PRP Records

Probable Primes Top 10000

(205869 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 ?
27512^349607-20109105243Enzo Doria06/2013
27522^349594-19085105239Enzo Doria05/2013
27532^349530+1874479105220Enzo Doria06/2016
2754(3^220528+8)/8081105215Lelio R Paula12/2013
27553^220464-112852105189Enzo Doria07/2014
27562^349419-17349105186Enzo Doria05/2013
27572^349400-2579105180Yves Minet07/2014
27588*5^150471+3105176Lelio R Paula11/2014
275913^94403+94105160Lelio R Paula12/2016
27602^349301-112309105151Enzo Doria06/2014
27619*2^349220+5105127Lelio R Paula09/2014
27627*3^220317+8105119Lelio R Paula09/2014
27637^124386+88105119Lelio R Paula11/2016
27642^349171-19657105111Enzo Doria06/2013
2765(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
2766(2^349111-5)/3105093Lelio R Paula12/2013
27672^348981-2797573105054Enzo Doria04/2016
27682^348869-6555105021Lelio R Paula01/2017
27695^150217+78104998Lelio R Paula11/2016
27702^348703-113005104971Enzo Doria06/2014
27722^348612-809104943Yves Minet05/2013
2771(73*10^104942-1)/9104943Robert Price01/2015
27732^348583-350407104934Enzo Doria06/2015
27742^348531-949104919Yves Minet05/2012
277520^80636-59104910Lelio R Paula12/2016
27762^348437+35104890Lelio R Paula09/2011
27772^348348+135104864Lelio R Paula09/2011
2778(2^348284+9)/25104843Lelio R Paula12/2013
277975^55914-74104843Norbert Schneider01/2015
27802^348268+255255104840Lelio R Paula01/2017
27815^149985-52104836Lelio R Paula11/2016
27822^348224-20249104826Enzo Doria06/2013
27832^348212-20105104823Enzo Doria06/2013
278420^80562+19104814Lelio R Paula12/2016
27852*10^104811-87104812Robert Price04/2018
27862^348149-20053104804Enzo Doria06/2013
27872^348095-171104788Lelio R Paula09/2011
27882^348003-20377104760Enzo Doria06/2013
27892^347994-741104757Lelio R Paula12/2016
2790(13*2^347972-1)/282309104746Lelio R Paula03/2014
27912^347910-109937104732Enzo Doria04/2014
27925^149794+28104702Lelio R Paula11/2016
2793105^51800-2104698Lelio R Paula10/2017
2794(16^86939+3^86939)/19104684Robert Price06/2013
2795(15^89009-1)/14104682Paul Bourdelais03/2010
27962^347731-18609104678Enzo Doria05/2013
27974*6^134519+7104677Lelio R Paula11/2014
27982^347612-18545104642Enzo Doria05/2013
27996^134465+95104635Lelio R Paula11/2016
28002^347517-17301104614Enzo Doria05/2013
28013^219222-310104596Lelio R Paula11/2016
2802(15*2^347399-1)/13104578Lelio R Paula03/2014
28032^347372-17853104570Enzo Doria05/2013
28042^347314+99104552Lelio R Paula09/2011
28052^347300-22233104548Enzo Doria06/2013
28062^347287-19845104544Enzo Doria06/2013
2807(31*2^347254-1)/891104533Lelio R Paula03/2014
28085*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
28097*2^347239-3104531Lelio R Paula09/2014
2810(3^219098-8)/514147439969104525Lelio R Paula12/2013
28115*3^219047+8104513Lelio R Paula09/2014
28122^347148-109073104502Enzo Doria04/2014
28132^347129-20145104497Enzo Doria06/2013
28142^346923-19585104435Enzo Doria05/2013
2815(11*2^346864-1)/175104416Lelio R Paula03/2014
28162^346854+346854^2+1104414Robert Price06/2014
28172^346834+11715104408Lelio R Paula04/2015
281879^55009+78104387Norbert Schneider02/2015
28193^218744+58104368Lelio R Paula11/2016
28202^346649+65104352Lelio R Paula09/2011
28212^346638-17265104349Enzo Doria05/2013
28232^346527-111817104316Enzo Doria05/2014
28226^134055+101104316Lelio R Paula11/2016
28246^134013+163104283Lelio R Paula11/2016
282518^83049-89104250Lelio R Paula01/2017
28262^346213+484049104221Enzo Doria04/2017
282718^83021-91104214Lelio R Paula01/2017
282810^104212+128779104213Patrick De Geest05/2016
282910^104212+237447104213Patrick De Geest05/2016
283010^104212+242139104213Patrick De Geest05/2016
283110^104212+269199104213Patrick De Geest05/2016
2832(10^104212-71)/1104212Serge Batalov12/2014
28332^346078+7695104180Lelio R Paula12/2016
