PRP Records

Probable Primes Top 10000

(173006 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 ?
25012^348612-809104943Yves Minet05/2013
25022^348583-350407104934Enzo Doria06/2015
25032^348531-949104919Yves Minet05/2012
250420^80636-59104910Lelio R Paula12/2016
25052^348437+35104890Lelio R Paula09/2011
25062^348348+135104864Lelio R Paula09/2011
2507(2^348284+9)/25104843Lelio R Paula12/2013
250875^55914-74104843Norbert Schneider01/2015
25092^348268+255255104840Lelio R Paula01/2017
25105^149985-52104836Lelio R Paula11/2016
25112^348224-20249104826Enzo Doria06/2013
25122^348212-20105104823Enzo Doria06/2013
251320^80562+19104814Lelio R Paula12/2016
25142^348149-20053104804Enzo Doria06/2013
25152^348095-171104788Lelio R Paula09/2011
25162^348003-20377104760Enzo Doria06/2013
25172^347994-741104757Lelio R Paula12/2016
2518(13*2^347972-1)/282309104746Lelio R Paula03/2014
25192^347910-109937104732Enzo Doria04/2014
25205^149794+28104702Lelio R Paula11/2016
2521(16^86939+3^86939)/19104684Robert Price06/2013
2522(15^89009-1)/14104682Paul Bourdelais03/2010
25232^347731-18609104678Enzo Doria05/2013
25244*6^134519+7104677Lelio R Paula11/2014
25252^347612-18545104642Enzo Doria05/2013
25266^134465+95104635Lelio R Paula11/2016
25272^347517-17301104614Enzo Doria05/2013
25283^219222-310104596Lelio R Paula11/2016
2529(15*2^347399-1)/13104578Lelio R Paula03/2014
25302^347372-17853104570Enzo Doria05/2013
25312^347314+99104552Lelio R Paula09/2011
25322^347300-22233104548Enzo Doria06/2013
25332^347287-19845104544Enzo Doria06/2013
2534(31*2^347254-1)/891104533Lelio R Paula03/2014
25355*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
25367*2^347239-3104531Lelio R Paula09/2014
2537(3^219098-8)/514147439969104525Lelio R Paula12/2013
25385*3^219047+8104513Lelio R Paula09/2014
25392^347148-109073104502Enzo Doria04/2014
25402^347129-20145104497Enzo Doria06/2013
25412^346923-19585104435Enzo Doria05/2013
2542(11*2^346864-1)/175104416Lelio R Paula03/2014
25432^346854+346854^2+1104414Robert Price06/2014
25442^346834+11715104408Lelio R Paula04/2015
254579^55009+78104387Norbert Schneider02/2015
25463^218744+58104368Lelio R Paula11/2016
25472^346649+65104352Lelio R Paula09/2011
25482^346638-17265104349Enzo Doria05/2013
25502^346527-111817104316Enzo Doria05/2014
25496^134055+101104316Lelio R Paula11/2016
25516^134013+163104283Lelio R Paula11/2016
255218^83049-89104250Lelio R Paula01/2017
25532^346213+484049104221Enzo Doria04/2017
255418^83021-91104214Lelio R Paula01/2017
255510^104212+128779104213Patrick De Geest05/2016
255610^104212+237447104213Patrick De Geest05/2016
255710^104212+242139104213Patrick De Geest05/2016
255810^104212+269199104213Patrick De Geest05/2016
2559(10^104212-71)/1104212Serge Batalov12/2014
25602^346078+7695104180Lelio R Paula12/2016
25612^346055-19537104173Enzo Doria05/2013
2562(3*2^346057+1)/77104173Lelio R Paula12/2013
25632^346037-20125104168Enzo Doria06/2013
2564(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
25656^133854-17993104159Enzo Doria03/2013
25662^345990+1874239104154Enzo Doria06/2016
25672^345988-20373104153Enzo Doria06/2013
25683*5^148968+8104125Lelio R Paula11/2014
2569p(21253)#/2+8104113Robert Price01/2017
2570322^41507+41507^322104094Norbert Schneider12/2014
25716^133768-17423104092Enzo Doria03/2013
25722^345786-19557104092Enzo Doria05/2013
25732^345704-149104068Lelio R Paula09/2011
25746^133704-17273104042Enzo Doria02/2013
2575(3*2^345590-1)/23104033Lelio R Paula03/2014
2576(19*2^345590+1)/33859104030Lelio R Paula12/2013
25772^345547+11104021Lelio R Paula09/2011
25782^345504+723104008Lelio R Paula09/2011
25792^345498-20037104006Enzo Doria06/2013
258018^82854-37104005Lelio R Paula01/2017
25812^345486-109065104002Enzo Doria04/2014
25822^345487-1851507104002Enzo Doria08/2015
25832^345476+777103999Lelio R Paula09/2011
