PRP Records

Probable Primes Top 10000

(172142 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 ?
57512^233383+9406570256Lelio R Paula04/2012
575249471!3-656170253Robert Price11/2015
57537^83121+6^(83121-1)70246Robert Price03/2016
575423*10^70240-770242Robert Price03/2016
5755(71*10^70227-53)/970228Robert Price10/2015
5756(2^233247-9)/1770214Lelio R Paula05/2012
5757(11^67421-2^67421)/970211Robert Price01/2013
5758(23*10^70209-41)/970210Robert Price03/2015
5759(29*10^70194-11)/970195Robert Price04/2015
57603^147109+19670189Lelio R Paula05/2014
5761(34*10^70191-7)/9/3/40583/57304770181Makoto Morimoto05/2016
57629^73538+8^(73538+1)70174Robert Price06/2016
57632*5^100391+770171Lelio R Paula10/2014
576499^35156-270159Lelio R Paula08/2013
5765(68*10^70148+7)/370150Robert Price03/2016
576611^67360-603070149Enzo Doria01/2013
576749391!3+3^4939170128Robert Price09/2015
5768(229*10^70122-1)/370124Robert Price12/2016
57697^82975-9270123Lelio R Paula07/2014
577065^38670+5870106Lelio R Paula01/2016
5771105^34684+34684^10570103Serge Batalov05/2014
5772134^32955-13370099Norbert Schneider03/2015
57742^232836-22790370091Enzo Doria12/2012
57732^232837-185917370091Enzo Doria03/2016
57753*2^232820+570087Lelio R Paula04/2014
57772^232799+9019570080Lelio R Paula02/2013
57762^232799-11223770080Enzo Doria06/2014
57782^232759+26214570068Lelio R Paula04/2012
57793*2^232750+770066Lelio R Paula04/2014
578012^64918-1170059Lelio R Paula01/2015
57817^82899-1270058Lelio R Paula09/2013
5782(22*10^70051-13)/970052Robert Price03/2015
5783(2^232685-7)/251462570039Lelio R Paula04/2012
578418^55786-536370027Enzo Doria03/2013
5785(2^(77537*3+1)+243)/770023Kevin Acres11/2013
57862^232602+16970021Lelio R Paula02/2012
57872^232580+7213370014Enzo Doria04/2016
57884*6^89958-770002Lelio R Paula09/2014
578910^70000+8048770001Milton L. Brown05/2006
579010^69999+13485770000Patrick De Geest02/2007
579510^70000-927370000Patrick De Geest08/2009
5791(79*10^69999-7)/970000Robert Price01/2015
5794((2^43112609)/10^38420)%10^7000070000Michael Vang10/2016
5792(2^756839/10^36014)%10^7000070000Michael Vang12/2016
5793(2^74207281/10^32641)%10^7000070000Michael Vang12/2016
579610^69999-8825169999Patrick De Geest08/2009
57972^232507+108969992Lelio R Paula04/2012
5798(17*2^232445+1)/569974Lelio R Paula08/2012
57997^82778+4869956Lelio R Paula09/2013
58007*2^232381+369955Lelio R Paula04/2014
58012^232362-11054169948Enzo Doria05/2014
58022^232326-11239169938Enzo Doria06/2014
58033^146575+23669935Lelio R Paula09/2013
580430^47341-2969929Norbert Schneider02/2014
58055^100040-6869925Lelio R Paula09/2013
58062^232045-1729569853Lelio R Paula04/2012
5807(2^231987+78557)/9569834Lelio R Paula05/2012
58082^231955+7424369826Yves Minet03/2011
58092^231946-1587369823Enzo Doria04/2013
581018^55618+9569816Lelio R Paula09/2013
58116^89712+5^(89712-1)69810Robert Price02/2016
58122^231870+13569800Lelio R Paula02/2012
5813(23*2^231827-1)/417969785Lelio R Paula01/2014
58142^231778+5461569773Lelio R Paula04/2012
5815(19*2^231780+1)/23569772Lelio R Paula08/2012
581614^60866+2769761Lelio R Paula09/2013
581713^62619-4469755Lelio R Paula09/2013
5818(2^231715-509203)/3569752Lelio R Paula05/2012
58192^231711-11046769752Enzo Doria05/2014
5820(19^54547+18^54547)/3769751Robert Price08/2013
5821(23*2^231697-1)/4569748Lelio R Paula01/2014
58222^231696-186149969748Enzo Doria03/2016
58232^231684-14769744Lelio R Paula02/2012
5824(23*2^231686-1)/118369743Lelio R Paula01/2014
58252^231591-47739769716Paul Bourdelais03/2013
582611^66916-42069686Enzo Doria08/2012
58275^99680-1370669674Enzo Doria02/2013
5828(8*10^69674-53)/969674Robert Price11/2014
5829(77*10^69656-23)/969657Robert Price10/2015
58306^89509+13169652Lelio R Paula09/2013
5831(78557*2^231349+1)/3569647Lelio R Paula06/2014