28342^346055-19537104173Enzo Doria05/2013
2835(3*2^346057+1)/77104173Lelio R Paula12/2013
28362^346037-20125104168Enzo Doria06/2013
2837(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
28386^133854-17993104159Enzo Doria03/2013
28392^345990+1874239104154Enzo Doria06/2016
28402^345988-20373104153Enzo Doria06/2013
28413*5^148968+8104125Lelio R Paula11/2014
2842p(21253)#/2+8104113Robert Price01/2017
2843322^41507+41507^322104094Norbert Schneider12/2014
28446^133768-17423104092Enzo Doria03/2013
28452^345786-19557104092Enzo Doria05/2013
2846171^46606-2104072Lelio R Paula10/2017
28472^345704-149104068Lelio R Paula09/2011
28486^133704-17273104042Enzo Doria02/2013
2849(3*2^345590-1)/23104033Lelio R Paula03/2014
2850(19*2^345590+1)/33859104030Lelio R Paula12/2013
28512^345547+11104021Lelio R Paula09/2011
28522^345504+723104008Lelio R Paula09/2011
28532^345498-20037104006Enzo Doria06/2013
285418^82854-37104005Lelio R Paula01/2017
28552^345486-109065104002Enzo Doria04/2014
28562^345487-1851507104002Enzo Doria08/2015
28572^345476+777103999Lelio R Paula09/2011
2858(5*2^345321-1)/3103953Lelio R Paula03/2014
2859(2^345267-9)/539049127103927Lelio R Paula12/2013
2860(78557*2^345163+1)/78589103905Lelio R Paula07/2014
28612^345106-112181103888Enzo Doria06/2014
28622^345079+99103880Lelio R Paula09/2011
286311^99736-1500103865Enzo Doria12/2012
28642^344842-20157103808Enzo Doria06/2013
2865(47*2^344822+1)/1071103801Lelio R Paula05/2015
28662^344802-20765103796Enzo Doria06/2013
28672^344794-3821103794Yves Minet05/2011
28682^344782-109103103790Enzo Doria04/2014
28693^217521-112292103784Enzo Doria06/2014
28702^344759-3505103783Lelio R Paula11/2016
28712^344735-147103776Lelio R Paula09/2011
2872L(496533)-p(496533)103770Robert Price02/2018
28732*10^103749-69103750Robert Price03/2018
2874(55459*2^344617+1)/3103745Lelio R Paula07/2014
28752^344607-108891103738Enzo Doria03/2014
28762^344541-19561103718Enzo Doria05/2013
2877(1017*2^344529-1)/569103714Lelio R Paula05/2015
2878(4*10^103703-1)/3103704Serge Batalov08/2009
28792^344444-455103688Yves Minet03/2012
2880(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
28812^344317-109933103650Enzo Doria04/2014
28822^344309-1852033103648Enzo Doria08/2015
28832^344213-21253103619Enzo Doria06/2013
28842^344196-465103614Lelio R Paula11/2016
28852^344187-20001103611Enzo Doria06/2013
2886(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
288720^79621-19^79621103590Jean-Louis Charton03/2011
2888Phi(155391,10)/1243129103586Maksym Voznyy09/2015
28892^344085-20365103580Enzo Doria06/2013
28905^148169+54103566Lelio R Paula11/2016
28912^344017-108795103560Enzo Doria03/2014
28922^343971-5077103546Lelio R Paula09/2011
28932^343899+141103524Lelio R Paula08/2011
28946^133029-67103517Lelio R Paula11/2016
2895(17*2^343877+1)/13625103515Lelio R Paula12/2013
2896(136*10^103474-1)/9103476Serge Batalov12/2014
28975^148014-24103458Lelio R Paula11/2016
28982^343604+9931103436Yves Minet01/2011
28992^343601-21189103435Enzo Doria06/2013
29002^343508-115229103407Enzo Doria06/2015
2901(509203*2^343491-1)/16147103403Lelio R Paula05/2015
29023^216685-113056103386Enzo Doria07/2014
290344^62903-43^62903103379Jean-Louis Charton08/2012
290411^99262-20103371Lelio R Paula12/2016
2905(509203*2^343357-1)/5103366Lelio R Paula05/2015
29062^343356-2791889103361Enzo Doria03/2016
2907Phi(104989,10)/2939693103350Maksym Voznyy09/2015
29082^343182-171103309Lelio R Paula08/2011
2909(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
29102^343079-1835611103278Enzo Doria05/2015
29112^343063-1147103273Yves Minet06/2013
29129*6^132689+7103254Lelio R Paula11/2014
29132^342979-18085103247Enzo Doria05/2013
29142^342966-16995103244Lelio R Paula11/2016
29155^147650+16103203Lelio R Paula11/2016
2916gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
