PRP Records

Probable Primes Top 10000

(205869 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 ?
775111^58849-604061285Enzo Doria02/2013
775243694!3-361264Robert Price10/2014
775358*(10^(3*20420)-1)/111-161260Robert Price10/2014
77542^203490+1290961257Lelio R Paula10/2011
7755(16*10^61251-31)/361252Robert Price03/2016
775620^47077-570361249Enzo Doria03/2013
77572^203434-11308161240Enzo Doria07/2014
77595^87606+461234Wojciech Florek11/2005
77582^203412-16761234Lelio R Paula08/2011
77612^203402+108961231Lelio R Paula10/2011
7760(8*10^61230+67)/361231Robert Price01/2017
7762(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
77631265^19732+19732^126561211Serge Batalov05/2014
77642^203330+14561209Lelio R Paula08/2011
77656^78647-13761200Lelio R Paula04/2013
776685^31718+8461198Norbert Schneider10/2015
776711^58763-27061196Enzo Doria07/2012
77682^203285-11232161195Enzo Doria06/2014
77692^203253-99514361186Paul Bourdelais11/2012
777015319^9862+9862^1531961184Hans Havermann07/2016
77717^72395-4461181Lelio R Paula04/2013
7772(49*10^61167-67)/961168Robert Price08/2017
77735*2^203176-761163Lelio R Paula04/2014
7774(26*10^61156-413)/961157Robert Price10/2017
77757^72358+5461150Lelio R Paula04/2013
77762^203133-11177561150Enzo Doria05/2014
7777(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
77782^203112-1800961143Enzo Doria05/2013
777943607!3+72961129Robert Price09/2014
77802^203065-11485361129Enzo Doria05/2015
77813^128111+19661125Lelio R Paula04/2013
7782128^29007+29007^12861124Serge Batalov05/2014
77834*10^61119+4961120Robert Price08/2017
778422355*2^203009-361117Donovan Johnson03/2004
77852^203018+3361115Lelio R Paula08/2011
77862^203017-161561115Lelio R Paula10/2011
778716697^4570+4570^1669761110Hans Havermann12/2016
77882^202998-1724161109Enzo Doria05/2013
778920^46964+9361102Lelio R Paula06/2013
7790(55*10^61097-1)/961098Ray Chandler02/2012
779120^46960-546361097Enzo Doria03/2013
7792(11*10^61095+49)/361096Robert Price05/2016
77932^202934-595561090Lelio R Paula10/2011
779419^47772-6861089Lelio R Paula05/2013
77952^202877-49942361073Paul Bourdelais03/2013
77962^202763-1712561038Enzo Doria05/2013
7797(23*2^202756+1)/961037Lelio R Paula03/2012
779814788^13355+13355^1478861011Hans Havermann12/2016
779916069^6258+6258^1606961005Hans Havermann12/2016
78005^87276-1433661004Enzo Doria02/2013
780150^35899-49^3589960992Robert Price12/2012
78022^202599-304960989Yves Minet10/2014
78032^202535-11157160970Enzo Doria05/2014
7804(13*10^60966+107)/360967Robert Price11/2017
780610^60959+5760960Patrick De Geest12/2008
78056*10^60959-9160960Robert Price11/2017
780810^60959-6095960959Henri Lifchitz08/2002
780710^60959-2917760959Patrick De Geest08/2008
78095^87206+4^(87206+1)60955Robert Price07/2016
78102^202476-1590960952Enzo Doria04/2013
78112^202472-1751360951Enzo Doria05/2013
781214858^12651+12651^1485860950Hans Havermann12/2016
78132^202389-5869560926Lelio R Paula09/2011
78143^127597-3460880Lelio R Paula04/2013
781515088^10831+10831^1508860876Hans Havermann12/2016
78162^202198-11326160868Enzo Doria07/2014
78172^202182+13560863Lelio R Paula08/2011
78182^202176+8560862Lelio R Paula08/2011
78195183^16384+5182^1638460860Henri Lifchitz01/2007
7820(31*2^202163+1)/360859Lelio R Paula03/2012
782114708^13707+13707^1470860847Hans Havermann12/2016
78222^202112+202112^2-160842Robert Price04/2014
7823(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
782464743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
7825(19*2^202098-1)/679560836Lelio R Paula01/2014
7826(6^78175-11)/560832Paul Bourdelais11/2011
78272^202063+160560828Lelio R Paula09/2011
78282^202058+85960826Lelio R Paula09/2011
78291576^19021+19021^157660821Serge Batalov05/2014
7830(2^202009+3)/600560807Lelio R Paula03/2012
783110^60776+360777Robert Price01/2011
783210^60776-1481960776Patrick De Geest12/2012
783355*10^60772+760774Robert Price10/2017