5832(11*10^69645+19)/369646Robert Price03/2016
583311^66875-2869644Lelio R Paula09/2013
58342^231347+7148369643Enzo Doria04/2016
5835(14^60763+3^60763)/1769641Robert Price04/2013
5836(4*10^69626+173)/369627Robert Price01/2017
58372^231289+25569625Lelio R Paula04/2012
58382^231234-11291369609Enzo Doria06/2014
5839(265*10^69602-7)/369604Robert Price07/2016
58402^231182-11284169593Enzo Doria06/2014
5841(15*2^231129+1)/2369577Lelio R Paula08/2012
58423^145806-2869568Lelio R Paula09/2013
5843(265*10^69554-7)/369556Robert Price07/2016
58442^231052-11315969554Enzo Doria07/2014
584511^66784-869549Lelio R Paula09/2013
5846Phi(104409,10)/229699969546Maksym Voznyy07/2015
58472^231016-11052369543Enzo Doria05/2014
58482^231014+57729457569543Lelio R Paula02/2016
584914^60658+6769522Lelio R Paula09/2013
58505^99418+3669491Lelio R Paula06/2013
58517^82203-3069470Lelio R Paula09/2013
58525^99359-2^9936069449Mike Oakes12/2010
5853(29*2^230684+1)/139569442Lelio R Paula08/2012
5854(19*10^69424+77)/369425Robert Price08/2016
585519^54287-9669420Lelio R Paula09/2013
58562^230541+5890569400Lelio R Paula04/2012
58572^230506+1270569390Lelio R Paula02/2013
58588*6^89156-569378Lelio R Paula09/2014
58592^230438-11134769369Enzo Doria05/2014
58602^230428-9969366Lelio R Paula02/2012
58613*10^69354+1769355Robert Price03/2017
5862(493*10^69340-7)/969342Robert Price07/2016
58636^89072+5369312Lelio R Paula09/2013
5864155^31639+269300Lelio R Paula05/2013
58653*7^81965-469269Lelio R Paula09/2014
5866(86*10^69260-77)/969261Robert Price05/2016
58679*5^99087+469260Lelio R Paula09/2014
58683^145145+266069252Lelio R Paula09/2013
586911^66492-114069245Enzo Doria11/2012
58705*3^145129-469245Lelio R Paula04/2014
58717*3^145126+869244Lelio R Paula04/2014
587211^66480-237069232Enzo Doria12/2012
58732^229962-6569226Lelio R Paula02/2012
58742^229958-11073369225Enzo Doria05/2014
5875V(332407)69225Serge Batalov03/2015
58766^88959+769224Lelio R Paula09/2013
587715^58855-9469219Lelio R Paula09/2013
5878(2^229838+47)/1208169185Lelio R Paula04/2012
58793^144952+9869160Lelio R Paula09/2013
58805^98941-7269157Lelio R Paula06/2013
5881(17*2^229604-1)/22969117Lelio R Paula01/2014
58822^229585-106369112Yves Minet11/2012
5883(13*2^229567-1)/1969107Lelio R Paula01/2014
5884(13*2^229393-1)/569055Lelio R Paula01/2014
5885(53*10^69050-17)/969051Robert Price09/2015
58862^229305-186853369028Enzo Doria04/2016
58872^229297+138569026Lelio R Paula04/2012
588818^54986-244169023Enzo Doria03/2013
5889(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
58905^98736-1463669014Enzo Doria02/2013
5891(13^61949-5^61949)/869007Robert Price03/2013
5892(2^229227+5)/61169002Lelio R Paula04/2012
58932^229216-11327969001Enzo Doria07/2014
589410^68994+5191368995Patrick De Geest03/2016
589610^68994-10^5814-168994Serge Batalov01/2011
589510^68994-8294768994Patrick De Geest03/2016
5897(17*2^229136-1)/238168975Lelio R Paula01/2014
58982^229113+10768970Lelio R Paula02/2012
589911^66202-441068943Enzo Doria01/2013
590012^63883+568942Lelio R Paula07/2013
5901(9913*2^229002-1)/39990368935Lelio R Paula04/2015
59022^228962-11158168925Enzo Doria05/2014
59032^228944+8168920Henri Lifchitz01/2007
590411^66174-5468914Lelio R Paula09/2013
59052^228913-11126568910Enzo Doria05/2014
59062^228902+7351968907Enzo Doria04/2016
5907(47*2^228884+1)/6368901Lelio R Paula04/2015
59082^228821+7642768882Enzo Doria05/2016
59093^144340+5068868Lelio R Paula09/2013
59102^228758-11296768864Enzo Doria06/2014
59112^228743-11137968859Enzo Doria05/2014
59122^228741-11091168858Enzo Doria05/2014
5914lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
59133*5^98511-868857Lelio R Paula09/2014
59152^228717+46768851Lelio R Paula02/2011
5916Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
5917(509203*2^228665-1)/3568840Lelio R Paula04/2015
