PRP Records

Probable Primes Top 10000

(202622 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 ?
275110^104212+242139104213Patrick De Geest05/2016
275210^104212+269199104213Patrick De Geest05/2016
2753(10^104212-71)/1104212Serge Batalov12/2014
27542^346078+7695104180Lelio R Paula12/2016
27552^346055-19537104173Enzo Doria05/2013
2756(3*2^346057+1)/77104173Lelio R Paula12/2013
27572^346037-20125104168Enzo Doria06/2013
2758(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
27596^133854-17993104159Enzo Doria03/2013
27602^345990+1874239104154Enzo Doria06/2016
27612^345988-20373104153Enzo Doria06/2013
27623*5^148968+8104125Lelio R Paula11/2014
2763p(21253)#/2+8104113Robert Price01/2017
2764322^41507+41507^322104094Norbert Schneider12/2014
27656^133768-17423104092Enzo Doria03/2013
27662^345786-19557104092Enzo Doria05/2013
2767171^46606-2104072Lelio R Paula10/2017
27682^345704-149104068Lelio R Paula09/2011
27696^133704-17273104042Enzo Doria02/2013
2770(3*2^345590-1)/23104033Lelio R Paula03/2014
2771(19*2^345590+1)/33859104030Lelio R Paula12/2013
27722^345547+11104021Lelio R Paula09/2011
27732^345504+723104008Lelio R Paula09/2011
27742^345498-20037104006Enzo Doria06/2013
277518^82854-37104005Lelio R Paula01/2017
27762^345486-109065104002Enzo Doria04/2014
27772^345487-1851507104002Enzo Doria08/2015
27782^345476+777103999Lelio R Paula09/2011
2779(5*2^345321-1)/3103953Lelio R Paula03/2014
2780(2^345267-9)/539049127103927Lelio R Paula12/2013
2781(78557*2^345163+1)/78589103905Lelio R Paula07/2014
27822^345106-112181103888Enzo Doria06/2014
27832^345079+99103880Lelio R Paula09/2011
278411^99736-1500103865Enzo Doria12/2012
27852^344842-20157103808Enzo Doria06/2013
2786(47*2^344822+1)/1071103801Lelio R Paula05/2015
27872^344802-20765103796Enzo Doria06/2013
27882^344794-3821103794Yves Minet05/2011
27892^344782-109103103790Enzo Doria04/2014
27903^217521-112292103784Enzo Doria06/2014
27912^344759-3505103783Lelio R Paula11/2016
27922^344735-147103776Lelio R Paula09/2011
2793(55459*2^344617+1)/3103745Lelio R Paula07/2014
27942^344607-108891103738Enzo Doria03/2014
27952^344541-19561103718Enzo Doria05/2013
2796(1017*2^344529-1)/569103714Lelio R Paula05/2015
2797(4*10^103703-1)/3103704Serge Batalov08/2009
27982^344444-455103688Yves Minet03/2012
2799(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
28002^344317-109933103650Enzo Doria04/2014
28012^344309-1852033103648Enzo Doria08/2015
28022^344213-21253103619Enzo Doria06/2013
28032^344196-465103614Lelio R Paula11/2016
28042^344187-20001103611Enzo Doria06/2013
2805(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
280620^79621-19^79621103590Jean-Louis Charton03/2011
2807Phi(155391,10)/1243129103586Maksym Voznyy09/2015
28082^344085-20365103580Enzo Doria06/2013
28095^148169+54103566Lelio R Paula11/2016
28102^344017-108795103560Enzo Doria03/2014
28112^343971-5077103546Lelio R Paula09/2011
28122^343899+141103524Lelio R Paula08/2011
28136^133029-67103517Lelio R Paula11/2016
2814(17*2^343877+1)/13625103515Lelio R Paula12/2013
2815(136*10^103474-1)/9103476Serge Batalov12/2014
28165^148014-24103458Lelio R Paula11/2016
28172^343604+9931103436Yves Minet01/2011
28182^343601-21189103435Enzo Doria06/2013
28192^343508-115229103407Enzo Doria06/2015
2820(509203*2^343491-1)/16147103403Lelio R Paula05/2015
28213^216685-113056103386Enzo Doria07/2014
282244^62903-43^62903103379Jean-Louis Charton08/2012
282311^99262-20103371Lelio R Paula12/2016
2824(509203*2^343357-1)/5103366Lelio R Paula05/2015
28252^343356-2791889103361Enzo Doria03/2016
2826Phi(104989,10)/2939693103350Maksym Voznyy09/2015
28272^343182-171103309Lelio R Paula08/2011
2828(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
28292^343079-1835611103278Enzo Doria05/2015
28302^343063-1147103273Yves Minet06/2013
28319*6^132689+7103254Lelio R Paula11/2014
