PRP Records

Probable Primes Top 10000

(218736 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 ?
6501(31*2^235307+1)/370836Lelio R Paula06/2012
65022^235308+13570835Lelio R Paula02/2012
6503r(35414,90)*1000+91170831Patrick De Geest07/2004
65042^235274+15970825Lelio R Paula02/2012
65053^148409+7070810Lelio R Paula11/2014
6506(19*10^70794+17)/970795Robert Price03/2015
65072^235108-23270970775Paul Bourdelais03/2013
6508(2^235099-2^117550+1)/57077211/2006
650919^55325-670748Lelio R Paula08/2014
6510257^29356+29356^25770746Norbert Schneider10/2014
651122*10^70729+370731Robert Price10/2017
65122^234956+1171570729Lelio R Paula05/2012
6513(7*10^70727-43)/970727Robert Price10/2014
65142^234890-3034170709Enzo Doria11/2012
651517^57461+1470703Lelio R Paula01/2015
6516(9179*2^234834-1)/570696Lelio R Paula04/2015
65172*10^70688+5170689Robert Price10/2017
6518123^33822-12270685Norbert Schneider01/2015
65197*10^70680-9970681Robert Price11/2017
6520(21*2^234772-1)/209570672Lelio R Paula01/2014
6521(29*2^234686-1)/2114570645Lelio R Paula01/2014
6522(15*2^234688-1)/527814170643Lelio R Paula01/2014
65242^234655-6770639Lelio R Paula02/2012
6523(79*10^70638-61)/970639Robert Price10/2015
65252^234652-17370638Lelio R Paula02/2012
65262^234618-364570628Lelio R Paula05/2012
6527(2^234610-5)/1970624Lelio R Paula05/2012
65284*5^101038+970624Lelio R Paula10/2014
65292^234603+7196370623Enzo Doria04/2016
65302^234600-11312970622Enzo Doria07/2014
65312^234586+970618Lelio R Paula02/2012
65323^148008+2670618Robert Price11/2013
6533(7*10^70616-151)/970616Robert Price09/2017
653465^38947+3270608Lelio R Paula01/2016
6535(2^234488-3)/1170587Lelio R Paula05/2012
6536(3*2^234451+1)/3570576Lelio R Paula08/2012
6537Phi(159495,10)70560Maksym Voznyy09/2015
65382^234383-403570557Lelio R Paula05/2012
65392^234315-11124170536Enzo Doria05/2014
654014^61526+9770517Lelio R Paula01/2015
6541(3*2^234170+1)/1370492Lelio R Paula08/2012
654251^41281-50^4128170491Robert Price02/2013
65432^234141-11212370484Enzo Doria06/2014
65442^234139+1228570483Lelio R Paula04/2012
65452^234133-316370482Yves Minet04/2009
65462^234115+8370476Lelio R Paula02/2012
65472^234114-159570476Lelio R Paula05/2012
654824^51061-23^5106170475Robert Price07/2012
654919471^16428-270467Faysal YAtim09/2005
65507^83381+1270466Robert Price01/2014
65512^234067-11142770462Enzo Doria05/2014
6552(266*10^70457+1)/370459Robert Price02/2016
6553(31*2^234041-1)/9770453Lelio R Paula01/2014
65542^234026+1290970449Lelio R Paula04/2012
65552^233965-1970431Lelio R Paula02/2012
6556(5*2^233932-1)/17970419Lelio R Paula01/2014
65572^233908-1710970414Enzo Doria05/2013
6558695^24772+24772^69570402Norbert Schneider09/2016
65593*5^100719-270401Lelio R Paula10/2014
65602^233829-11135570390Enzo Doria05/2014
6561(19775^16384+1)/270388Henri Lifchitz03/2007
65627*3^147519+870386Lelio R Paula04/2014
6563141^32749-270385Lelio R Paula10/2017
65645*7^83265+270368Lelio R Paula10/2014
6565(23*10^70363+97)/370364Robert Price02/2017
6566(23*2^233749-1)/3532570363Lelio R Paula01/2014
65675^100652-1391670353Enzo Doria02/2013
656845^42555-270353Lelio R Paula08/2013
65692^233661-6170339Lelio R Paula02/2012
65702^233523-11224970298Enzo Doria06/2014
65715*3^147324-870293Lelio R Paula04/2014
65722^233488-1306570287Enzo Doria11/2012
6573(3^147322+8)/4285170286Lelio R Paula06/2012
6574(22*10^70259+161)/370260Robert Price02/2017
65752^233388+46570257Lelio R Paula11/2012
657614^61299+5970257Lelio R Paula01/2015
65772^233383+9406570256Lelio R Paula04/2012
657849471!3-656170253Robert Price11/2015
65797^83121+6^(83121-1)70246Robert Price03/2016
6580(197*10^70241-11)/370243Robert Price10/2017
658123*10^70240-770242Robert Price03/2016
6582(71*10^70227-53)/970228Robert Price10/2015
6583(2^233247-9)/1770214Lelio R Paula05/2012