59188^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
591911^66074-105068809Enzo Doria11/2012
59202^228484+18168781Lelio R Paula02/2012
59212^228479-5869568780Lelio R Paula04/2012
59222^228465-1585368775Enzo Doria04/2013
592311^66040-540068774Enzo Doria01/2013
5924(13*2^228441-1)/57568766Lelio R Paula01/2014
5925(17*2^228393+1)/29568752Lelio R Paula08/2012
59262*10^68744+4168745Robert Price01/2017
592711^66011-15068744Enzo Doria08/2012
5928(13*2^228304-1)/8168726Lelio R Paula01/2014
59292^228295-11107968724Enzo Doria05/2014
5930(3^144039+7)/2268723Lelio R Paula04/2012
5931(8*10^68722+49)/368723Robert Price03/2016
5932(35*10^68718+1)/968719Serge Batalov11/2010
59332^228271-22827168717Henri Lifchitz11/2004
59342^228257+8287568713Lelio R Paula02/2013
59353^144013+4068712Lelio R Paula09/2013
593613^61671-8668699Lelio R Paula09/2013
593717^55828-7268694Lelio R Paula09/2013
59386^88259+6168679Lelio R Paula09/2013
593918^54699-568663Lelio R Paula09/2013
594033^45216+268662Lelio R Paula05/2013
5942(2^228073-5)/368657Lelio R Paula04/2012
5941(2^(6*38012+1)-5)/368657Kevin Acres11/2013
59432^228055-11160768652Enzo Doria05/2014
59442^228054-11476168652Enzo Doria05/2015
59452^228041+118568648Lelio R Paula04/2012
59462^228040-103768647Yves Minet11/2012
59472*F(328450)-168642Henri Lifchitz12/2009
59485^98201-3468640Lelio R Paula06/2013
59499^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
59507*2^227780-368570Lelio R Paula04/2014
59512^227733-12168555Lelio R Paula02/2012
59522^227702-1696768546Enzo Doria05/2013
59532^227689-11165568542Enzo Doria05/2014
5954gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
59555^98051+268535Ray Chandler07/2011
59565*10^68524+5168525Robert Price01/2017
5957(11*10^68520-149)/368521Robert Price01/2017
595819^53573-7868507Lelio R Paula09/2013
5959(68*10^68504+13)/968505Ray Chandler10/2010
59609*5^98003+468503Lelio R Paula09/2014
59612^227528+5168493Lelio R Paula02/2012
59623^143497+868466Lelio R Paula04/2012
59632^227430-9568464Lelio R Paula02/2012
59643*5^97934-268454Lelio R Paula09/2014
596520^52613+7768452Lelio R Paula09/2013
59662^227371+3276968446Lelio R Paula04/2012
5967(3^143465+4)/2127042006768440Lelio R Paula04/2012
5968CopelandErdos(68433)68433Eric W. Weisstein08/2013
59692^227323+7543168432Enzo Doria04/2016
59702^227314-196568429Lelio R Paula04/2012
59712^227303-11061768426Enzo Doria05/2014
59727^80963+6668422Lelio R Paula07/2013
59732^227290+7384968422Enzo Doria04/2016
5974(14^59693-1)/1368415Paul Bourdelais06/2008
59752^227256-278624968411Enzo Doria03/2016
59768*10^68400-768401Dmitry Domanov11/2010
5977(15*2^227228-1)/58368401Lelio R Paula01/2014
59782^227210+186916968398Enzo Doria05/2016
59792^227159-183863568382Enzo Doria05/2015
59802^227115-780768369Lelio R Paula10/2009
59812^227078-4735568358Lelio R Paula04/2012
5982(2^227063-1017)/34968351Lelio R Paula04/2012
59832^227057+14809168351Lelio R Paula04/2012
59842^227046+18768348Lelio R Paula02/2012
598511^65608-72068324Enzo Doria11/2012
59862^226894-12368302Lelio R Paula02/2012
598710^68297+14155968298Patrick De Geest05/2013
598810^68297-9368297Robert Price05/2011
5989680^24107-679^2410768284Jean-Louis Charton07/2010
599012^63267+5968277Lelio R Paula07/2013
59912^226785-115968270Yves Minet11/2012
59927^80769+9068258Lelio R Paula07/2013
59932^226741+6658768256Yves Minet10/2010
59942^226720-11240368250Enzo Doria06/2014
5995(78557*2^226694+1)/368247Lelio R Paula06/2014
5996(83*10^68231+7)/968232Robert Price10/2015
599765^37636+1668231Lelio R Paula01/2016
59985^97615-4^(97615+1)68230Robert Price04/2016
599912^63200-4368205Lelio R Paula07/2013
6000-330*Bern(21940)/22379062073368201Serge Batalov04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 18 2017 12:02 (Time in France)

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