PRP Records

Probable Primes Top 10000

(181746 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 ?
25012^351435-109077105793Enzo Doria04/2014
25022^351393+1089105780Lelio R Paula01/2017
25032^351364+72631105772Enzo Doria04/2016
25042^351305+1872467105754Enzo Doria05/2016
25053^221649+16105754Lelio R Paula11/2016
25068*3^221637-5105749Lelio R Paula09/2014
25072^351279-2780449105746Enzo Doria03/2016
250815^89903-26105735Lelio R Paula02/2017
25092^351213-73105726Lelio R Paula10/2011
25102^351192-4589105720Yves Minet07/2011
251120^81250-33105709Lelio R Paula12/2016
25122^351076-113159105685Enzo Doria07/2014
251393^53688-2105684Lelio R Paula09/2013
25142^351060-4559105680Yves Minet07/2011
251511^101473-750105674Enzo Doria11/2012
25163*5^151181-8105672Lelio R Paula11/2014
251715^89831-34105650Lelio R Paula02/2017
251911^101448-360105648Enzo Doria08/2012
25183*7^125011+4105648Lelio R Paula11/2014
25202^350943-113269105645Enzo Doria07/2014
25212^350868-19725105622Enzo Doria06/2013
25222^350858-59291105619Enzo Doria10/2015
25232^350851+135105617Lelio R Paula10/2011
25242^350841-741105614Lelio R Paula01/2017
25258*10^105571+3105572Robert Price08/2015
25262*5^151026-3105563Lelio R Paula11/2014
2527(2^350702+5)/34264674063105562Lelio R Paula12/2013
25286^135647-5^135647105554Jean-Louis Charton02/2009
25293^221211+236105545Lelio R Paula11/2016
253010^105515+33105516Lelio R Paula11/2016
253110^105515-41033105515Patrick De Geest12/2016
2532(29*2^350473-1)/267927105499Lelio R Paula03/2014
253317^85732-72105489Lelio R Paula01/2017
25342^350307-110329105453Enzo Doria05/2014
25352^350253-20365105437Enzo Doria06/2013
2536(3*29^72089-1075)/4105423Curtis Bright05/2015
25372^350139-109009105403Enzo Doria04/2014
25383*5^150763+4105380Lelio R Paula11/2014
253912^97643+91105375Lelio R Paula02/2017
25406*5^150744-7105367Lelio R Paula11/2014
25412^349996-112169105360Enzo Doria06/2014
254211^101142-1080105329Enzo Doria12/2012
2543(68*10^105320-41)/9105321Robert Price10/2013
25443^220712-9934105307Enzo Doria05/2014
25457*10^105296+9105297Robert Price09/2015
25462^349739+1873373105282Enzo Doria06/2016
25477^124574+24105278Lelio R Paula11/2016
25482^349708-20957105273Enzo Doria06/2013
25492^349649-20469105255Enzo Doria06/2013
25502^349607-20109105243Enzo Doria06/2013
25512^349594-19085105239Enzo Doria05/2013
25522^349530+1874479105220Enzo Doria06/2016
2553(3^220528+8)/8081105215Lelio R Paula12/2013
25543^220464-112852105189Enzo Doria07/2014
25552^349419-17349105186Enzo Doria05/2013
25562^349400-2579105180Yves Minet07/2014
25578*5^150471+3105176Lelio R Paula11/2014
255813^94403+94105160Lelio R Paula12/2016
25592^349301-112309105151Enzo Doria06/2014
25609*2^349220+5105127Lelio R Paula09/2014
25617*3^220317+8105119Lelio R Paula09/2014
25627^124386+88105119Lelio R Paula11/2016
25632^349171-19657105111Enzo Doria06/2013
2564(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
2565(2^349111-5)/3105093Lelio R Paula12/2013
25662^348981-2797573105054Enzo Doria04/2016
25672^348869-6555105021Lelio R Paula01/2017
25685^150217+78104998Lelio R Paula11/2016
25692^348703-113005104971Enzo Doria06/2014
25712^348612-809104943Yves Minet05/2013
2570(73*10^104942-1)/9104943Robert Price01/2015
25722^348583-350407104934Enzo Doria06/2015
25732^348531-949104919Yves Minet05/2012
257420^80636-59104910Lelio R Paula12/2016
25752^348437+35104890Lelio R Paula09/2011
25762^348348+135104864Lelio R Paula09/2011
2577(2^348284+9)/25104843Lelio R Paula12/2013
257875^55914-74104843Norbert Schneider01/2015
25792^348268+255255104840Lelio R Paula01/2017
25805^149985-52104836Lelio R Paula11/2016
25812^348224-20249104826Enzo Doria06/2013
25822^348212-20105104823Enzo Doria06/2013
258320^80562+19104814Lelio R Paula12/2016
25842^348149-20053104804Enzo Doria06/2013