28322^342979-18085103247Enzo Doria05/2013
28332^342966-16995103244Lelio R Paula11/2016
28345^147650+16103203Lelio R Paula11/2016
2835gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
28362^342817+2707067103199Enzo Doria03/2016
283743^63177-42103198Theodore Burton02/2007
28382^342805-21025103195Enzo Doria06/2013
28392^342714+12285103168Lelio R Paula11/2016
284018^82178-4481103156Enzo Doria03/2013
28412^342665-17349103153Enzo Doria05/2013
28422^342612+175103137Lelio R Paula08/2011
28435*2^342585-3103130Lelio R Paula09/2014
28442^342503-19209103104Enzo Doria05/2013
28452^342476+51103096Lelio R Paula08/2011
28462^342460-18885103091Enzo Doria05/2013
28477^121968+82103075Lelio R Paula10/2016
28482^342392-108863103071Enzo Doria03/2014
28493^216014+28103065Lelio R Paula11/2016
28502^342353-108879103059Enzo Doria03/2014
285110^103055+276081103056Patrick De Geest12/2016
285210^103055-53103055Lelio R Paula11/2016
28537^121933+4103046Lelio R Paula11/2014
285419^80560-68103017Lelio R Paula10/2016
28552^342209+76607103016Enzo Doria05/2016
2857328^40945+40945^328103013Norbert Schneider12/2014
285612^95454-91103013Lelio R Paula10/2016
285865^56809-64^56809102990Robert Price08/2013
28595^147338-6102985Lelio R Paula11/2014
28602^342084-112739102978Enzo Doria06/2014
28619*6^132330+7102974Lelio R Paula11/2014
28622^342034-16737102963Enzo Doria05/2013
2863(9787*2^342011-1)/25102959Lelio R Paula05/2015
2864(3^215802-5)/124343756102956Lelio R Paula12/2013
28652^341991-17421102950Enzo Doria05/2013
28662^341969-112225102943Enzo Doria06/2014
2867(9787*2^341864-1)/3102915Lelio R Paula05/2015
28692^341859+1869413102910Enzo Doria05/2016
286810^102909+61102910Lelio R Paula11/2016
287010^102909-67049102909Patrick De Geest12/2016
28712^341659+1836773102850Enzo Doria03/2016
28722^341608-110639102835Enzo Doria05/2014
287310^102824+49102825Lelio R Paula11/2016
287410^102824-168011102824Patrick De Geest12/2016
287511^98708-8102794Lelio R Paula10/2016
28762^341466+4429102792Lelio R Paula09/2011
28772^341460-107102790Lelio R Paula08/2011
2878(2^341388+47)/21014943102761Lelio R Paula12/2013
28792^341355+21102759Lelio R Paula08/2011
28802^341246+40755102726Lelio R Paula11/2016
2881(2^341256-5)/991699102723Lelio R Paula12/2013
28827^121547+78102720Lelio R Paula10/2016
28832^341223-461197102719Enzo Doria06/2015
28852^341190-20577102709Enzo Doria06/2013
2884(27*2^341212+1)/84674449102709Lelio R Paula12/2013
28866^131976-65102698Lelio R Paula10/2016
28872^341134+2533102692Henri Lifchitz09/2005
288813^92184-54102688Lelio R Paula10/2016
28892^341116-20873102687Enzo Doria06/2013
28902^341094-19953102680Enzo Doria06/2013
28912^341053+129102668Lelio R Paula08/2011
2893(31*2^341006-1)/3102655Lelio R Paula03/2014
28927^121471+94102655Lelio R Paula10/2016
28952^341004-173102653Lelio R Paula08/2011
289420^78901+3102653Lelio R Paula10/2016
28965^146853-52102646Lelio R Paula10/2016
28972^340969-216931102642Enzo Doria05/2014
28982^340952+1870021102637Enzo Doria05/2016
28995*2^340940-3102634Lelio R Paula08/2014
2900(6^131891+1)/7102631Paul Bourdelais01/2010
2901(4*10^102612+83)/3102613Robert Price02/2018
290275^54717+74102598Norbert Schneider01/2015
29032^340806-20393102593Enzo Doria06/2013
2904(2^340790+5)/138267102583Lelio R Paula12/2013
29056^131821+77102577Lelio R Paula10/2016
29062^340688-29102558Henri Lifchitz05/2005
29072^340685-109101102557Enzo Doria04/2014
290865^56567-64102552Norbert Schneider11/2014
29092^340547-108897102515Enzo Doria03/2014
29107^121268+82102484Lelio R Paula10/2016
2911(6883*2^340443-1)/162401102483Lelio R Paula05/2015
29122^340434-5955102481Lelio R Paula11/2016
2913(2^340381+47)/7102465Lelio R Paula12/2013
2914111^50095+110102461Norbert Schneider04/2017
29152^340291-20301102438Enzo Doria06/2013
291612^94915+89102431Lelio R Paula10/2016
29172^340208-20373102413Enzo Doria06/2013