29172^342817+2707067103199Enzo Doria03/2016
291843^63177-42103198Theodore Burton02/2007
29192^342805-21025103195Enzo Doria06/2013
29202^342714+12285103168Lelio R Paula11/2016
292118^82178-4481103156Enzo Doria03/2013
29222^342665-17349103153Enzo Doria05/2013
29232^342612+175103137Lelio R Paula08/2011
29245*2^342585-3103130Lelio R Paula09/2014
29252^342503-19209103104Enzo Doria05/2013
29262^342476+51103096Lelio R Paula08/2011
29272^342460-18885103091Enzo Doria05/2013
29287^121968+82103075Lelio R Paula10/2016
29292^342392-108863103071Enzo Doria03/2014
29303^216014+28103065Lelio R Paula11/2016
29312^342353-108879103059Enzo Doria03/2014
293210^103055+276081103056Patrick De Geest12/2016
293310^103055-53103055Lelio R Paula11/2016
29347^121933+4103046Lelio R Paula11/2014
293519^80560-68103017Lelio R Paula10/2016
29362^342209+76607103016Enzo Doria05/2016
2938328^40945+40945^328103013Norbert Schneider12/2014
293712^95454-91103013Lelio R Paula10/2016
293965^56809-64^56809102990Robert Price08/2013
29405^147338-6102985Lelio R Paula11/2014
29412^342084-112739102978Enzo Doria06/2014
29429*6^132330+7102974Lelio R Paula11/2014
29432^342034-16737102963Enzo Doria05/2013
2944(9787*2^342011-1)/25102959Lelio R Paula05/2015
2945(3^215802-5)/124343756102956Lelio R Paula12/2013
29462^341991-17421102950Enzo Doria05/2013
29472^341969-112225102943Enzo Doria06/2014
2948(9787*2^341864-1)/3102915Lelio R Paula05/2015
29492^341859+1869413102910Enzo Doria05/2016
295010^102909+61102910Lelio R Paula11/2016
295110^102909-67049102909Patrick De Geest12/2016
29522^341659+1836773102850Enzo Doria03/2016
29532^341608-110639102835Enzo Doria05/2014
295410^102824+49102825Lelio R Paula11/2016
295510^102824-168011102824Patrick De Geest12/2016
295611^98708-8102794Lelio R Paula10/2016
29572^341466+4429102792Lelio R Paula09/2011
29582^341460-107102790Lelio R Paula08/2011
2959(2^341388+47)/21014943102761Lelio R Paula12/2013
29602^341355+21102759Lelio R Paula08/2011
29612^341246+40755102726Lelio R Paula11/2016
2962(2^341256-5)/991699102723Lelio R Paula12/2013
29637^121547+78102720Lelio R Paula10/2016
29642^341223-461197102719Enzo Doria06/2015
29652^341190-20577102709Enzo Doria06/2013
2966(27*2^341212+1)/84674449102709Lelio R Paula12/2013
29676^131976-65102698Lelio R Paula10/2016
29682^341134+2533102692Henri Lifchitz09/2005
296913^92184-54102688Lelio R Paula10/2016
29702^341116-20873102687Enzo Doria06/2013
29712^341094-19953102680Enzo Doria06/2013
29722^341053+129102668Lelio R Paula08/2011
2973(31*2^341006-1)/3102655Lelio R Paula03/2014
29747^121471+94102655Lelio R Paula10/2016
29762^341004-173102653Lelio R Paula08/2011
297520^78901+3102653Lelio R Paula10/2016
29775^146853-52102646Lelio R Paula10/2016
29782^340969-216931102642Enzo Doria05/2014
29792^340952+1870021102637Enzo Doria05/2016
29805*2^340940-3102634Lelio R Paula08/2014
2981(6^131891+1)/7102631Paul Bourdelais01/2010
2982(4*10^102612+83)/3102613Robert Price02/2018
298375^54717+74102598Norbert Schneider01/2015
29842^340806-20393102593Enzo Doria06/2013
2985(2^340790+5)/138267102583Lelio R Paula12/2013
29866^131821+77102577Lelio R Paula10/2016
29872^340688-29102558Henri Lifchitz05/2005
29882^340685-109101102557Enzo Doria04/2014
298965^56567-64102552Norbert Schneider11/2014
29902^340547-108897102515Enzo Doria03/2014
29917^121268+82102484Lelio R Paula10/2016
2992(6883*2^340443-1)/162401102483Lelio R Paula05/2015
29932^340434-5955102481Lelio R Paula11/2016
2994(2^340381+47)/7102465Lelio R Paula12/2013
2995111^50095+110102461Norbert Schneider04/2017
29962^340291-20301102438Enzo Doria06/2013
299712^94915+89102431Lelio R Paula10/2016
29982^340208-20373102413Enzo Doria06/2013
29996^131598-17273102404Enzo Doria02/2013
30002^340115-21181102385Enzo Doria06/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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