25852^348095-171104788Lelio R Paula09/2011
25862^348003-20377104760Enzo Doria06/2013
25872^347994-741104757Lelio R Paula12/2016
2588(13*2^347972-1)/282309104746Lelio R Paula03/2014
25892^347910-109937104732Enzo Doria04/2014
25905^149794+28104702Lelio R Paula11/2016
2591(16^86939+3^86939)/19104684Robert Price06/2013
2592(15^89009-1)/14104682Paul Bourdelais03/2010
25932^347731-18609104678Enzo Doria05/2013
25944*6^134519+7104677Lelio R Paula11/2014
25952^347612-18545104642Enzo Doria05/2013
25966^134465+95104635Lelio R Paula11/2016
25972^347517-17301104614Enzo Doria05/2013
25983^219222-310104596Lelio R Paula11/2016
2599(15*2^347399-1)/13104578Lelio R Paula03/2014
26002^347372-17853104570Enzo Doria05/2013
26012^347314+99104552Lelio R Paula09/2011
26022^347300-22233104548Enzo Doria06/2013
26032^347287-19845104544Enzo Doria06/2013
2604(31*2^347254-1)/891104533Lelio R Paula03/2014
26055*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
26067*2^347239-3104531Lelio R Paula09/2014
2607(3^219098-8)/514147439969104525Lelio R Paula12/2013
26085*3^219047+8104513Lelio R Paula09/2014
26092^347148-109073104502Enzo Doria04/2014
26102^347129-20145104497Enzo Doria06/2013
26112^346923-19585104435Enzo Doria05/2013
2612(11*2^346864-1)/175104416Lelio R Paula03/2014
26132^346854+346854^2+1104414Robert Price06/2014
26142^346834+11715104408Lelio R Paula04/2015
261579^55009+78104387Norbert Schneider02/2015
26163^218744+58104368Lelio R Paula11/2016
26172^346649+65104352Lelio R Paula09/2011
26182^346638-17265104349Enzo Doria05/2013
26202^346527-111817104316Enzo Doria05/2014
26196^134055+101104316Lelio R Paula11/2016
26216^134013+163104283Lelio R Paula11/2016
262218^83049-89104250Lelio R Paula01/2017
26232^346213+484049104221Enzo Doria04/2017
262418^83021-91104214Lelio R Paula01/2017
262510^104212+128779104213Patrick De Geest05/2016
262610^104212+237447104213Patrick De Geest05/2016
262710^104212+242139104213Patrick De Geest05/2016
262810^104212+269199104213Patrick De Geest05/2016
2629(10^104212-71)/1104212Serge Batalov12/2014
26302^346078+7695104180Lelio R Paula12/2016
26312^346055-19537104173Enzo Doria05/2013
2632(3*2^346057+1)/77104173Lelio R Paula12/2013
26332^346037-20125104168Enzo Doria06/2013
2634(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
26356^133854-17993104159Enzo Doria03/2013
26362^345990+1874239104154Enzo Doria06/2016
26372^345988-20373104153Enzo Doria06/2013
26383*5^148968+8104125Lelio R Paula11/2014
2639p(21253)#/2+8104113Robert Price01/2017
2640322^41507+41507^322104094Norbert Schneider12/2014
26416^133768-17423104092Enzo Doria03/2013
26422^345786-19557104092Enzo Doria05/2013
26432^345704-149104068Lelio R Paula09/2011
26446^133704-17273104042Enzo Doria02/2013
2645(3*2^345590-1)/23104033Lelio R Paula03/2014
2646(19*2^345590+1)/33859104030Lelio R Paula12/2013
26472^345547+11104021Lelio R Paula09/2011
26482^345504+723104008Lelio R Paula09/2011
26492^345498-20037104006Enzo Doria06/2013
265018^82854-37104005Lelio R Paula01/2017
26512^345486-109065104002Enzo Doria04/2014
26522^345487-1851507104002Enzo Doria08/2015
26532^345476+777103999Lelio R Paula09/2011
2654(5*2^345321-1)/3103953Lelio R Paula03/2014
2655(2^345267-9)/539049127103927Lelio R Paula12/2013
2656(78557*2^345163+1)/78589103905Lelio R Paula07/2014
26572^345106-112181103888Enzo Doria06/2014
26582^345079+99103880Lelio R Paula09/2011
265911^99736-1500103865Enzo Doria12/2012
26602^344842-20157103808Enzo Doria06/2013
2661(47*2^344822+1)/1071103801Lelio R Paula05/2015
26622^344802-20765103796Enzo Doria06/2013
26632^344794-3821103794Yves Minet05/2011
26642^344782-109103103790Enzo Doria04/2014
26653^217521-112292103784Enzo Doria06/2014
26662^344759-3505103783Lelio R Paula11/2016
26672^344735-147103776Lelio R Paula09/2011
2668(55459*2^344617+1)/3103745Lelio R Paula07/2014