6584(11^67421-2^67421)/970211Robert Price01/2013
6585(23*10^70209-41)/970210Robert Price03/2015
6586(29*10^70194-11)/970195Robert Price04/2015
65873^147109+19670189Lelio R Paula05/2014
6588(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
65899^73538+8^(73538+1)70174Robert Price06/2016
65902*5^100391+770171Lelio R Paula10/2014
659199^35156-270159Lelio R Paula08/2013
6592(68*10^70148+7)/370150Robert Price03/2016
659311^67360-603070149Enzo Doria01/2013
6594(35*10^70130-377)/970131Robert Price12/2017
659549391!3+3^4939170128Robert Price09/2015
6596(229*10^70122-1)/370124Robert Price12/2016
65977^82975-9270123Lelio R Paula07/2014
659865^38670+5870106Lelio R Paula01/2016
6599105^34684+34684^10570103Serge Batalov05/2014
6600134^32955-13370099Norbert Schneider03/2015
66012^232836-22790370091Enzo Doria12/2012
66022^232837-185917370091Enzo Doria03/2016
66033*2^232820+570087Lelio R Paula04/2014
66052^232799+9019570080Lelio R Paula02/2013
66042^232799-11223770080Enzo Doria06/2014
66062^232759+26214570068Lelio R Paula04/2012
66073*2^232750+770066Lelio R Paula04/2014
660812^64918-1170059Lelio R Paula01/2015
66097^82899-1270058Lelio R Paula09/2013
6610(22*10^70051-13)/970052Robert Price03/2015
6611(2^232685-7)/251462570039Lelio R Paula04/2012
661218^55786-536370027Enzo Doria03/2013
6613(2^(77537*3+1)+243)/770023Kevin Acres11/2013
66142^232602+16970021Lelio R Paula02/2012
6615(137^32768+29^32768)/270016Jeppe Stig Nielsen04/2018
66162^232580+7213370014Enzo Doria04/2016
66174*6^89958-770002Lelio R Paula09/2014
661810^70000+8048770001Milton L. Brown05/2006
661910^69999+13485770000Patrick De Geest02/2007
662410^70000-927370000Patrick De Geest08/2009
6623(79*10^69999-7)/970000Robert Price01/2015
6622((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
6620(2^756839/10^36014)%10^7000070000Michael Vang12/2016
6621(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
662510^69999-8825169999Patrick De Geest08/2009
66262^232507+108969992Lelio R Paula04/2012
6627(17*2^232445+1)/569974Lelio R Paula08/2012
6628(529^25693+1)/53069972Richard Fischer12/2017
66297^82778+4869956Lelio R Paula09/2013
66307*2^232381+369955Lelio R Paula04/2014
66312^232362-11054169948Enzo Doria05/2014
66322^232326-11239169938Enzo Doria06/2014
66333^146575+23669935Lelio R Paula09/2013
663430^47341-2969929Norbert Schneider02/2014
66355^100040-6869925Lelio R Paula09/2013
6636(35*10^69866-593)/969867Robert Price08/2017
66372^232045-1729569853Lelio R Paula04/2012
6638(2^231987+78557)/9569834Lelio R Paula05/2012
66392^231955+7424369826Yves Minet03/2011
66402^231946-1587369823Enzo Doria04/2013
664118^55618+9569816Lelio R Paula09/2013
66426^89712+5^(89712-1)69810Robert Price02/2016
66432^231870+13569800Lelio R Paula02/2012
6644(23*2^231827-1)/417969785Lelio R Paula01/2014
66452^231778+5461569773Lelio R Paula04/2012
6646(19*2^231780+1)/23569772Lelio R Paula08/2012
664714^60866+2769761Lelio R Paula09/2013
664813^62619-4469755Lelio R Paula09/2013
6649(2^231715-509203)/3569752Lelio R Paula05/2012
66502^231711-11046769752Enzo Doria05/2014
6651(19^54547+18^54547)/3769751Robert Price08/2013
6652(23*2^231697-1)/4569748Lelio R Paula01/2014
66532^231696-186149969748Enzo Doria03/2016
66542^231684-14769744Lelio R Paula02/2012
6655(23*2^231686-1)/118369743Lelio R Paula01/2014
66562^231591-47739769716Paul Bourdelais03/2013
665711^66916-42069686Enzo Doria08/2012
66595^99680-1370669674Enzo Doria02/2013
6658(8*10^69674-53)/969674Robert Price11/2014
6660(44*10^69663-413)/969664Robert Price10/2017
6661(77*10^69656-23)/969657Robert Price10/2015
66626^89509+13169652Lelio R Paula09/2013
6663(78557*2^231349+1)/3569647Lelio R Paula06/2014
6664(11*10^69645+19)/369646Robert Price03/2016
666511^66875-2869644Lelio R Paula09/2013
66662^231347+7148369643Enzo Doria04/2016
