PRP Records

Probable Primes Top 10000

(291517 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 (> 50000) Who ? When ?
1(10^8177207-1)/98177207Ryan Propper + Sergey Batalov05/2021
2(10^5794777-1)/95794777Ryan Propper + Sergey Batalov04/2021
3(2^15135397+1)/34556209Ryan Propper06/2021
42^13380298-274027872Jeff Gilchrist /Diepeveen-Reix-Underwood-Gilchrist03/2021
5(2^13372531+1)/34025533Ryan Propper09/2013
6(2^13347311+1)/34017941Ryan Propper09/2013
7(2^12720787-1)/1119429257/175573124547437977/84809998784211069913829294Anonymous10/2022
8(2^12503723-2^6251862+1)/53763995Ryan Propper + Sergey Batalov07/2020
9(2^10443557-1)/372893259948073143811GIMPS-fre_games07/2020
102^9092392+402912737083Engracio Esmenda / Five or Bust02/2011
11(17^1990523-1)/162449236Paul Bourdelais08/2020
12(35963^524288+1)/22388581Ryan Propper08/2022
13(11^2264611+1)/122358349Paul Bourdelais07/2021
14(5^3300593-1)/42307015Anonymous02/2022
15(2^7313983-1)/3054920802761932201714Oliver Kruse03/2018
16(2^7080247-1)/156822217506727/11283326312536321/96329405483303395932131318Gord Palameta10/2017
17(11^1868983-1)/101946345Paul Bourdelais06/2021
18(3^3598867-1)/21717096Ryan Propper12/2021
19(13^1503503-1)/121674817Paul Bourdelais04/2020
20(10^1600787+1)/111600786Paul Bourdelais05/2020
21(18^1270141-1)/171594372Paul Bourdelais12/2021
22(14^1385203+1)/151587619Paul Bourdelais02/2022
23(2^5243339-2^2621670+1)/51578402Ryan Propper + Sergey Batalov06/2020
24(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
252^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
26(2^4834891-1)/1701881633/706596885755771455425Gord Palameta01/2017
27(187503^262144+1)/21382288Ryan Propper08/2022
282^4583176+21311379674Ben Maloney / Five or Bust09/2009
29F(6530879)1364873Ryan Propper08/2022
30(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
31(13^1199467+1)/141336138Paul Bourdelais12/2015
32(5^1888279-1)/41319850Paul Bourdelais04/2018
33(5^1856147+1)/61297391Paul Bourdelais02/2019
34(3^2704981-1)/21290604Ryan Propper12/2021
35(20^984349-1)/191280667Paul Bourdelais09/2021
36(2^4194304+1026473)/31262611Tony Prest / Never Odd Or Even07/2017
37(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
38(14^1091401+1)/151250885Paul Bourdelais03/2014
39(16^1025393+1)/171234695Paul Bourdelais08/2014
40(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
41(3^2533963+1)/41209008Paul Bourdelais03/2020
42L(5466311)1142392Ryan Propper08/2022
432^3690839-18684071111054Enzo Doria03/2021
442^3678448+3845411107324Enzo Doria03/2022
452^3668660+18888011104377Enzo Doria03/2020
46(106*23^800873-7)/111090573Curtis Bright05/2015
47(7^1264699-1)/61068794Paul Bourdelais01/2014
48(6^1365019-1)/51062191Paul Bourdelais12/2019
49(3^2215303-1)/21056968Paul Bourdelais02/2019
5010^1043372+71043373Alfred Reich12/2021
51(2^3464473-1)/6048745082991771042896Anand Nair10/2014
52(6^1313371+1)/71022001Paul Bourdelais01/2019
53(2^3352132+9)/51009092Tony Prest / Never Odd Or Even06/2018
54(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/674729942211009003Tony Prest / Never Odd Or Even08/2019
55(2^3351556+159)/5/7/7/2927/14552647/117615601/7068740758371008886Tony Prest / Never Odd Or Even08/2019
56(2^3351346+113)/3/548533/39539021/946508381271008831Tony Prest / Never Odd Or Even11/2022
57(2^3350899+115)/3/3/11/4091008717Tony Prest / Never Odd Or Even04/2020
58(2^3350068+183)/953/157612311008461Tony Prest / Never Odd Or Even03/2020