26692^344607-108891103738Enzo Doria03/2014
26702^344541-19561103718Enzo Doria05/2013
2671(1017*2^344529-1)/569103714Lelio R Paula05/2015
2672(4*10^103703-1)/3103704Serge Batalov08/2009
26732^344444-455103688Yves Minet03/2012
2674(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
26752^344317-109933103650Enzo Doria04/2014
26762^344309-1852033103648Enzo Doria08/2015
26772^344213-21253103619Enzo Doria06/2013
26782^344196-465103614Lelio R Paula11/2016
26792^344187-20001103611Enzo Doria06/2013
268020^79621-19^79621103590Jean-Louis Charton03/2011
2681Phi(155391,10)/1243129103586Maksym Voznyy09/2015
26822^344085-20365103580Enzo Doria06/2013
26835^148169+54103566Lelio R Paula11/2016
26842^344017-108795103560Enzo Doria03/2014
26852^343971-5077103546Lelio R Paula09/2011
26862^343899+141103524Lelio R Paula08/2011
26876^133029-67103517Lelio R Paula11/2016
2688(17*2^343877+1)/13625103515Lelio R Paula12/2013
2689(136*10^103474-1)/9103476Serge Batalov12/2014
26905^148014-24103458Lelio R Paula11/2016
26912^343604+9931103436Yves Minet01/2011
26922^343601-21189103435Enzo Doria06/2013
26932^343508-115229103407Enzo Doria06/2015
2694(509203*2^343491-1)/16147103403Lelio R Paula05/2015
26953^216685-113056103386Enzo Doria07/2014
269644^62903-43^62903103379Jean-Louis Charton08/2012
269711^99262-20103371Lelio R Paula12/2016
2698(509203*2^343357-1)/5103366Lelio R Paula05/2015
26992^343356-2791889103361Enzo Doria03/2016
2700Phi(104989,10)/2939693103350Maksym Voznyy09/2015
27012^343182-171103309Lelio R Paula08/2011
2702(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
27032^343079-1835611103278Enzo Doria05/2015
27042^343063-1147103273Yves Minet06/2013
27059*6^132689+7103254Lelio R Paula11/2014
27062^342979-18085103247Enzo Doria05/2013
27072^342966-16995103244Lelio R Paula11/2016
27085^147650+16103203Lelio R Paula11/2016
2709gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
27102^342817+2707067103199Enzo Doria03/2016
271143^63177-42103198Theodore Burton02/2007
27122^342805-21025103195Enzo Doria06/2013
27132^342714+12285103168Lelio R Paula11/2016
271418^82178-4481103156Enzo Doria03/2013
27152^342665-17349103153Enzo Doria05/2013
27162^342612+175103137Lelio R Paula08/2011
27175*2^342585-3103130Lelio R Paula09/2014
27182^342503-19209103104Enzo Doria05/2013
27192^342476+51103096Lelio R Paula08/2011
27202^342460-18885103091Enzo Doria05/2013
27217^121968+82103075Lelio R Paula10/2016
27222^342392-108863103071Enzo Doria03/2014
27233^216014+28103065Lelio R Paula11/2016
27242^342353-108879103059Enzo Doria03/2014
272510^103055+276081103056Patrick De Geest12/2016
272610^103055-53103055Lelio R Paula11/2016
27277^121933+4103046Lelio R Paula11/2014
272819^80560-68103017Lelio R Paula10/2016
27292^342209+76607103016Enzo Doria05/2016
2731328^40945+40945^328103013Norbert Schneider12/2014
273012^95454-91103013Lelio R Paula10/2016
273265^56809-64^56809102990Robert Price08/2013
27335^147338-6102985Lelio R Paula11/2014
27342^342084-112739102978Enzo Doria06/2014
27359*6^132330+7102974Lelio R Paula11/2014
27362^342034-16737102963Enzo Doria05/2013
2737(9787*2^342011-1)/25102959Lelio R Paula05/2015
2738(3^215802-5)/124343756102956Lelio R Paula12/2013
27392^341991-17421102950Enzo Doria05/2013
27402^341969-112225102943Enzo Doria06/2014
2741(9787*2^341864-1)/3102915Lelio R Paula05/2015
27422^341859+1869413102910Enzo Doria05/2016
274310^102909+61102910Lelio R Paula11/2016
274410^102909-67049102909Patrick De Geest12/2016
27452^341659+1836773102850Enzo Doria03/2016
27462^341608-110639102835Enzo Doria05/2014
274710^102824+49102825Lelio R Paula11/2016
274810^102824-168011102824Patrick De Geest12/2016
274911^98708-8102794Lelio R Paula10/2016
27502^341466+4429102792Lelio R Paula09/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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