PRP Records

Probable Primes Top 10000

(177649 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 ?
250111^101142-1080105329Enzo Doria12/2012
2502(68*10^105320-41)/9105321Robert Price10/2013
25033^220712-9934105307Enzo Doria05/2014
25047*10^105296+9105297Robert Price09/2015
25052^349739+1873373105282Enzo Doria06/2016
25067^124574+24105278Lelio R Paula11/2016
25072^349708-20957105273Enzo Doria06/2013
25082^349649-20469105255Enzo Doria06/2013
25092^349607-20109105243Enzo Doria06/2013
25102^349594-19085105239Enzo Doria05/2013
25112^349530+1874479105220Enzo Doria06/2016
2512(3^220528+8)/8081105215Lelio R Paula12/2013
25133^220464-112852105189Enzo Doria07/2014
25142^349419-17349105186Enzo Doria05/2013
25152^349400-2579105180Yves Minet07/2014
25168*5^150471+3105176Lelio R Paula11/2014
251713^94403+94105160Lelio R Paula12/2016
25182^349301-112309105151Enzo Doria06/2014
25199*2^349220+5105127Lelio R Paula09/2014
25207*3^220317+8105119Lelio R Paula09/2014
25217^124386+88105119Lelio R Paula11/2016
25222^349171-19657105111Enzo Doria06/2013
2523(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
2524(2^349111-5)/3105093Lelio R Paula12/2013
25252^348981-2797573105054Enzo Doria04/2016
25262^348869-6555105021Lelio R Paula01/2017
25275^150217+78104998Lelio R Paula11/2016
25282^348703-113005104971Enzo Doria06/2014
25302^348612-809104943Yves Minet05/2013
2529(73*10^104942-1)/9104943Robert Price01/2015
25312^348583-350407104934Enzo Doria06/2015
25322^348531-949104919Yves Minet05/2012
253320^80636-59104910Lelio R Paula12/2016
25342^348437+35104890Lelio R Paula09/2011
25352^348348+135104864Lelio R Paula09/2011
2537(2^348284+9)/25104843Lelio R Paula12/2013
253675^55914-74104843Norbert Schneider01/2015
25382^348268+255255104840Lelio R Paula01/2017
25395^149985-52104836Lelio R Paula11/2016
25402^348224-20249104826Enzo Doria06/2013
25412^348212-20105104823Enzo Doria06/2013
254220^80562+19104814Lelio R Paula12/2016
25432^348149-20053104804Enzo Doria06/2013
25442^348095-171104788Lelio R Paula09/2011
25452^348003-20377104760Enzo Doria06/2013
25462^347994-741104757Lelio R Paula12/2016
2547(13*2^347972-1)/282309104746Lelio R Paula03/2014
25482^347910-109937104732Enzo Doria04/2014
25495^149794+28104702Lelio R Paula11/2016
2550(16^86939+3^86939)/19104684Robert Price06/2013
2551(15^89009-1)/14104682Paul Bourdelais03/2010
25522^347731-18609104678Enzo Doria05/2013
25534*6^134519+7104677Lelio R Paula11/2014
25542^347612-18545104642Enzo Doria05/2013
25556^134465+95104635Lelio R Paula11/2016
25562^347517-17301104614Enzo Doria05/2013
25573^219222-310104596Lelio R Paula11/2016
2558(15*2^347399-1)/13104578Lelio R Paula03/2014
25592^347372-17853104570Enzo Doria05/2013
25602^347314+99104552Lelio R Paula09/2011
25612^347300-22233104548Enzo Doria06/2013
25622^347287-19845104544Enzo Doria06/2013
2563(31*2^347254-1)/891104533Lelio R Paula03/2014
25645*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
25657*2^347239-3104531Lelio R Paula09/2014
2566(3^219098-8)/514147439969104525Lelio R Paula12/2013
25675*3^219047+8104513Lelio R Paula09/2014
25682^347148-109073104502Enzo Doria04/2014
25692^347129-20145104497Enzo Doria06/2013
25702^346923-19585104435Enzo Doria05/2013
2571(11*2^346864-1)/175104416Lelio R Paula03/2014
25722^346854+346854^2+1104414Robert Price06/2014
25732^346834+11715104408Lelio R Paula04/2015
257479^55009+78104387Norbert Schneider02/2015
25753^218744+58104368Lelio R Paula11/2016
25762^346649+65104352Lelio R Paula09/2011
25772^346638-17265104349Enzo Doria05/2013
25792^346527-111817104316Enzo Doria05/2014
25786^134055+101104316Lelio R Paula11/2016
25806^134013+163104283Lelio R Paula11/2016
258118^83049-89104250Lelio R Paula01/2017
25822^346213+484049104221Enzo Doria04/2017
258318^83021-91104214Lelio R Paula01/2017
258410^104212+128779104213Patrick De Geest05/2016
