PRP Records

Probable Primes Top 10000

(247113 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 ?
67512^234890-3034170709Enzo Doria11/2012
675217^57461+1470703Lelio R Paula01/2015
6753(9179*2^234834-1)/570696Lelio R Paula04/2015
67542*10^70688+5170689Robert Price10/2017
6755123^33822-12270685Norbert Schneider01/2015
67567*10^70680-9970681Robert Price11/2017
6757(21*2^234772-1)/209570672Lelio R Paula01/2014
6758(29*2^234686-1)/2114570645Lelio R Paula01/2014
6759(15*2^234688-1)/527814170643Lelio R Paula01/2014
67612^234655-6770639Lelio R Paula02/2012
6760(79*10^70638-61)/970639Robert Price10/2015
67622^234652-17370638Lelio R Paula02/2012
67632^234618-364570628Lelio R Paula05/2012
6764(2^234610-5)/1970624Lelio R Paula05/2012
67654*5^101038+970624Lelio R Paula10/2014
67662^234603+7196370623Enzo Doria04/2016
67672^234600-11312970622Enzo Doria07/2014
67682^234586+970618Lelio R Paula02/2012
67693^148008+2670618Robert Price11/2013
6770(7*10^70616-151)/970616Robert Price09/2017
677165^38947+3270608Lelio R Paula01/2016
6772(2^234488-3)/1170587Lelio R Paula05/2012
6773(3*2^234451+1)/3570576Lelio R Paula08/2012
6774Phi(159495,10)70560Maksym Voznyy09/2015
67752^234383-403570557Lelio R Paula05/2012
67762^234315-11124170536Enzo Doria05/2014
677714^61526+9770517Lelio R Paula01/2015
6778(3*2^234170+1)/1370492Lelio R Paula08/2012
677951^41281-50^4128170491Robert Price02/2013
67802^234141-11212370484Enzo Doria06/2014
67812^234139+1228570483Lelio R Paula04/2012
67822^234133-316370482Yves Minet04/2009
67832^234115+8370476Lelio R Paula02/2012
67842^234114-159570476Lelio R Paula05/2012
678524^51061-23^5106170475Robert Price07/2012
678619471^16428-270467Faysal YAtim09/2005
67877^83381+1270466Robert Price01/2014
67882^234067-11142770462Enzo Doria05/2014
6789(266*10^70457+1)/370459Robert Price02/2016
6790(31*2^234041-1)/9770453Lelio R Paula01/2014
67912^234026+1290970449Lelio R Paula04/2012
67922^233965-1970431Lelio R Paula02/2012
6793(5*2^233932-1)/17970419Lelio R Paula01/2014
67942^233908-1710970414Enzo Doria05/2013
6795695^24772+24772^69570402Norbert Schneider09/2016
67963*5^100719-270401Lelio R Paula10/2014
67972^233829-11135570390Enzo Doria05/2014
6798(19775^16384+1)/270388Henri Lifchitz03/2007
67997*3^147519+870386Lelio R Paula04/2014
6800141^32749-270385Lelio R Paula10/2017
68015*7^83265+270368Lelio R Paula10/2014
6802(23*10^70363+97)/370364Robert Price02/2017
6803(23*2^233749-1)/3532570363Lelio R Paula01/2014
68045^100652-1391670353Enzo Doria02/2013
680545^42555-270353Lelio R Paula08/2013
68062^233661-6170339Lelio R Paula02/2012
68072^233523-11224970298Enzo Doria06/2014
68085*3^147324-870293Lelio R Paula04/2014
68092^233488-1306570287Enzo Doria11/2012
6810(3^147322+8)/4285170286Lelio R Paula06/2012
6811(22*10^70259+161)/370260Robert Price02/2017
68122^233388+46570257Lelio R Paula11/2012
681314^61299+5970257Lelio R Paula01/2015
68142^233383+9406570256Lelio R Paula04/2012
681549471!3-656170253Robert Price11/2015
68167^83121+6^(83121-1)70246Robert Price03/2016
6817(197*10^70241-11)/370243Robert Price10/2017
681823*10^70240-770242Robert Price03/2016
6819(71*10^70227-53)/970228Robert Price10/2015
6820(2^233247-9)/1770214Lelio R Paula05/2012
6821(11^67421-2^67421)/970211Robert Price01/2013
6822(23*10^70209-41)/970210Robert Price03/2015
6823(29*10^70194-11)/970195Robert Price04/2015
68243^147109+19670189Lelio R Paula05/2014
6825(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
68269^73538+8^(73538+1)70174Robert Price06/2016
68272*5^100391+770171Lelio R Paula10/2014
682899^35156-270159Lelio R Paula08/2013
6829(68*10^70148+7)/370150Robert Price03/2016
683011^67360-603070149Enzo Doria01/2013
6831(35*10^70130-377)/970131Robert Price12/2017
683249391!3+3^4939170128Robert Price09/2015
6833(229*10^70122-1)/370124Robert Price12/2016
