PRP Records

Probable Primes Top 10000

(193407 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 ?
62513*5^100719-270401Lelio R Paula10/2014
62522^233829-11135570390Enzo Doria05/2014
6253(19775^16384+1)/270388Henri Lifchitz03/2007
62547*3^147519+870386Lelio R Paula04/2014
6255141^32749-270385Lelio R Paula10/2017
62565*7^83265+270368Lelio R Paula10/2014
6257(23*10^70363+97)/370364Robert Price02/2017
6258(23*2^233749-1)/3532570363Lelio R Paula01/2014
62595^100652-1391670353Enzo Doria02/2013
626045^42555-270353Lelio R Paula08/2013
62612^233661-6170339Lelio R Paula02/2012
62622^233523-11224970298Enzo Doria06/2014
62635*3^147324-870293Lelio R Paula04/2014
62642^233488-1306570287Enzo Doria11/2012
6265(3^147322+8)/4285170286Lelio R Paula06/2012
6266(22*10^70259+161)/370260Robert Price02/2017
62672^233388+46570257Lelio R Paula11/2012
626814^61299+5970257Lelio R Paula01/2015
62692^233383+9406570256Lelio R Paula04/2012
627049471!3-656170253Robert Price11/2015
62717^83121+6^(83121-1)70246Robert Price03/2016
6272(197*10^70241-11)/370243Robert Price10/2017
627323*10^70240-770242Robert Price03/2016
6274(71*10^70227-53)/970228Robert Price10/2015
6275(2^233247-9)/1770214Lelio R Paula05/2012
6276(11^67421-2^67421)/970211Robert Price01/2013
6277(23*10^70209-41)/970210Robert Price03/2015
6278(29*10^70194-11)/970195Robert Price04/2015
62793^147109+19670189Lelio R Paula05/2014
6280(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
62819^73538+8^(73538+1)70174Robert Price06/2016
62822*5^100391+770171Lelio R Paula10/2014
628399^35156-270159Lelio R Paula08/2013
6284(68*10^70148+7)/370150Robert Price03/2016
628511^67360-603070149Enzo Doria01/2013
6286(35*10^70130-377)/970131Robert Price12/2017
628749391!3+3^4939170128Robert Price09/2015
6288(229*10^70122-1)/370124Robert Price12/2016
62897^82975-9270123Lelio R Paula07/2014
629065^38670+5870106Lelio R Paula01/2016
6291105^34684+34684^10570103Serge Batalov05/2014
6292134^32955-13370099Norbert Schneider03/2015
62932^232836-22790370091Enzo Doria12/2012
62942^232837-185917370091Enzo Doria03/2016
62953*2^232820+570087Lelio R Paula04/2014
62972^232799+9019570080Lelio R Paula02/2013
62962^232799-11223770080Enzo Doria06/2014
62982^232759+26214570068Lelio R Paula04/2012
62993*2^232750+770066Lelio R Paula04/2014
630012^64918-1170059Lelio R Paula01/2015
63017^82899-1270058Lelio R Paula09/2013
6302(22*10^70051-13)/970052Robert Price03/2015
6303(2^232685-7)/251462570039Lelio R Paula04/2012
630418^55786-536370027Enzo Doria03/2013
6305(2^(77537*3+1)+243)/770023Kevin Acres11/2013
63062^232602+16970021Lelio R Paula02/2012
63072^232580+7213370014Enzo Doria04/2016
63084*6^89958-770002Lelio R Paula09/2014
630910^70000+8048770001Milton L. Brown05/2006
631010^69999+13485770000Patrick De Geest02/2007
631510^70000-927370000Patrick De Geest08/2009
6311(79*10^69999-7)/970000Robert Price01/2015
6312((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
6313(2^756839/10^36014)%10^7000070000Michael Vang12/2016
6314(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
631610^69999-8825169999Patrick De Geest08/2009
63172^232507+108969992Lelio R Paula04/2012
6318(17*2^232445+1)/569974Lelio R Paula08/2012
6319(529^25693+1)/53069972Richard Fischer12/2017
63207^82778+4869956Lelio R Paula09/2013
63217*2^232381+369955Lelio R Paula04/2014
63222^232362-11054169948Enzo Doria05/2014
63232^232326-11239169938Enzo Doria06/2014
63243^146575+23669935Lelio R Paula09/2013
632530^47341-2969929Norbert Schneider02/2014
63265^100040-6869925Lelio R Paula09/2013
6327(35*10^69866-593)/969867Robert Price08/2017
63282^232045-1729569853Lelio R Paula04/2012
6329(2^231987+78557)/9569834Lelio R Paula05/2012
63302^231955+7424369826Yves Minet03/2011
63312^231946-1587369823Enzo Doria04/2013
633218^55618+9569816Lelio R Paula09/2013
