PRP Records

Probable Primes Top 10000

(255312 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 ?
7501(21*2^234772-1)/209570672Lelio R Paula01/2014
7502(29*2^234686-1)/2114570645Lelio R Paula01/2014
7503(15*2^234688-1)/527814170643Lelio R Paula01/2014
75052^234655-6770639Lelio R Paula02/2012
7504(79*10^70638-61)/970639Robert Price10/2015
75062^234652-17370638Lelio R Paula02/2012
75072^234618-364570628Lelio R Paula05/2012
7508(2^234610-5)/1970624Lelio R Paula05/2012
75094*5^101038+970624Lelio R Paula10/2014
75102^234603+7196370623Enzo Doria04/2016
75112^234600-11312970622Enzo Doria07/2014
75122^234586+970618Lelio R Paula02/2012
75133^148008+2670618Robert Price11/2013
7514(7*10^70616-151)/970616Robert Price09/2017
751565^38947+3270608Lelio R Paula01/2016
751618363^6988+6988^1836370594Hans Havermann10/2019
7517(2^234488-3)/1170587Lelio R Paula05/2012
7518(3*2^234451+1)/3570576Lelio R Paula08/2012
7519Phi(159495,10)70560Maksym Voznyy09/2015
75202^234383-403570557Lelio R Paula05/2012
75212^234315-11124170536Enzo Doria05/2014
752214^61526+9770517Lelio R Paula01/2015
752314742^16915+16915^1474270512Norbert Schneider10/2019
7524(3*2^234170+1)/1370492Lelio R Paula08/2012
752551^41281-50^4128170491Robert Price02/2013
75262^234141-11212370484Enzo Doria06/2014
75272^234139+1228570483Lelio R Paula04/2012
75282^234133-316370482Yves Minet04/2009
75292^234115+8370476Lelio R Paula02/2012
75302^234114-159570476Lelio R Paula05/2012
753124^51061-23^5106170475Robert Price07/2012
753219471^16428-270467Faysal YAtim09/2005
75337^83381+1270466Robert Price01/2014
75342^234067-11142770462Enzo Doria05/2014
7535(266*10^70457+1)/370459Robert Price02/2016
7536(31*2^234041-1)/9770453Lelio R Paula01/2014
75372^234026+1290970449Lelio R Paula04/2012
75382^233965-1970431Lelio R Paula02/2012
7539(5*2^233932-1)/17970419Lelio R Paula01/2014
75402^233908-1710970414Enzo Doria05/2013
7541695^24772+24772^69570402Norbert Schneider09/2016
75423*5^100719-270401Lelio R Paula10/2014
75432^233829-11135570390Enzo Doria05/2014
7544(19775^16384+1)/270388Henri Lifchitz03/2007
75457*3^147519+870386Lelio R Paula04/2014
7546141^32749-270385Lelio R Paula10/2017
75475*7^83265+270368Lelio R Paula10/2014
7548(23*10^70363+97)/370364Robert Price02/2017
7549(23*2^233749-1)/3532570363Lelio R Paula01/2014
75505^100652-1391670353Enzo Doria02/2013
755145^42555-270353Lelio R Paula08/2013
75522^233661-6170339Lelio R Paula02/2012
75532^233523-11224970298Enzo Doria06/2014
75545*3^147324-870293Lelio R Paula04/2014
75552^233488-1306570287Enzo Doria11/2012
7556(3^147322+8)/4285170286Lelio R Paula06/2012
7557(22*10^70259+161)/370260Robert Price02/2017
75592^233388+46570257Lelio R Paula11/2012
755814^61299+5970257Lelio R Paula01/2015
75602^233383+9406570256Lelio R Paula04/2012
756149471!3-656170253Robert Price11/2015
75627^83121+6^(83121-1)70246Robert Price03/2016
7563(197*10^70241-11)/370243Robert Price10/2017
756423*10^70240-770242Robert Price03/2016
7565(71*10^70227-53)/970228Robert Price10/2015
756619825^3486+3486^1982570227Hans Havermann10/2019
756710815^17408+17408^1081570225Norbert Schneider05/2019
7568(2^233247-9)/1770214Lelio R Paula05/2012
7569(11^67421-2^67421)/970211Robert Price01/2013
7570(23*10^70209-41)/970210Robert Price03/2015
7571(29*10^70194-11)/970195Robert Price04/2015
75723^147109+19670189Lelio R Paula05/2014
7573(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
75749^73538+8^(73538+1)70174Robert Price06/2016
75752*5^100391+770171Lelio R Paula10/2014
757699^35156-270159Lelio R Paula08/2013
7577(68*10^70148+7)/370150Robert Price03/2016
757811^67360-603070149Enzo Doria01/2013
7579(35*10^70130-377)/970131Robert Price12/2017
758049391!3+3^4939170128Robert Price09/2015
7581(229*10^70122-1)/370124Robert Price12/2016
75827^82975-9270123Lelio R Paula07/2014
758320294^2853+2853^2029470122Hans Havermann10/2019
758465^38670+5870106Lelio R Paula01/2016