258510^104212+237447104213Patrick De Geest05/2016
258610^104212+242139104213Patrick De Geest05/2016
258710^104212+269199104213Patrick De Geest05/2016
2588(10^104212-71)/1104212Serge Batalov12/2014
25892^346078+7695104180Lelio R Paula12/2016
25902^346055-19537104173Enzo Doria05/2013
2591(3*2^346057+1)/77104173Lelio R Paula12/2013
25922^346037-20125104168Enzo Doria06/2013
2593(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
25946^133854-17993104159Enzo Doria03/2013
25952^345990+1874239104154Enzo Doria06/2016
25962^345988-20373104153Enzo Doria06/2013
25973*5^148968+8104125Lelio R Paula11/2014
2598p(21253)#/2+8104113Robert Price01/2017
2599322^41507+41507^322104094Norbert Schneider12/2014
26006^133768-17423104092Enzo Doria03/2013
26012^345786-19557104092Enzo Doria05/2013
26022^345704-149104068Lelio R Paula09/2011
26036^133704-17273104042Enzo Doria02/2013
2604(3*2^345590-1)/23104033Lelio R Paula03/2014
2605(19*2^345590+1)/33859104030Lelio R Paula12/2013
26062^345547+11104021Lelio R Paula09/2011
26072^345504+723104008Lelio R Paula09/2011
26082^345498-20037104006Enzo Doria06/2013
260918^82854-37104005Lelio R Paula01/2017
26102^345486-109065104002Enzo Doria04/2014
26112^345487-1851507104002Enzo Doria08/2015
26122^345476+777103999Lelio R Paula09/2011
2613(5*2^345321-1)/3103953Lelio R Paula03/2014
2614(2^345267-9)/539049127103927Lelio R Paula12/2013
2615(78557*2^345163+1)/78589103905Lelio R Paula07/2014
26162^345106-112181103888Enzo Doria06/2014
26172^345079+99103880Lelio R Paula09/2011
261811^99736-1500103865Enzo Doria12/2012
26192^344842-20157103808Enzo Doria06/2013
2620(47*2^344822+1)/1071103801Lelio R Paula05/2015
26212^344802-20765103796Enzo Doria06/2013
26222^344794-3821103794Yves Minet05/2011
26232^344782-109103103790Enzo Doria04/2014
26243^217521-112292103784Enzo Doria06/2014
26252^344759-3505103783Lelio R Paula11/2016
26262^344735-147103776Lelio R Paula09/2011
2627(55459*2^344617+1)/3103745Lelio R Paula07/2014
26282^344607-108891103738Enzo Doria03/2014
26292^344541-19561103718Enzo Doria05/2013
2630(1017*2^344529-1)/569103714Lelio R Paula05/2015
2631(4*10^103703-1)/3103704Serge Batalov08/2009
26322^344444-455103688Yves Minet03/2012
2633(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
26342^344317-109933103650Enzo Doria04/2014
26352^344309-1852033103648Enzo Doria08/2015
26362^344213-21253103619Enzo Doria06/2013
26372^344196-465103614Lelio R Paula11/2016
26382^344187-20001103611Enzo Doria06/2013
263920^79621-19^79621103590Jean-Louis Charton03/2011
2640Phi(155391,10)/1243129103586Maksym Voznyy09/2015
26412^344085-20365103580Enzo Doria06/2013
26425^148169+54103566Lelio R Paula11/2016
26432^344017-108795103560Enzo Doria03/2014
26442^343971-5077103546Lelio R Paula09/2011
26452^343899+141103524Lelio R Paula08/2011
26466^133029-67103517Lelio R Paula11/2016
2647(17*2^343877+1)/13625103515Lelio R Paula12/2013
2648(136*10^103474-1)/9103476Serge Batalov12/2014
26495^148014-24103458Lelio R Paula11/2016
26502^343604+9931103436Yves Minet01/2011
26512^343601-21189103435Enzo Doria06/2013
26522^343508-115229103407Enzo Doria06/2015
2653(509203*2^343491-1)/16147103403Lelio R Paula05/2015
26543^216685-113056103386Enzo Doria07/2014
265544^62903-43^62903103379Jean-Louis Charton08/2012
265611^99262-20103371Lelio R Paula12/2016
2657(509203*2^343357-1)/5103366Lelio R Paula05/2015
26582^343356-2791889103361Enzo Doria03/2016
2659Phi(104989,10)/2939693103350Maksym Voznyy09/2015
26602^343182-171103309Lelio R Paula08/2011
2661(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
26622^343079-1835611103278Enzo Doria05/2015
26632^343063-1147103273Yves Minet06/2013
26649*6^132689+7103254Lelio R Paula11/2014
26652^342979-18085103247Enzo Doria05/2013
26662^342966-16995103244Lelio R Paula11/2016
26675^147650+16103203Lelio R Paula11/2016