7834(6883*2^201869-1)/3560771Lelio R Paula04/2015
7835(27*2^201841-1)/4360760Lelio R Paula01/2014
78362^201822-17760755Lelio R Paula08/2011
7837(13*10^60744+17)/360745Robert Price06/2015
7838(31*2^201754-1)/9960734Lelio R Paula01/2014
7839(26*10^60717-71)/960718Robert Price03/2015
784037^38712-260709Lelio R Paula08/2013
78412^201657-11200360705Enzo Doria05/2014
7842(10^60703+3^60703)/1360702Robert Price01/2013
78432^201622-11281760695Enzo Doria06/2014
78442^201620-1717760694Enzo Doria05/2013
7845(2^201615-3)*6-760693Gilbert Mozzo05/2016
78462^201609-4978960691Henri Lifchitz03/2005
78472^201582-1906160683Enzo Doria05/2013
784843316!3+2760679Robert Price09/2014
7849(509203*2^201564-1)/506760679Lelio R Paula04/2015
78502^201560+10560676Lelio R Paula08/2011
7851(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
78522^201545-1802160672Enzo Doria05/2013
78532^201543+1171560671Lelio R Paula09/2011
78552^201512-11175560662Enzo Doria05/2014
7854p(13013)#/2+6460662Robert Price03/2017
785611^58248+1660660Lelio R Paula05/2013
78572^201496-2760657Lelio R Paula08/2011
78585*10^60655+5760656Robert Price11/2017
7859(7*10^60643+197)/360644Robert Price07/2017
78602^201426-1609760636Enzo Doria04/2013
7861(17*10^60631-11)/360632Robert Price07/2015
78626^77916-7760631Lelio R Paula04/2013
7863(27*2^201410-1)/49160630Lelio R Paula01/2014
78645^86727+9860620Lelio R Paula04/2013
786517^49266-2660620Lelio R Paula05/2013
786620^46589-3360614Lelio R Paula05/2013
78676^77889+6560610Lelio R Paula04/2013
7868139901#+14838760595Nicolas PALAU09/2016
78692^201285-11172360593Enzo Doria05/2014
787046199*2^201268+12964760593Paul Vanderveen11/2016
78723^126991-10060591Lelio R Paula04/2013
78712^201278-11162360591Enzo Doria05/2014
78735^86682-1600460589Enzo Doria05/2014
7874(865*10^60583-1)/960585Robert Price11/2017
7875(58*10^60579+221)/960580Robert Price02/2017
78769*2^201231-560578Lelio R Paula04/2014
78774*10^60572-8960573Robert Price08/2017
7878(78557*2^201207+1)/1306760571Lelio R Paula06/2014
78792^201186-6694560564Lelio R Paula09/2011
78802^201186-9439560564Lelio R Paula09/2011
788165^33403+3260557Lelio R Paula01/2016
7882103^30079+10260545Norbert Schneider10/2016
7883(1000159^10091+1)/100016060541Faysal YAtim08/2008
78842^201098-1771760537Enzo Doria05/2013
7885(3^126881+8)/482960534Lelio R Paula03/2012
78862^201074+7504960530Enzo Doria04/2016
788711^58111-129060517Enzo Doria11/2012
7888(509203*2^201012-1)/960516Lelio R Paula04/2015
78892^200911+571160481Lelio R Paula10/2011
7890(2^200912-3)/2360480Lelio R Paula03/2012
789118^48179-17^4817960478Jean-Louis Charton12/2010
789338^38281-37^3828160476Robert Price09/2012
78924*7^71560-360476Lelio R Paula09/2014
7894(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
7895lucasV(1,2,401712)+260464Mike Oakes01/2017
78962^200833-1849360457Enzo Doria05/2013
789720^46465-504360453Enzo Doria03/2013
78982^200810-1825760450Enzo Doria05/2013
78995^86466-1433660438Enzo Doria02/2013
7900Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
7901(29*2^200703-1)/23160417Lelio R Paula01/2014
79022^200682-101683160412Paul Bourdelais11/2012
79032^200617-1788160392Enzo Doria05/2013
7904(25^43201+1)/2660391Robert Price06/2013
79062^200609-13360390Lelio R Paula08/2011
79052^200608-1283760390Enzo Doria10/2012
79072^200607-1712160389Enzo Doria05/2013
790811^57975-162060375Enzo Doria11/2012
7909(9913*2^200538-1)/380160369Lelio R Paula04/2015
79105^86342+6460351Lelio R Paula04/2013
7911(14*10^60346-23)/960347Robert Price04/2015
79122^200457-829560344Lelio R Paula09/2011
79136^77546+11360343Lelio R Paula04/2013
791537^38461-36^3846160315Robert Price06/2012
79142^200361-1759360315Enzo Doria05/2013
791610103^15059-10660304Enzo Doria07/2012
79172^200301-1740160297Enzo Doria05/2013
7918(37*10^60290+71)/960291Robert Price04/2015
79192^200266-9439560287Lelio R Paula09/2011
79202^200261-11161360285Enzo Doria05/2014
792146^36238-4560256Norbert Schneider07/2014