63336^89712+5^(89712-1)69810Robert Price02/2016
63342^231870+13569800Lelio R Paula02/2012
6335(23*2^231827-1)/417969785Lelio R Paula01/2014
63362^231778+5461569773Lelio R Paula04/2012
6337(19*2^231780+1)/23569772Lelio R Paula08/2012
633814^60866+2769761Lelio R Paula09/2013
633913^62619-4469755Lelio R Paula09/2013
6341(2^231715-509203)/3569752Lelio R Paula05/2012
63402^231711-11046769752Enzo Doria05/2014
6342(19^54547+18^54547)/3769751Robert Price08/2013
6343(23*2^231697-1)/4569748Lelio R Paula01/2014
63442^231696-186149969748Enzo Doria03/2016
63452^231684-14769744Lelio R Paula02/2012
6346(23*2^231686-1)/118369743Lelio R Paula01/2014
63472^231591-47739769716Paul Bourdelais03/2013
634811^66916-42069686Enzo Doria08/2012
63495^99680-1370669674Enzo Doria02/2013
6350(8*10^69674-53)/969674Robert Price11/2014
6351(44*10^69663-413)/969664Robert Price10/2017
6352(77*10^69656-23)/969657Robert Price10/2015
63536^89509+13169652Lelio R Paula09/2013
6354(78557*2^231349+1)/3569647Lelio R Paula06/2014
6355(11*10^69645+19)/369646Robert Price03/2016
635611^66875-2869644Lelio R Paula09/2013
63572^231347+7148369643Enzo Doria04/2016
6358(14^60763+3^60763)/1769641Robert Price04/2013
6359(4*10^69626+173)/369627Robert Price01/2017
63602^231289+25569625Lelio R Paula04/2012
63612^231234-11291369609Enzo Doria06/2014
6362(265*10^69602-7)/369604Robert Price07/2016
63632^231182-11284169593Enzo Doria06/2014
6364(15*2^231129+1)/2369577Lelio R Paula08/2012
63653^145806-2869568Lelio R Paula09/2013
6366(265*10^69554-7)/369556Robert Price07/2016
63672^231052-11315969554Enzo Doria07/2014
636811^66784-869549Lelio R Paula09/2013
6369Phi(104409,10)/229699969546Maksym Voznyy07/2015
63702^231016-11052369543Enzo Doria05/2014
63712^231014+57729457569543Lelio R Paula02/2016
637214^60658+6769522Lelio R Paula09/2013
63735^99418+3669491Lelio R Paula06/2013
63747^82203-3069470Lelio R Paula09/2013
6375(63^38609-1)/6269469Paul Bourdelais08/2017
63765^99359-2^9936069449Mike Oakes12/2010
6377(29*2^230684+1)/139569442Lelio R Paula08/2012
6378(19*10^69424+77)/369425Robert Price08/2016
637919^54287-9669420Lelio R Paula09/2013
63802^230541+5890569400Lelio R Paula04/2012
63812^230506+1270569390Lelio R Paula02/2013
63828*6^89156-569378Lelio R Paula09/2014
63832^230438-11134769369Enzo Doria05/2014
63842^230428-9969366Lelio R Paula02/2012
6385(62^38699+1)/6369362Paul Bourdelais08/2017
63863*10^69354+1769355Robert Price03/2017
6387(493*10^69340-7)/969342Robert Price07/2016
6388(41*10^69321+373)/969322Robert Price04/2017
63896^89072+5369312Lelio R Paula09/2013
6390155^31639+269300Lelio R Paula05/2013
63913*7^81965-469269Lelio R Paula09/2014
6392(16*10^69265+41)/369266Robert Price10/2017
6393(86*10^69260-77)/969261Robert Price05/2016
63949*5^99087+469260Lelio R Paula09/2014
63953^145145+266069252Lelio R Paula09/2013
639611^66492-114069245Enzo Doria11/2012
63975*3^145129-469245Lelio R Paula04/2014
63987*3^145126+869244Lelio R Paula04/2014
639911^66480-237069232Enzo Doria12/2012
64002^229962-6569226Lelio R Paula02/2012
64012^229958-11073369225Enzo Doria05/2014
6402V(332407)69225Serge Batalov03/2015
64036^88959+769224Lelio R Paula09/2013
640415^58855-9469219Lelio R Paula09/2013
6405(2^229838+47)/1208169185Lelio R Paula04/2012
64063^144952+9869160Lelio R Paula09/2013
64075^98941-7269157Lelio R Paula06/2013
6408(17*2^229604-1)/22969117Lelio R Paula01/2014
64092^229585-106369112Yves Minet11/2012
6410(13*2^229567-1)/1969107Lelio R Paula01/2014
6411(13*2^229393-1)/569055Lelio R Paula01/2014
6412(53*10^69050-17)/969051Robert Price09/2015
6413(43*10^69048+47)/969049Robert Price12/2017
64142^229305-186853369028Enzo Doria04/2016
64152^229297+138569026Lelio R Paula04/2012
641618^54986-244169023Enzo Doria03/2013
6417(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
64185^98736-1463669014Enzo Doria02/2013