7585105^34684+34684^10570103Serge Batalov05/2014
758618597^5882+5882^1859770102Hans Havermann10/2019
7587134^32955-13370099Norbert Schneider03/2015
75902^232836-22790370091Enzo Doria12/2012
75892^232837-185917370091Enzo Doria03/2016
758817778^8761+8761^1777870091Hans Havermann10/2019
75913*2^232820+570087Lelio R Paula04/2014
75932^232799+9019570080Lelio R Paula02/2013
75922^232799-11223770080Enzo Doria06/2014
759417894^8247+8247^1789470079Hans Havermann09/2019
75952^232759+26214570068Lelio R Paula04/2012
759616817^14670+14670^1681770067Hans Havermann09/2019
75973*2^232750+770066Lelio R Paula04/2014
759812^64918-1170059Lelio R Paula01/2015
75997^82899-1270058Lelio R Paula09/2013
7600(22*10^70051-13)/970052Robert Price03/2015
760116428^16615-16615^1642870042Norbert Schneider11/2019
7602(2^232685-7)/251462570039Lelio R Paula04/2012
760318^55786-536370027Enzo Doria03/2013
7604(2^(77537*3+1)+243)/770023Kevin Acres11/2013
76052^232602+16970021Lelio R Paula02/2012
7606(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
76072^232580+7213370014Enzo Doria04/2016
76084*6^89958-770002Lelio R Paula09/2014
760910^70000+8048770001Milton L. Brown05/2006
761010^69999+13485770000Patrick De Geest02/2007
761110^70000-927370000Patrick De Geest08/2009
7612(79*10^69999-7)/970000Robert Price01/2015
7615((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
7613(2^756839/10^36014)%10^7000070000Michael Vang12/2016
7614(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
761610^69999-8825169999Patrick De Geest08/2009
76172^232507+108969992Lelio R Paula04/2012
7618(17*2^232445+1)/569974Lelio R Paula08/2012
7619(529^25693+1)/53069972Richard Fischer12/2017
76207^82778+4869956Lelio R Paula09/2013
76217*2^232381+369955Lelio R Paula04/2014
762219305^4204+4204^1930569955Hans Havermann10/2019
76232^232362-11054169948Enzo Doria05/2014
762419442^3957+3957^1944269940Hans Havermann09/2019
76252^232326-11239169938Enzo Doria06/2014
76263^146575+23669935Lelio R Paula09/2013
762730^47341-2969929Norbert Schneider02/2014
76285^100040-6869925Lelio R Paula09/2013
76299946^17491+17491^994669923Norbert Schneider07/2019
763016351^16592-16592^1635169912Norbert Schneider11/2019
7631(35*10^69866-593)/969867Robert Price08/2017
76322^232045-1729569853Lelio R Paula04/2012
7633(2^231987+78557)/9569834Lelio R Paula05/2012
76342^231955+7424369826Yves Minet03/2011
76352^231946-1587369823Enzo Doria04/2013
763618^55618+9569816Lelio R Paula09/2013
76376^89712+5^(89712-1)69810Robert Price02/2016
76382^231870+13569800Lelio R Paula02/2012
7639(23*2^231827-1)/417969785Lelio R Paula01/2014
76402^231778+5461569773Lelio R Paula04/2012
7641(19*2^231780+1)/23569772Lelio R Paula08/2012
764214^60866+2769761Lelio R Paula09/2013
764313^62619-4469755Lelio R Paula09/2013
7644(2^231715-509203)/3569752Lelio R Paula05/2012
76452^231711-11046769752Enzo Doria05/2014
7646(19^54547+18^54547)/3769751Robert Price08/2013
7647(23*2^231697-1)/4569748Lelio R Paula01/2014
76482^231696-186149969748Enzo Doria03/2016
76492^231684-14769744Lelio R Paula02/2012
7650(23*2^231686-1)/118369743Lelio R Paula01/2014
76512^231591-47739769716Paul Bourdelais03/2013
765216916^13209+13209^1691669709Hans Havermann09/2019
765316568^16095+16095^1656869697Hans Havermann09/2019
765411^66916-42069686Enzo Doria08/2012
76555^99680-1370669674Enzo Doria02/2013
7656(8*10^69674-53)/969674Robert Price11/2014
7657(44*10^69663-413)/969664Robert Price10/2017
765818950^4743+4743^1895069662Hans Havermann10/2019
7659(77*10^69656-23)/969657Robert Price10/2015
76606^89509+13169652Lelio R Paula09/2013
7661(78557*2^231349+1)/3569647Lelio R Paula06/2014
7662(11*10^69645+19)/369646Robert Price03/2016
766311^66875-2869644Lelio R Paula09/2013
76642^231347+7148369643Enzo Doria04/2016
7665(14^60763+3^60763)/1769641Robert Price04/2013
7666(4*10^69626+173)/369627Robert Price01/2017
76672^231289+25569625Lelio R Paula04/2012