792213^54091+9460255Lelio R Paula05/2013
7923311^24171-15460253Enzo Doria07/2012
79242^200120-8108960243Paul Bourdelais01/2012
79253^126262+868060243Lelio R Paula04/2013
792643031!3-5904960239Robert Price12/2015
79272^200100-11126960237Enzo Doria05/2014
7928(29*2^200069-1)/537360225Lelio R Paula01/2014
792920^46283-192360216Enzo Doria03/2013
79302^200011-11207560210Enzo Doria05/2014
79312^200002+7453960207Enzo Doria04/2016
7932(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
7933(28*10^60180+149)/360181Robert Price10/2017
79342^199872+9360168Donovan Johnson06/2008
79356^77321+7760168Lelio R Paula04/2013
7936(86*10^60165-77)/960166Robert Price05/2016
7937(2^199868+78557)/2337360162Lelio R Paula05/2012
79387^71180+8260155Lelio R Paula04/2013
79402^199814-11229560151Enzo Doria06/2014
7939(51^35227-1)/5060151Paul Bourdelais08/2017
794142964!3-8160135Robert Price09/2014
79422^199709-5160119Lelio R Paula05/2011
79432^199700-11162360116Enzo Doria05/2014
7944(15185*2^199681-1)/15960112Lelio R Paula04/2015
79452^199672+253360108Henri Lifchitz09/2004
794620^46198-1160105Lelio R Paula04/2013
79472^199657+9325760103Yves Minet03/2010
79483^125967-11060102Lelio R Paula10/2012
79492^199654-1881360102Enzo Doria05/2013
7950(29*10^60100+19)/360101Robert Price01/2017
79512^199615-2*199615+160091Robert Price04/2018
7952129^28468+28468^12960085Serge Batalov05/2014
79532^199572-1587360078Enzo Doria04/2013
79549*2^199559+760075Lelio R Paula03/2014
79552^199527-11191960064Enzo Doria05/2014
79562^199522+8287560063Lelio R Paula10/2012
79575^85928-7260062Lelio R Paula10/2012
795839^37749+3860062Norbert Schneider05/2014
79596^77182-14360060Lelio R Paula10/2012
79602^199502-214560057Lelio R Paula06/2011
79612^199493+425760054Lelio R Paula06/2011
79622^199488+4075560052Lelio R Paula06/2011
7963(2^199451+9)/2561960037Lelio R Paula02/2012
79642^199425-6160033Lelio R Paula05/2011
7965(85*10^60026+23)/960027Robert Price11/2015
796665^33107+6260021Lelio R Paula01/2016
79682^199362-121560014Lelio R Paula06/2011
79672^199362-11163360014Enzo Doria05/2014
79691537^18832+18832^153760012Serge Batalov05/2014
79702^199324-1743360003Enzo Doria05/2013
797110^60000+20433160001Milton L. Brown04/2006
797210^60000+8712960001Milton L. Brown04/2006
7973143^27838-260001Lelio R Paula10/2017
798710^59999+6519760000Patrick De Geest04/2005
798810^60000-3252960000Patrick De Geest08/2009
7989(10^60000+2249)/960000Makoto Morimoto09/2016
7990((2^43112609)/10^24296)%10^6000060000Michael Vang10/2016
7991(2^57885161/10^105090)%10^6000060000Michael Vang10/2016
7992(2^42643801/10^58945)%10^6000060000Michael Vang10/2016
7974(2^37156667/10^243655)%10^6000060000Michael Vang10/2016
7975(2^30402457/10^69028)%10^6000060000Michael Vang11/2016
7976(2^32582657/10^248088)%10^6000060000Michael Vang11/2016
7977(2^32582657/10^238942)%10^6000060000Michael Vang11/2016
7978(2^24036583/10^13547)%10^6000060000Michael Vang11/2016
7979(2^20996011/10^131008)%10^6000060000Michael Vang11/2016
7980(2^13466917/10^79774)%10^6000060000Michael Vang11/2016
7981(2^13466917/10^102581)%10^6000060000Michael Vang11/2016
7982(2^6972593/10^339640)%10^6000060000Michael Vang11/2016
7983(2^2976221/10^65464)%10^6000060000Michael Vang12/2016
7984(2^1398269/10^61138)%10^6000060000Michael Vang12/2016
7985(2^3021377/10^418881)%10^6000060000Michael Vang12/2016
7986(2^1257787/10^164080)%10^6000060000Michael Vang12/2016
799610^59999-51626759999Patrick De Geest06/2009
799520^46116-4159999Lelio R Paula03/2013
7993(2^74207281/10^184638)%10^6000059999Michael Vang10/2016
7994(2^25964951/10^135429)%10^6000059999Michael Vang11/2016
79976^77100-5559996Lelio R Paula10/2012
7999(19*2^199274+1)/16159987Lelio R Paula07/2012
7998(23^44053+1)/2459987Robert Price06/2013
80009^62848+6^62848-2^6284859973Mike Oakes08/2010


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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