2668gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
26692^342817+2707067103199Enzo Doria03/2016
267043^63177-42103198Theodore Burton02/2007
26712^342805-21025103195Enzo Doria06/2013
26722^342714+12285103168Lelio R Paula11/2016
267318^82178-4481103156Enzo Doria03/2013
26742^342665-17349103153Enzo Doria05/2013
26752^342612+175103137Lelio R Paula08/2011
26765*2^342585-3103130Lelio R Paula09/2014
26772^342503-19209103104Enzo Doria05/2013
26782^342476+51103096Lelio R Paula08/2011
26792^342460-18885103091Enzo Doria05/2013
26807^121968+82103075Lelio R Paula10/2016
26812^342392-108863103071Enzo Doria03/2014
26823^216014+28103065Lelio R Paula11/2016
26832^342353-108879103059Enzo Doria03/2014
268410^103055+276081103056Patrick De Geest12/2016
268510^103055-53103055Lelio R Paula11/2016
26867^121933+4103046Lelio R Paula11/2014
268719^80560-68103017Lelio R Paula10/2016
26882^342209+76607103016Enzo Doria05/2016
2690328^40945+40945^328103013Norbert Schneider12/2014
268912^95454-91103013Lelio R Paula10/2016
269165^56809-64^56809102990Robert Price08/2013
26925^147338-6102985Lelio R Paula11/2014
26932^342084-112739102978Enzo Doria06/2014
26949*6^132330+7102974Lelio R Paula11/2014
26952^342034-16737102963Enzo Doria05/2013
2696(9787*2^342011-1)/25102959Lelio R Paula05/2015
2697(3^215802-5)/124343756102956Lelio R Paula12/2013
26982^341991-17421102950Enzo Doria05/2013
26992^341969-112225102943Enzo Doria06/2014
2700(9787*2^341864-1)/3102915Lelio R Paula05/2015
27012^341859+1869413102910Enzo Doria05/2016
270210^102909+61102910Lelio R Paula11/2016
270310^102909-67049102909Patrick De Geest12/2016
27042^341659+1836773102850Enzo Doria03/2016
27052^341608-110639102835Enzo Doria05/2014
270610^102824+49102825Lelio R Paula11/2016
270710^102824-168011102824Patrick De Geest12/2016
270811^98708-8102794Lelio R Paula10/2016
27092^341466+4429102792Lelio R Paula09/2011
27102^341460-107102790Lelio R Paula08/2011
2711(2^341388+47)/21014943102761Lelio R Paula12/2013
27122^341355+21102759Lelio R Paula08/2011
27132^341246+40755102726Lelio R Paula11/2016
2714(2^341256-5)/991699102723Lelio R Paula12/2013
27157^121547+78102720Lelio R Paula10/2016
27162^341223-461197102719Enzo Doria06/2015
27182^341190-20577102709Enzo Doria06/2013
2717(27*2^341212+1)/84674449102709Lelio R Paula12/2013
27196^131976-65102698Lelio R Paula10/2016
27202^341134+2533102692Henri Lifchitz09/2005
272113^92184-54102688Lelio R Paula10/2016
27222^341116-20873102687Enzo Doria06/2013
27232^341094-19953102680Enzo Doria06/2013
27242^341053+129102668Lelio R Paula08/2011
2725(31*2^341006-1)/3102655Lelio R Paula03/2014
27267^121471+94102655Lelio R Paula10/2016
27282^341004-173102653Lelio R Paula08/2011
272720^78901+3102653Lelio R Paula10/2016
27295^146853-52102646Lelio R Paula10/2016
27302^340969-216931102642Enzo Doria05/2014
27312^340952+1870021102637Enzo Doria05/2016
27325*2^340940-3102634Lelio R Paula08/2014
2733(6^131891+1)/7102631Paul Bourdelais01/2010
273475^54717+74102598Norbert Schneider01/2015
27352^340806-20393102593Enzo Doria06/2013
2736(2^340790+5)/138267102583Lelio R Paula12/2013
27376^131821+77102577Lelio R Paula10/2016
27382^340688-29102558Henri Lifchitz05/2005
27392^340685-109101102557Enzo Doria04/2014
274065^56567-64102552Norbert Schneider11/2014
27412^340547-108897102515Enzo Doria03/2014
27427^121268+82102484Lelio R Paula10/2016
2743(6883*2^340443-1)/162401102483Lelio R Paula05/2015
27442^340434-5955102481Lelio R Paula11/2016
2745(2^340381+47)/7102465Lelio R Paula12/2013
2746111^50095+110102461Norbert Schneider04/2017
27472^340291-20301102438Enzo Doria06/2013
274812^94915+89102431Lelio R Paula10/2016
27492^340208-20373102413Enzo Doria06/2013
27506^131598-17273102404Enzo Doria02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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