59(2^3349565+57)/23/263/778931008311Tony Prest / Never Odd Or Even03/2020
60(2^3349080+137)/3/79/80604190991008162Tony Prest / Never Odd Or Even07/2020
61(2^3349027+183)/23/1277/11638321/50448485271008137Tony Prest / Never Odd Or Even09/2022
62(2^3348456+23)/3/411007984Tony Prest / Never Odd Or Even01/2019
63(2^3348338+213)/71007950Tony Prest / Never Odd Or Even10/2018
64(2^3348184+123)/12491/3229442631007892Tony Prest / Never Odd Or Even01/2021
65(2^3348131+207)/5/11/41/43/12661193081/868684167491007862Tony Prest / Never Odd Or Even05/2021
66(2^3348111+245)/9721/215412555797/198704945240871007854Tony Prest / Never Odd Or Even05/2021
67(2^3347690+143)/3/7/167/5858771007746Tony Prest / Never Odd Or Even06/2020
68(2^3347613+103)/3/5/1948091007726Tony Prest / Never Odd Or Even02/2020
69(2^3347274+143)/3/3/3/234786457/34840035575691007608Tony Prest / Never Odd Or Even07/2022
70(2^3346590+185)/3/31/83/2201765933/3262109845431007400Tony Prest / Never Odd Or Even04/2021
71(2^3346468+257)/3/7/13/71/108471007379Tony Prest / Never Odd Or Even05/2020
72L(4819961)1007313Ryan Propper07/2022
73(2^3345946+187)/7/31229571007223Tony Prest / Never Odd Or Even03/2019
742^3345603+631007127Tony Prest / Never Odd Or Even05/2018
75(2^3345474+255)/19/29/25571007082Tony Prest / Never Odd Or Even12/2019
76(2^3345364+43)/53/79/109/2389/10889/168383091007035Tony Prest / Never Odd Or Even07/2022
77(2^3345080+247)/31/39671006965Tony Prest / Never Odd Or Even03/2019
78(2^3343888+209)/3/3/5/31/1791006606Tony Prest / Never Odd Or Even11/2019
79(2^3343774+115)/122391006573Tony Prest / Never Odd Or Even10/2018
80(2^3343633+105)/1371006532Tony Prest / Never Odd Or Even10/2018
81(2^3343714+149)/3/11/17/6047/23869/3993469/1713889507211006530Tony Prest / Never Odd Or Even01/2021
82(2^3343629+183)/5/35107/2154259/282128297091006511Tony Prest / Never Odd Or Even05/2022
83(2^3343142+13)/587/212195573363/37759700667191006360Tony Prest / Never Odd Or Even05/2018
84(2^3342880+215)/3/7/157/239/8211006299Tony Prest / Never Odd Or Even04/2020
85(2^3342588+95)/3/619/13174671553/227610668471006196Tony Prest / Never Odd Or Even08/2018
86(2^3322799+505)/31000262Stefano Morozzi08/2022
872^3322077+6591000045Stefano Morozzi04/2022
88211185^54364+54364^2111851000027Gabor Levai05/2022
9210^999999+5934991000000Peter Kaiser02/2013
8910^999999+308267*10^292000+11000000Sergey Batalov09/2021
90138159533888769035882147()973433052122012098003208^4096+11000000Anonymous11/2021
91138159533888769035882147()973433052122012098115876^4096+11000000Anonymous11/2021
9510^999999-172473999999Patrick De Geest12/2016
9310^999999-1087604*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
9410^999999-1022306*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
96(7^1178033+1)/8995553Paul Bourdelais01/2019
9710^995256+7995257Alfred Reich11/2021
98F(4740217)990647Ryan Propper07/2022
992^3223639+74333970413Enzo Doria10/2021
1002^3118435+73793938743Enzo Doria01/2021
1012^3037438+1885789914360Enzo Doria05/2019
1022^3032354+74209912830Enzo Doria01/2020
1032^3018556+31908676Robert Price09/2019
104(3^1896463+1)/4904843Paul Bourdelais01/2020
105Tau(181^72558)900969Nik Lygeros / Olivier Rozier / LR team07/2018
1062^2976221+2041857895932Makoto Morimoto09/2014
107(35^568453-1)/34877729Paul Bourdelais10/2021
108L(4161629)869730Ryan Propper07/2022
109(2^2860553+1)/(3*1528891204123*11630352659013691)861084Gord Palameta03/2019
1102^2843446+1885789855963Enzo Doria05/2019
1113^1753088+2836436Paul Bourdelais03/2022