6667(14^60763+3^60763)/1769641Robert Price04/2013
6668(4*10^69626+173)/369627Robert Price01/2017
66692^231289+25569625Lelio R Paula04/2012
66702^231234-11291369609Enzo Doria06/2014
6671(265*10^69602-7)/369604Robert Price07/2016
66722^231182-11284169593Enzo Doria06/2014
6673(15*2^231129+1)/2369577Lelio R Paula08/2012
66743^145806-2869568Lelio R Paula09/2013
6675(265*10^69554-7)/369556Robert Price07/2016
66762^231052-11315969554Enzo Doria07/2014
667711^66784-869549Lelio R Paula09/2013
6678Phi(104409,10)/229699969546Maksym Voznyy07/2015
66792^231016-11052369543Enzo Doria05/2014
66802^231014+57729457569543Lelio R Paula02/2016
668114^60658+6769522Lelio R Paula09/2013
66825^99418+3669491Lelio R Paula06/2013
66837^82203-3069470Lelio R Paula09/2013
6684(63^38609-1)/6269469Paul Bourdelais08/2017
66855^99359-2^9936069449Mike Oakes12/2010
6686(29*2^230684+1)/139569442Lelio R Paula08/2012
6687(19*10^69424+77)/369425Robert Price08/2016
668819^54287-9669420Lelio R Paula09/2013
66892^230541+5890569400Lelio R Paula04/2012
66902^230506+1270569390Lelio R Paula02/2013
66918*6^89156-569378Lelio R Paula09/2014
66922^230438-11134769369Enzo Doria05/2014
66932^230428-9969366Lelio R Paula02/2012
6694(62^38699+1)/6369362Paul Bourdelais08/2017
66953*10^69354+1769355Robert Price03/2017
6696(493*10^69340-7)/969342Robert Price07/2016
6697(41*10^69321+373)/969322Robert Price04/2017
66986^89072+5369312Lelio R Paula09/2013
6699155^31639+269300Lelio R Paula05/2013
67003*7^81965-469269Lelio R Paula09/2014
6701(16*10^69265+41)/369266Robert Price10/2017
6702(86*10^69260-77)/969261Robert Price05/2016
67039*5^99087+469260Lelio R Paula09/2014
67043^145145+266069252Lelio R Paula09/2013
670611^66492-114069245Enzo Doria11/2012
67055*3^145129-469245Lelio R Paula04/2014
67077*3^145126+869244Lelio R Paula04/2014
670811^66480-237069232Enzo Doria12/2012
67092^229962-6569226Lelio R Paula02/2012
67102^229958-11073369225Enzo Doria05/2014
6711V(332407)69225Serge Batalov03/2015
67126^88959+769224Lelio R Paula09/2013
671315^58855-9469219Lelio R Paula09/2013
6714(2^229838+47)/1208169185Lelio R Paula04/2012
67153^144952+9869160Lelio R Paula09/2013
67165^98941-7269157Lelio R Paula06/2013
6717(17*2^229604-1)/22969117Lelio R Paula01/2014
67182^229585-106369112Yves Minet11/2012
6719(13*2^229567-1)/1969107Lelio R Paula01/2014
6720(13*2^229393-1)/569055Lelio R Paula01/2014
6721(53*10^69050-17)/969051Robert Price09/2015
6722(43*10^69048+47)/969049Robert Price12/2017
67232^229305-186853369028Enzo Doria04/2016
67242^229297+138569026Lelio R Paula04/2012
672518^54986-244169023Enzo Doria03/2013
6726(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
67275^98736-1463669014Enzo Doria02/2013
6728(13^61949-5^61949)/869007Robert Price03/2013
6729(2^229227+5)/61169002Lelio R Paula04/2012
67302^229216-11327969001Enzo Doria07/2014
673110^68994+5191368995Patrick De Geest03/2016
673310^68994-10^5814-168994Serge Batalov01/2011
673210^68994-8294768994Patrick De Geest03/2016
6734(17*2^229136-1)/238168975Lelio R Paula01/2014
67352^229113+10768970Lelio R Paula02/2012
673611^66202-441068943Enzo Doria01/2013
673712^63883+568942Lelio R Paula07/2013
6738(9913*2^229002-1)/39990368935Lelio R Paula04/2015
67392^228962-11158168925Enzo Doria05/2014
67402^228944+8168920Henri Lifchitz01/2007
674111^66174-5468914Lelio R Paula09/2013
67422^228913-11126568910Enzo Doria05/2014
67432^228902+7351968907Enzo Doria04/2016
6744(47*2^228884+1)/6368901Lelio R Paula04/2015
67452^228821+7642768882Enzo Doria05/2016
67463^144340+5068868Lelio R Paula09/2013
67472^228758-11296768864Enzo Doria06/2014
67482^228743-11137968859Enzo Doria05/2014
67492^228741-11091168858Enzo Doria05/2014
67503*5^98511-868857Lelio R Paula09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

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