766819794^3287+3287^1979469612Hans Havermann09/2019
76692^231234-11291369609Enzo Doria06/2014
7670(265*10^69602-7)/369604Robert Price07/2016
76712^231182-11284169593Enzo Doria06/2014
7672(15*2^231129+1)/2369577Lelio R Paula08/2012
76733^145806-2869568Lelio R Paula09/2013
7674(265*10^69554-7)/369556Robert Price07/2016
76752^231052-11315969554Enzo Doria07/2014
7676(10^9+1)*(10^129+1)*(10^831+1)*(10^107199+1)/1001/(10^387+1)/(10^2493+1)/(10^35733+1)69552Makoto Kamada03/2019
767711^66784-869549Lelio R Paula09/2013
7678Phi(104409,10)/229699969546Maksym Voznyy07/2015
76792^231016-11052369543Enzo Doria05/2014
76802^231014+57729457569543Lelio R Paula02/2016
768114^60658+6769522Lelio R Paula09/2013
76825^99418+3669491Lelio R Paula06/2013
76837^82203-3069470Lelio R Paula09/2013
7684(63^38609-1)/6269469Paul Bourdelais08/2017
76855^99359-2^9936069449Mike Oakes12/2010
7686(29*2^230684+1)/139569442Lelio R Paula08/2012
768717692^8411+8411^1769269439Hans Havermann09/2019
7688(19*10^69424+77)/369425Robert Price08/2016
768919^54287-9669420Lelio R Paula09/2013
769020739^2222+2222^2073969409Hans Havermann09/2019
76912^230541+5890569400Lelio R Paula04/2012
76922^230506+1270569390Lelio R Paula02/2013
76938*6^89156-569378Lelio R Paula09/2014
76942^230438-11134769369Enzo Doria05/2014
76952^230428-9969366Lelio R Paula02/2012
7696(62^38699+1)/6369362Paul Bourdelais08/2017
76973*10^69354+1769355Robert Price03/2017
7698(493*10^69340-7)/969342Robert Price07/2016
7699(41*10^69321+373)/969322Robert Price04/2017
77006^89072+5369312Lelio R Paula09/2013
7701155^31639+269300Lelio R Paula05/2013
77023*7^81965-469269Lelio R Paula09/2014
7703(16*10^69265+41)/369266Robert Price10/2017
7704(86*10^69260-77)/969261Robert Price05/2016
77059*5^99087+469260Lelio R Paula09/2014
77063^145145+266069252Lelio R Paula09/2013
770711^66492-114069245Enzo Doria11/2012
77085*3^145129-469245Lelio R Paula04/2014
77097*3^145126+869244Lelio R Paula04/2014
771011^66480-237069232Enzo Doria12/2012
77112^229962-6569226Lelio R Paula02/2012
77122^229958-11073369225Enzo Doria05/2014
7713V(332407)69225Serge Batalov03/2015
77146^88959+769224Lelio R Paula09/2013
771515^58855-9469219Lelio R Paula09/2013
7716159773#-p(159773)69212Henri Lifchitz12/2018
771720223^2638+2638^2022369189Hans Havermann09/2019
7718(2^229838+47)/1208169185Lelio R Paula04/2012
77193^144952+9869160Lelio R Paula09/2013
77205^98941-7269157Lelio R Paula06/2013
772163329!4+25669147Robert Price09/2019
772216422^16229+16229^1642269142Hans Havermann09/2019
7723(17*2^229604-1)/22969117Lelio R Paula01/2014
77242^229585-106369112Yves Minet11/2012
7725(13*2^229567-1)/1969107Lelio R Paula01/2014
7726(13*2^229393-1)/569055Lelio R Paula01/2014
7727(53*10^69050-17)/969051Robert Price09/2015
7728(43*10^69048+47)/969049Robert Price12/2017
77292^229305-186853369028Enzo Doria04/2016
77302^229297+138569026Lelio R Paula04/2012
773118^54986-244169023Enzo Doria03/2013
7732(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
77335^98736-1463669014Enzo Doria02/2013
7734(13^61949-5^61949)/869007Robert Price03/2013
7735(2^229227+5)/61169002Lelio R Paula04/2012
77362^229216-11327969001Enzo Doria07/2014
773710^68994+5191368995Patrick De Geest03/2016
773910^68994-10^5814-168994Serge Batalov01/2011
773810^68994-8294768994Patrick De Geest03/2016
7740(17*2^229136-1)/238168975Lelio R Paula01/2014
77412^229113+10768970Lelio R Paula02/2012
774216877^12198+12198^1687768965Hans Havermann09/2019
774311^66202-441068943Enzo Doria01/2013
774412^63883+568942Lelio R Paula07/2013
7745(9913*2^229002-1)/39990368935Lelio R Paula04/2015
77462^228962-11158168925Enzo Doria05/2014
77472^228944+8168920Henri Lifchitz01/2007
774811^66174-5468914Lelio R Paula09/2013
774916756^12959+12959^1675668911Hans Havermann09/2019
77502^228913-11126568910Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 14 2019 11:13 (Time in France)

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