112(12^769543-1)/11830476Paul Bourdelais12/2014
1132^2740174+1884385824875Enzo Doria01/2019
114Tau(229^63498)824146Nik Lygeros / Olivier Rozier / LR team07/2020
115(9^860029+1)/10820676Paul Bourdelais09/2020
1162^2723045+60227819719Enzo Doria01/2020
1172^2711746+74179816317Enzo Doria11/2019
118(2^2687383+1)/(3*440088720954577)808968Gord Palameta03/2019
119(31^535571-1)/30798729Alexander Zhirkov08/2019
120(64*10^779465-1)/81779465Serge Batalov09/2014
121(64*10^762811-1)/9762812Serge Batalov09/2014
1222^2515946+60529757376Enzo Doria10/2018
123(15^639833-1)/14752501Paul Bourdelais04/2019
1242^2442546+74209735280Enzo Doria03/2020
125(10^718580+269)/9718580Serge Batalov12/2014
126(99^357779+1)/100713995Paul Bourdelais02/2022
127(81^370421+1)/82706942Paul Bourdelais12/2021
128(2^2327417-1)/23915387348002001700606Anand Nair08/2014
129F(3340367)698096Henri Lifchitz03/2018
130(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
1312^2291342+73519689763Enzo Doria12/2018
132(10^685224+89)/9685224Serge Batalov12/2014
133F(3244369)678033Henri Lifchitz09/2017
1342^2249255+28433677094Ben Maloney / Five or Bust01/2009
135(10^675470+269)/9675470Serge Batalov12/2014
136Tau(151^56086)672156Nik Lygeros / Olivier Rozier / LR team10/2017
137(9^703393+1)/10671207Paul Bourdelais08/2015
138(121^320483+1)/122667496Paul Bourdelais08/2019
1392^2213586+71389666356Enzo Doria04/2018
1402^2205444+3663905Paul Bourdelais08/2020
1412^2191232+105659627Stefano Morozzi10/2021
1422^2187054+1886719658369Enzo Doria11/2018
143(6^840316-11)/5653893Paul Bourdelais06/2020
144(15^551927+1)/16649116Paul Bourdelais07/2013
1452^2153756+72181648346Enzo Doria04/2018
146(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
147Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
1482^2119239+684443637955Enzo Doria11/2018
1492^2117699+89637491Stefano Morozzi10/2021
1502^2107382+105634385Stefano Morozzi10/2021
151(51*21^479149-1243)/4633542Curtis Bright11/2015
1522^2099459+71663632001Enzo Doria07/2018
153Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
1542^2097791+60563631499Enzo Doria04/2018
1552^2086750-3628175Paul Bourdelais05/2020
1562^2083766+73519627277Enzo Doria01/2019
157(20^472709-1)/19615008Paul Bourdelais01/2015
158PIPrime(613373)613373Adrian Bondrescu05/2016
15911^586020-2610277Paul Bourdelais11/2021
160(19^476929+1)/20609874Paul Bourdelais03/2015
1612^2019811+1867211608024Enzo Doria04/2018
162F(2904353)606974Henri Lifchitz07/2014
1632^2014720+71893606492Enzo Doria04/2018
164L(2894561)604928Ryan Propper06/2022
165(18^481147+1)/19603970Paul Bourdelais07/2011
166200^262144+119^262144603202Kellen Shenton08/2022
167(15^505117-1)/14594063Paul Bourdelais01/2015
168(152^270217-1)/(152-1)589570Michael Stocker06/2015
169Phi(177147,94259)587458Anonymous09/2022
1702^1950002+1867369587010Enzo Doria02/2018
1712^1940812+3584243Paul Bourdelais06/2020
1722^1923104+153578912Stefano Morozzi07/2021
173(3^1205459+1)/4575150Paul Bourdelais08/2015
1742^1882800+384541566780Enzo Doria12/2017
175(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
1762^1882474+71389566682Enzo Doria04/2018
177(6^727496-11)/5566102Paul Bourdelais08/2019
1782^1875552+3564598Paul Bourdelais04/2020
1793^1180181-2563090Jorge Coveiro05/2020
1802^1852265+1890425557588Enzo Doria11/2017
1815^797390-2557352Paul Bourdelais03/2021
1828^615997-7^615997556301Jean-Louis Charton07/2009
183Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