29186^131598-17273102404Enzo Doria02/2013
29192^340115-21181102385Enzo Doria06/2013
2920(55459*2^340090+1)/1591102379Lelio R Paula07/2014
292189^52511-88^52511102365Robert Price06/2015
29223^214539-112756102362Enzo Doria07/2014
29232^340000-19877102351Enzo Doria06/2013
29242^339990-114845102348Enzo Doria05/2015
2925(3^214516-2)/51383102346Lelio R Paula12/2013
292620^78661-99102341Lelio R Paula09/2016
29272^339951-19585102336Enzo Doria05/2013
2928(13*2^339943+1)/45102333Lelio R Paula12/2013
29292^339889+29327102317Yves Minet06/2010
29302^339834-109493102301Enzo Doria04/2014
2931(11^98221-5^98221)/6102286Robert Price01/2013
29323^214365+1820102279Lelio R Paula10/2016
2933(11*2^339705-1)/183102261Lelio R Paula03/2014
29342^339694-16995102259Lelio R Paula09/2016
29357^120985-38102245Lelio R Paula10/2016
293610^102244+122961102245Patrick De Geest12/2016
293710^102244-27102244Lelio R Paula09/2016
29387^120982-62102242Lelio R Paula10/2016
29394*6^131382-5102236Lelio R Paula11/2014
29402^339586-1091102226Yves Minet11/2012
294111^98161-3072000102225Enzo Doria12/2012
29429*7^120961-4102225Lelio R Paula11/2014
29435*3^214250+2102224Serge Batalov10/2010
294412^94713-59102213Lelio R Paula10/2016
294512^94705+89102204Lelio R Paula10/2016
29462^339407-177102172Lelio R Paula08/2011
29472^339355+65102157Lelio R Paula07/2011
2948(2^339323+47)/880715102141Lelio R Paula12/2013
29492^339168+21102100Lelio R Paula07/2011
29502^339167-108807102100Enzo Doria03/2014
29512^339156+163102097Lelio R Paula08/2011
2952(2^338982-7)/1754517102038Lelio R Paula12/2013
29532^338891-18885102017Enzo Doria05/2013
29542^338829-113239101998Enzo Doria07/2014
29552^338828-113297101998Enzo Doria07/2014
29562^338796+93101988Donovan Johnson06/2008
2957lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
2958(71^55079-1)/70101964Paul Bourdelais08/2017
29592^338682-19865101954Enzo Doria06/2013
2960(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
29612^338568+37101920Lelio R Paula07/2011
29622^338559-1858777101917Enzo Doria04/2016
2963(9*2^338520+1)/365101904Lelio R Paula12/2013
29642^338497-17041101898Enzo Doria05/2013
29652^338475+54615101892Lelio R Paula10/2016
29662^338426-19797101877Enzo Doria06/2013
29672^338368-20369101859Enzo Doria06/2013
29682^338366+74179101859Enzo Doria04/2016
29692^338280-19745101833Enzo Doria06/2013
2970(3*2^338236-1)/347101818Lelio R Paula03/2014
29716^130841+103101815Lelio R Paula10/2016
29732^338122-20117101785Enzo Doria06/2013
2972(2^338139+5)/905333101785Lelio R Paula12/2013
297435^65917-7092101781Enzo Doria03/2013
29752^338010-19833101752Enzo Doria06/2013
29763^213215-76101730Lelio R Paula09/2016
29772^337930+63101728Lelio R Paula07/2011
29782^337920+1869661101725Enzo Doria05/2016
29792^337859-19645101706Enzo Doria05/2013
29802^337754+1869169101675Enzo Doria05/2016
2981(31*2^337677-1)/593101650Lelio R Paula03/2014
298211^97605-24101646Lelio R Paula10/2016
29838^112539-112539101633Robert Price01/2014
29842^337515-19869101603Enzo Doria06/2013
29852^337473+719101590Lelio R Paula08/2011
2986(2^337485-509203)/656647157101585Lelio R Paula12/2013
29872^337452-108815101584Enzo Doria03/2014
29882^337453+1185101584Lelio R Paula09/2016
29892^337410-113561101571Enzo Doria08/2014
29902^337387+855101564Lelio R Paula09/2016
29912^337367-17295101558Lelio R Paula09/2016
29922^337342-109035101551Enzo Doria04/2014
29932^337267-19101528Lelio R Paula07/2011
29942^337183-19989101503Enzo Doria06/2013
29952^337149+72425101492Enzo Doria04/2016
29962^337101-20241101478Enzo Doria06/2013
29972^337035-20001101458Enzo Doria06/2013
29982^337017-16995101453Lelio R Paula09/2016
29992^336979-115315101441Enzo Doria06/2015
30002^336970-20885101439Enzo Doria06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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