68347^82975-9270123Lelio R Paula07/2014
683565^38670+5870106Lelio R Paula01/2016
6836105^34684+34684^10570103Serge Batalov05/2014
6837134^32955-13370099Norbert Schneider03/2015
68382^232836-22790370091Enzo Doria12/2012
68392^232837-185917370091Enzo Doria03/2016
68403*2^232820+570087Lelio R Paula04/2014
68422^232799+9019570080Lelio R Paula02/2013
68412^232799-11223770080Enzo Doria06/2014
68432^232759+26214570068Lelio R Paula04/2012
68443*2^232750+770066Lelio R Paula04/2014
684512^64918-1170059Lelio R Paula01/2015
68467^82899-1270058Lelio R Paula09/2013
6847(22*10^70051-13)/970052Robert Price03/2015
6848(2^232685-7)/251462570039Lelio R Paula04/2012
684918^55786-536370027Enzo Doria03/2013
6850(2^(77537*3+1)+243)/770023Kevin Acres11/2013
68512^232602+16970021Lelio R Paula02/2012
6852(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
68532^232580+7213370014Enzo Doria04/2016
68544*6^89958-770002Lelio R Paula09/2014
685510^70000+8048770001Milton L. Brown05/2006
685610^69999+13485770000Patrick De Geest02/2007
686110^70000-927370000Patrick De Geest08/2009
6860(79*10^69999-7)/970000Robert Price01/2015
6859((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
6857(2^756839/10^36014)%10^7000070000Michael Vang12/2016
6858(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
686210^69999-8825169999Patrick De Geest08/2009
68632^232507+108969992Lelio R Paula04/2012
6864(17*2^232445+1)/569974Lelio R Paula08/2012
6865(529^25693+1)/53069972Richard Fischer12/2017
68667^82778+4869956Lelio R Paula09/2013
68677*2^232381+369955Lelio R Paula04/2014
68682^232362-11054169948Enzo Doria05/2014
68692^232326-11239169938Enzo Doria06/2014
68703^146575+23669935Lelio R Paula09/2013
687130^47341-2969929Norbert Schneider02/2014
68725^100040-6869925Lelio R Paula09/2013
6873(35*10^69866-593)/969867Robert Price08/2017
68742^232045-1729569853Lelio R Paula04/2012
6875(2^231987+78557)/9569834Lelio R Paula05/2012
68762^231955+7424369826Yves Minet03/2011
68772^231946-1587369823Enzo Doria04/2013
687818^55618+9569816Lelio R Paula09/2013
68796^89712+5^(89712-1)69810Robert Price02/2016
68802^231870+13569800Lelio R Paula02/2012
6881(23*2^231827-1)/417969785Lelio R Paula01/2014
68822^231778+5461569773Lelio R Paula04/2012
6883(19*2^231780+1)/23569772Lelio R Paula08/2012
688414^60866+2769761Lelio R Paula09/2013
688513^62619-4469755Lelio R Paula09/2013
6886(2^231715-509203)/3569752Lelio R Paula05/2012
68872^231711-11046769752Enzo Doria05/2014
6888(19^54547+18^54547)/3769751Robert Price08/2013
6889(23*2^231697-1)/4569748Lelio R Paula01/2014
68902^231696-186149969748Enzo Doria03/2016
68912^231684-14769744Lelio R Paula02/2012
6892(23*2^231686-1)/118369743Lelio R Paula01/2014
68932^231591-47739769716Paul Bourdelais03/2013
689411^66916-42069686Enzo Doria08/2012
68965^99680-1370669674Enzo Doria02/2013
6895(8*10^69674-53)/969674Robert Price11/2014
6897(44*10^69663-413)/969664Robert Price10/2017
6898(77*10^69656-23)/969657Robert Price10/2015
68996^89509+13169652Lelio R Paula09/2013
6900(78557*2^231349+1)/3569647Lelio R Paula06/2014
6901(11*10^69645+19)/369646Robert Price03/2016
690211^66875-2869644Lelio R Paula09/2013
69032^231347+7148369643Enzo Doria04/2016
6904(14^60763+3^60763)/1769641Robert Price04/2013
6905(4*10^69626+173)/369627Robert Price01/2017
69062^231289+25569625Lelio R Paula04/2012
69072^231234-11291369609Enzo Doria06/2014
6908(265*10^69602-7)/369604Robert Price07/2016
69092^231182-11284169593Enzo Doria06/2014
6910(15*2^231129+1)/2369577Lelio R Paula08/2012
69113^145806-2869568Lelio R Paula09/2013
6912(265*10^69554-7)/369556Robert Price07/2016
69132^231052-11315969554Enzo Doria07/2014
691411^66784-869549Lelio R Paula09/2013
6915Phi(104409,10)/229699969546Maksym Voznyy07/2015
69162^231016-11052369543Enzo Doria05/2014
69172^231014+57729457569543Lelio R Paula02/2016