184((((((((((1361^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840)^3+1623568555154Serge Batalov08/2013
185(42^337081-1)/41547165Paul Bourdelais09/2021
186(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
18710^538640-3538640Paul Bourdelais01/2021
1882^1787167+71963537991Enzo Doria12/2018
189(12^495953+1)/13535223Paul Bourdelais11/2018
1902^1773644+72511533921Enzo Doria10/2018
191(92^271639-1)/91533440Paul Bourdelais02/2022
192(11559^131072+1)/2532535Serge Batalov04/2018
193(85^275881-1)/84532289Paul Bourdelais02/2022
1942^1762004-3530417Paul Bourdelais04/2020
195(73^280697+1)/74523028Paul Bourdelais02/2022
196(21^394579+1)/22521719Paul Bourdelais10/2018
1972^1730246+384439520856Enzo Doria09/2017
198(55^299087+1)/56520519Paul Bourdelais02/2022
199(18^414269-1)/17520020Paul Bourdelais12/2014
20020^396120-3515365Paul Bourdelais01/2021
201(62^286483+1)/63513488Paul Bourdelais02/2022
202(20^393257+1)/21511638Paul Bourdelais12/2014
20310^509546+3509547Paul Bourdelais01/2021
204(72^273149-1)/71507327Paul Bourdelais02/2022
205107890^49423+49423^107890506429Miklos Levai02/2022
206(14^441697-1)/13506241Paul Bourdelais12/2014
2073^1059503-2^1059503505512Mike Oakes04/2012
208101542^92885+92885^101542504465Gabor Levai04/2022
209105098^61113+61113^105098503014Miklos Levai09/2022
2102^1670703+60293502932Enzo Doria11/2017
211(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
212101311^90816+90816^101311502317Gabor Levai12/2021
213101643^87368+87368^101643502254Gabor Levai11/2022
214101863^84922+84922^101863502085Gabor Levai10/2022
215100207^99856+99856^100207500973Gabor Levai11/2021
216101839^83028+83028^101839500969Gabor Levai11/2022
217100263^98600+98600^100263500702Gabor Levai09/2021
218101761^82168+82168^101761500126Gabor Levai03/2022
2192^1661176+336631500064Tony Prest / Never Odd Or Even09/2019
220101070^88579+88579^101070500027Gabor Levai01/2022
221(85^259159-1)/84500025Paul Bourdelais11/2021
2222^1660973+368139500003Tony Prest / Never Odd Or Even08/2020
2232^1660964-382425500000Tony Prest / Never Odd Or Even05/2020
224(87^257689-1)/86499791Paul Bourdelais01/2021
225(64*10^499210+53)/9499211Serge Batalov03/2015
226Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
22729^339887-28^339887497051Jean-Louis Charton05/2019
228(2^1629469-1)/644908484660139264379223490496Gord Palameta11/2017
22910^487291+7487292Alfred Reich06/2021
2302^1617579+1889543486940Enzo Doria09/2017
231L(2316773)484177Serge Batalov06/2017
232(57^275669-1)/56484039Paul Bourdelais04/2021
23310^480684-3480684Paul Bourdelais01/2021
2342^1595483+184133480289Enzo Doria07/2017
2352^1594947+3480127Paul Bourdelais07/2019
236(94^241993-1)/93477482Paul Bourdelais09/2020
2372^1585195+1888373477192Enzo Doria08/2017
238(33^313553+1)/34476134Paul Bourdelais02/2021
2393^994536+16474515Robert Price10/2020
2402^1575391+71483474240Enzo Doria04/2018
241(2^1572882+5)/3473485Serge Batalov08/2015
242(6^608099-1)/5473193Paul Bourdelais05/2010
2433^989124+16471933Robert Price10/2020
2442^1567006+1888099471716Enzo Doria05/2017
2452^1563067+1889813470531Enzo Doria08/2017
2462^1549797+60197466536Enzo Doria02/2018
2472^1549030+1887619466305Enzo Doria05/2017
248416^177481-415^177481464840Jean-Louis Charton12/2016
249(78^245183-1)/77463908Paul Bourdelais02/2021
2502^1522569+71657458339Enzo Doria04/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 28 2022 11:49 (Time in France)

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