2584(5*2^345321-1)/3103953Lelio R Paula03/2014
2585(2^345267-9)/539049127103927Lelio R Paula12/2013
2586(78557*2^345163+1)/78589103905Lelio R Paula07/2014
25872^345106-112181103888Enzo Doria06/2014
25882^345079+99103880Lelio R Paula09/2011
258911^99736-1500103865Enzo Doria12/2012
25902^344842-20157103808Enzo Doria06/2013
2591(47*2^344822+1)/1071103801Lelio R Paula05/2015
25922^344802-20765103796Enzo Doria06/2013
25932^344794-3821103794Yves Minet05/2011
25942^344782-109103103790Enzo Doria04/2014
25953^217521-112292103784Enzo Doria06/2014
25962^344759-3505103783Lelio R Paula11/2016
25972^344735-147103776Lelio R Paula09/2011
2598(55459*2^344617+1)/3103745Lelio R Paula07/2014
25992^344607-108891103738Enzo Doria03/2014
26002^344541-19561103718Enzo Doria05/2013
2601(1017*2^344529-1)/569103714Lelio R Paula05/2015
2602(4*10^103703-1)/3103704Serge Batalov08/2009
26032^344444-455103688Yves Minet03/2012
26042^344317-109933103650Enzo Doria04/2014
26052^344309-1852033103648Enzo Doria08/2015
26062^344213-21253103619Enzo Doria06/2013
26072^344196-465103614Lelio R Paula11/2016
26082^344187-20001103611Enzo Doria06/2013
260920^79621-19^79621103590Jean-Louis Charton03/2011
2610Phi(155391,10)/1243129103586Maksym Voznyy09/2015
26112^344085-20365103580Enzo Doria06/2013
26125^148169+54103566Lelio R Paula11/2016
26132^344017-108795103560Enzo Doria03/2014
26142^343971-5077103546Lelio R Paula09/2011
26152^343899+141103524Lelio R Paula08/2011
26166^133029-67103517Lelio R Paula11/2016
2617(17*2^343877+1)/13625103515Lelio R Paula12/2013
2618(136*10^103474-1)/9103476Serge Batalov12/2014
26195^148014-24103458Lelio R Paula11/2016
26202^343604+9931103436Yves Minet01/2011
26212^343601-21189103435Enzo Doria06/2013
26222^343508-115229103407Enzo Doria06/2015
2623(509203*2^343491-1)/16147103403Lelio R Paula05/2015
26243^216685-113056103386Enzo Doria07/2014
262544^62903-43^62903103379Jean-Louis Charton08/2012
262611^99262-20103371Lelio R Paula12/2016
2627(509203*2^343357-1)/5103366Lelio R Paula05/2015
26282^343356-2791889103361Enzo Doria03/2016
2629Phi(104989,10)/2939693103350Maksym Voznyy09/2015
26302^343182-171103309Lelio R Paula08/2011
2631(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
26322^343079-1835611103278Enzo Doria05/2015
26332^343063-1147103273Yves Minet06/2013
26349*6^132689+7103254Lelio R Paula11/2014
26352^342979-18085103247Enzo Doria05/2013
26362^342966-16995103244Lelio R Paula11/2016
26375^147650+16103203Lelio R Paula11/2016
2638gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
26392^342817+2707067103199Enzo Doria03/2016
264043^63177-42103198Theodore Burton02/2007
26412^342805-21025103195Enzo Doria06/2013
26422^342714+12285103168Lelio R Paula11/2016
264318^82178-4481103156Enzo Doria03/2013
26442^342665-17349103153Enzo Doria05/2013
26452^342612+175103137Lelio R Paula08/2011
26465*2^342585-3103130Lelio R Paula09/2014
26472^342503-19209103104Enzo Doria05/2013
26482^342476+51103096Lelio R Paula08/2011
26492^342460-18885103091Enzo Doria05/2013
26507^121968+82103075Lelio R Paula10/2016
26512^342392-108863103071Enzo Doria03/2014
26523^216014+28103065Lelio R Paula11/2016
26532^342353-108879103059Enzo Doria03/2014
265410^103055+276081103056Patrick De Geest12/2016
265510^103055-53103055Lelio R Paula11/2016
26567^121933+4103046Lelio R Paula11/2014
265719^80560-68103017Lelio R Paula10/2016
26582^342209+76607103016Enzo Doria05/2016
2660328^40945+40945^328103013Norbert Schneider12/2014
265912^95454-91103013Lelio R Paula10/2016
266165^56809-64^56809102990Robert Price08/2013
26625^147338-6102985Lelio R Paula11/2014
26632^342084-112739102978Enzo Doria06/2014
26649*6^132330+7102974Lelio R Paula11/2014
26652^342034-16737102963Enzo Doria05/2013
2666(9787*2^342011-1)/25102959Lelio R Paula05/2015
2667(3^215802-5)/124343756102956Lelio R Paula12/2013