691814^60658+6769522Lelio R Paula09/2013
69195^99418+3669491Lelio R Paula06/2013
69207^82203-3069470Lelio R Paula09/2013
6921(63^38609-1)/6269469Paul Bourdelais08/2017
69225^99359-2^9936069449Mike Oakes12/2010
6923(29*2^230684+1)/139569442Lelio R Paula08/2012
6924(19*10^69424+77)/369425Robert Price08/2016
692519^54287-9669420Lelio R Paula09/2013
69262^230541+5890569400Lelio R Paula04/2012
69272^230506+1270569390Lelio R Paula02/2013
69288*6^89156-569378Lelio R Paula09/2014
69292^230438-11134769369Enzo Doria05/2014
69302^230428-9969366Lelio R Paula02/2012
6931(62^38699+1)/6369362Paul Bourdelais08/2017
69323*10^69354+1769355Robert Price03/2017
6933(493*10^69340-7)/969342Robert Price07/2016
6934(41*10^69321+373)/969322Robert Price04/2017
69356^89072+5369312Lelio R Paula09/2013
6936155^31639+269300Lelio R Paula05/2013
69373*7^81965-469269Lelio R Paula09/2014
6938(16*10^69265+41)/369266Robert Price10/2017
6939(86*10^69260-77)/969261Robert Price05/2016
69409*5^99087+469260Lelio R Paula09/2014
69413^145145+266069252Lelio R Paula09/2013
694311^66492-114069245Enzo Doria11/2012
69425*3^145129-469245Lelio R Paula04/2014
69447*3^145126+869244Lelio R Paula04/2014
694511^66480-237069232Enzo Doria12/2012
69462^229962-6569226Lelio R Paula02/2012
69472^229958-11073369225Enzo Doria05/2014
6948V(332407)69225Serge Batalov03/2015
69496^88959+769224Lelio R Paula09/2013
695015^58855-9469219Lelio R Paula09/2013
6951(2^229838+47)/1208169185Lelio R Paula04/2012
69523^144952+9869160Lelio R Paula09/2013
69535^98941-7269157Lelio R Paula06/2013
6954(17*2^229604-1)/22969117Lelio R Paula01/2014
69552^229585-106369112Yves Minet11/2012
6956(13*2^229567-1)/1969107Lelio R Paula01/2014
6957(13*2^229393-1)/569055Lelio R Paula01/2014
6958(53*10^69050-17)/969051Robert Price09/2015
6959(43*10^69048+47)/969049Robert Price12/2017
69602^229305-186853369028Enzo Doria04/2016
69612^229297+138569026Lelio R Paula04/2012
696218^54986-244169023Enzo Doria03/2013
6963(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
69645^98736-1463669014Enzo Doria02/2013
6965(13^61949-5^61949)/869007Robert Price03/2013
6966(2^229227+5)/61169002Lelio R Paula04/2012
69672^229216-11327969001Enzo Doria07/2014
696810^68994+5191368995Patrick De Geest03/2016
697010^68994-10^5814-168994Serge Batalov01/2011
696910^68994-8294768994Patrick De Geest03/2016
6971(17*2^229136-1)/238168975Lelio R Paula01/2014
69722^229113+10768970Lelio R Paula02/2012
697311^66202-441068943Enzo Doria01/2013
697412^63883+568942Lelio R Paula07/2013
6975(9913*2^229002-1)/39990368935Lelio R Paula04/2015
69762^228962-11158168925Enzo Doria05/2014
69772^228944+8168920Henri Lifchitz01/2007
697811^66174-5468914Lelio R Paula09/2013
69792^228913-11126568910Enzo Doria05/2014
69802^228902+7351968907Enzo Doria04/2016
6981(47*2^228884+1)/6368901Lelio R Paula04/2015
69822^228821+7642768882Enzo Doria05/2016
69833^144340+5068868Lelio R Paula09/2013
69842^228758-11296768864Enzo Doria06/2014
69852^228743-11137968859Enzo Doria05/2014
69862^228741-11091168858Enzo Doria05/2014
6988lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
69873*5^98511-868857Lelio R Paula09/2014
69892^228717+46768851Lelio R Paula02/2011
6990Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
6991(509203*2^228665-1)/3568840Lelio R Paula04/2015
69928^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
699311^66074-105068809Enzo Doria11/2012
6994(68*10^68798-11)/368800Robert Price10/2017
69952^228484+18168781Lelio R Paula02/2012
69962^228479-5869568780Lelio R Paula04/2012
69972^228465-1585368775Enzo Doria04/2013
699811^66040-540068774Enzo Doria01/2013
6999(13*2^228441-1)/57568766Lelio R Paula01/2014
7000(17*2^228393+1)/29568752Lelio R Paula08/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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