6419(13^61949-5^61949)/869007Robert Price03/2013
6420(2^229227+5)/61169002Lelio R Paula04/2012
64212^229216-11327969001Enzo Doria07/2014
642210^68994+5191368995Patrick De Geest03/2016
642410^68994-10^5814-168994Serge Batalov01/2011
642310^68994-8294768994Patrick De Geest03/2016
6425(17*2^229136-1)/238168975Lelio R Paula01/2014
64262^229113+10768970Lelio R Paula02/2012
642711^66202-441068943Enzo Doria01/2013
642812^63883+568942Lelio R Paula07/2013
6429(9913*2^229002-1)/39990368935Lelio R Paula04/2015
64302^228962-11158168925Enzo Doria05/2014
64312^228944+8168920Henri Lifchitz01/2007
643211^66174-5468914Lelio R Paula09/2013
64332^228913-11126568910Enzo Doria05/2014
64342^228902+7351968907Enzo Doria04/2016
6435(47*2^228884+1)/6368901Lelio R Paula04/2015
64362^228821+7642768882Enzo Doria05/2016
64373^144340+5068868Lelio R Paula09/2013
64382^228758-11296768864Enzo Doria06/2014
64392^228743-11137968859Enzo Doria05/2014
64402^228741-11091168858Enzo Doria05/2014
6442lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
64413*5^98511-868857Lelio R Paula09/2014
64432^228717+46768851Lelio R Paula02/2011
6444Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
6445(509203*2^228665-1)/3568840Lelio R Paula04/2015
64468^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
644711^66074-105068809Enzo Doria11/2012
6448(68*10^68798-11)/368800Robert Price10/2017
64492^228484+18168781Lelio R Paula02/2012
64502^228479-5869568780Lelio R Paula04/2012
64512^228465-1585368775Enzo Doria04/2013
645211^66040-540068774Enzo Doria01/2013
6453(13*2^228441-1)/57568766Lelio R Paula01/2014
6454(17*2^228393+1)/29568752Lelio R Paula08/2012
64552*10^68744+4168745Robert Price01/2017
645611^66011-15068744Enzo Doria08/2012
6457(13*2^228304-1)/8168726Lelio R Paula01/2014
64582^228295-11107968724Enzo Doria05/2014
6460(3^144039+7)/2268723Lelio R Paula04/2012
6459(8*10^68722+49)/368723Robert Price03/2016
6461(35*10^68718+1)/968719Serge Batalov11/2010
64622^228271-22827168717Henri Lifchitz11/2004
64632^228257+8287568713Lelio R Paula02/2013
64643^144013+4068712Lelio R Paula09/2013
646513^61671-8668699Lelio R Paula09/2013
6466(46*10^68698+683)/968699Robert Price12/2017
646717^55828-7268694Lelio R Paula09/2013
64686^88259+6168679Lelio R Paula09/2013
646918^54699-568663Lelio R Paula09/2013
647033^45216+268662Lelio R Paula05/2013
6471(2^228073-5)/368657Lelio R Paula04/2012
6472(2^(6*38012+1)-5)/368657Kevin Acres11/2013
64732^228055-11160768652Enzo Doria05/2014
64742^228054-11476168652Enzo Doria05/2015
64752^228041+118568648Lelio R Paula04/2012
64762^228040-103768647Yves Minet11/2012
64772*F(328450)-168642Henri Lifchitz12/2009
64785^98201-3468640Lelio R Paula06/2013
64799^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
64807*2^227780-368570Lelio R Paula04/2014
64812^227733-12168555Lelio R Paula02/2012
64822^227702-1696768546Enzo Doria05/2013
64832^227689-11165568542Enzo Doria05/2014
6484gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
64855^98051+268535Ray Chandler07/2011
64865*10^68524+5168525Robert Price01/2017
6487(11*10^68520-149)/368521Robert Price01/2017
648819^53573-7868507Lelio R Paula09/2013
6489(68*10^68504+13)/968505Ray Chandler10/2010
64909*5^98003+468503Lelio R Paula09/2014
64912^227528+5168493Lelio R Paula02/2012
64923^143497+868466Lelio R Paula04/2012
64932^227430-9568464Lelio R Paula02/2012
6494(8*10^68455+13)/368456Robert Price11/2017
64953*5^97934-268454Lelio R Paula09/2014
649620^52613+7768452Lelio R Paula09/2013
64972^227371+3276968446Lelio R Paula04/2012
6498(3^143465+4)/2127042006768440Lelio R Paula04/2012
6499CopelandErdos(68433)68433Eric W. Weisstein08/2013
65002^227323+7543168432Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 12 2017 10:35 (Time in France)

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