geest04/2016
724410^59913-7412359913Patrick De Geest03/2016
7245t(199528)59890Robert Price01/2015
72462^198903-1790159876Enzo Doria05/2013
7247gcd(V(776555),5*F(155311)*(F(155311)+1)+1)59858Serge Batalov04/2015
7248(3^125447+7)/259854Lelio R Paula04/2012
72495^85630+4^(85630-1)59853Robert Price03/2016
72502^198824-213559852Yves Minet06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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