26682^341991-17421102950Enzo Doria05/2013
26692^341969-112225102943Enzo Doria06/2014
2670(9787*2^341864-1)/3102915Lelio R Paula05/2015
26712^341859+1869413102910Enzo Doria05/2016
267210^102909+61102910Lelio R Paula11/2016
267310^102909-67049102909Patrick De Geest12/2016
26742^341659+1836773102850Enzo Doria03/2016
26752^341608-110639102835Enzo Doria05/2014
267610^102824+49102825Lelio R Paula11/2016
267710^102824-168011102824Patrick De Geest12/2016
267811^98708-8102794Lelio R Paula10/2016
26792^341466+4429102792Lelio R Paula09/2011
26802^341460-107102790Lelio R Paula08/2011
2681(2^341388+47)/21014943102761Lelio R Paula12/2013
26822^341355+21102759Lelio R Paula08/2011
26832^341246+40755102726Lelio R Paula11/2016
2684(2^341256-5)/991699102723Lelio R Paula12/2013
26857^121547+78102720Lelio R Paula10/2016
26862^341223-461197102719Enzo Doria06/2015
26882^341190-20577102709Enzo Doria06/2013
2687(27*2^341212+1)/84674449102709Lelio R Paula12/2013
26896^131976-65102698Lelio R Paula10/2016
26902^341134+2533102692Henri Lifchitz09/2005
269113^92184-54102688Lelio R Paula10/2016
26922^341116-20873102687Enzo Doria06/2013
26932^341094-19953102680Enzo Doria06/2013
26942^341053+129102668Lelio R Paula08/2011
2696(31*2^341006-1)/3102655Lelio R Paula03/2014
26957^121471+94102655Lelio R Paula10/2016
26982^341004-173102653Lelio R Paula08/2011
269720^78901+3102653Lelio R Paula10/2016
26995^146853-52102646Lelio R Paula10/2016
27002^340969-216931102642Enzo Doria05/2014
27012^340952+1870021102637Enzo Doria05/2016
27025*2^340940-3102634Lelio R Paula08/2014
2703(6^131891+1)/7102631Paul Bourdelais01/2010
270475^54717+74102598Norbert Schneider01/2015
27052^340806-20393102593Enzo Doria06/2013
2706(2^340790+5)/138267102583Lelio R Paula12/2013
27076^131821+77102577Lelio R Paula10/2016
27082^340688-29102558Henri Lifchitz05/2005
27092^340685-109101102557Enzo Doria04/2014
271065^56567-64102552Norbert Schneider11/2014
27112^340547-108897102515Enzo Doria03/2014
27127^121268+82102484Lelio R Paula10/2016
2713(6883*2^340443-1)/162401102483Lelio R Paula05/2015
27142^340434-5955102481Lelio R Paula11/2016
2715(2^340381+47)/7102465Lelio R Paula12/2013
2716111^50095+110102461Norbert Schneider04/2017
27172^340291-20301102438Enzo Doria06/2013
271812^94915+89102431Lelio R Paula10/2016
27192^340208-20373102413Enzo Doria06/2013
27206^131598-17273102404Enzo Doria02/2013
27212^340115-21181102385Enzo Doria06/2013
2722(55459*2^340090+1)/1591102379Lelio R Paula07/2014
272389^52511-88^52511102365Robert Price06/2015
27243^214539-112756102362Enzo Doria07/2014
27252^340000-19877102351Enzo Doria06/2013
27262^339990-114845102348Enzo Doria05/2015
2727(3^214516-2)/51383102346Lelio R Paula12/2013
272820^78661-99102341Lelio R Paula09/2016
27292^339951-19585102336Enzo Doria05/2013
2730(13*2^339943+1)/45102333Lelio R Paula12/2013
27312^339889+29327102317Yves Minet06/2010
27322^339834-109493102301Enzo Doria04/2014
2733(11^98221-5^98221)/6102286Robert Price01/2013
27343^214365+1820102279Lelio R Paula10/2016
2735(11*2^339705-1)/183102261Lelio R Paula03/2014
27362^339694-16995102259Lelio R Paula09/2016
27377^120985-38102245Lelio R Paula10/2016
273810^102244+122961102245Patrick De Geest12/2016
273910^102244-27102244Lelio R Paula09/2016
27407^120982-62102242Lelio R Paula10/2016
27414*6^131382-5102236Lelio R Paula11/2014
27422^339586-1091102226Yves Minet11/2012
274311^98161-3072000102225Enzo Doria12/2012
27449*7^120961-4102225Lelio R Paula11/2014
27455*3^214250+2102224Serge Batalov10/2010
274612^94713-59102213Lelio R Paula10/2016
274712^94705+89102204Lelio R Paula10/2016
27482^339407-177102172Lelio R Paula08/2011
27492^339355+65102157Lelio R Paula07/2011
2750(2^339323+47)/880715102141Lelio R Paula12/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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