PRP Records

Probable Primes Top 10000

(280389 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 ?
12^13380298-274027872Jeff Gilchrist /Diepeveen-Reix-Underwood-Gilchrist03/2021
2(2^13372531+1)/34025533Ryan Propper09/2013
3(2^13347311+1)/34017941Ryan Propper09/2013
4(2^12503723-2^6251862+1)/53763995Ryan Propper + Sergey Batalov07/2020
5(2^10443557-1)/372893259948073143811GIMPS-fre_games07/2020
62^9092392+402912737083Engracio Esmenda / Five or Bust02/2011
7(17^1990523-1)/162449236Paul Bourdelais08/2020
8(2^7313983-1)/3054920802761932201714Oliver Kruse03/2018
9(2^7080247-1)/156822217506727/11283326312536321/96329405483303395932131318Gord Palameta10/2017
10(13^1503503-1)/121674817Paul Bourdelais04/2020
11(10^1600787+1)/111600786Paul Bourdelais05/2020
12(2^5243339-2^2621670+1)/51578402Ryan Propper + Sergey Batalov06/2020
13(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
142^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
15(2^4834891-1)/1701881633/706596885755771455425Gord Palameta01/2017
162^4583176+21311379674Ben Maloney / Five or Bust09/2009
17(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
18(13^1199467+1)/141336138Paul Bourdelais12/2015
19(5^1888279-1)/41319850Paul Bourdelais04/2018
20(5^1856147+1)/61297391Paul Bourdelais02/2019
21(2^4194304+1026473)/31262611Tony Prest / Never Odd Or Even07/2017
22(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
23(14^1091401+1)/151250885Paul Bourdelais03/2014
24(16^1025393+1)/171234695Paul Bourdelais08/2014
25(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
26(3^2533963+1)/41209008Paul Bourdelais03/2020
272^3690839-18684071111054Enzo Doria03/2021
282^3668660+18888011104377Enzo Doria03/2020
29(106*23^800873-7)/111090573Curtis Bright05/2015
30(7^1264699-1)/61068794Paul Bourdelais01/2014
31(6^1365019-1)/51062191Paul Bourdelais12/2019
32(3^2215303-1)/21056968Paul Bourdelais02/2019
33(2^3464473-1)/6048745082991771042896Anand Nair10/2014
34(6^1313371+1)/71022001Paul Bourdelais01/2019
35(2^3352132+9)/51009092Tony Prest / Never Odd Or Even06/2018
36(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/674729942211009003Tony Prest / Never Odd Or Even08/2019
37(2^3351556+159)/5/7/7/2927/14552647/117615601/7068740758371008886Tony Prest / Never Odd Or Even08/2019
38(2^3350899+115)/3/3/11/4091008717Tony Prest / Never Odd Or Even04/2020
39(2^3350068+183)/953/157612311008461Tony Prest / Never Odd Or Even03/2020
40(2^3349565+57)/23/263/778931008311Tony Prest / Never Odd Or Even03/2020
41(2^3349080+137)/3/79/80604190991008162Tony Prest / Never Odd Or Even07/2020
42(2^3348456+23)/3/411007984Tony Prest / Never Odd Or Even01/2019
43(2^3348338+213)/71007950Tony Prest / Never Odd Or Even10/2018
44(2^3348184+123)/12491/3229442631007892Tony Prest / Never Odd Or Even01/2021
45(2^3347690+143)/3/7/167/5858771007746Tony Prest / Never Odd Or Even06/2020
46(2^3347613+103)/3/5/1948091007726Tony Prest / Never Odd Or Even02/2020
47(2^3346590+185)/3/31/83/2201765933/3262109845431007400Tony Prest / Never Odd Or Even04/2021
48(2^3346468+257)/3/7/13/71/108471007379Tony Prest / Never Odd Or Even05/2020
49(2^3345946+187)/7/31229571007223Tony Prest / Never Odd Or Even03/2019
502^3345603+631007127Tony Prest / Never Odd Or Even05/2018
51(2^3345474+255)/19/29/25571007082Tony Prest / Never Odd Or Even12/2019
52(2^3345080+247)/31/39671006965Tony Prest / Never Odd Or Even03/2019
53(2^3343888+209)/3/3/5/31/1791006606Tony Prest / Never Odd Or Even11/2019
54(2^3343774+115)/122391006573Tony Prest / Never Odd Or Even10/2018
55(2^3343633+105)/1371006532Tony Prest / Never Odd Or Even10/2018
56(2^3343714+149)/3/11/17/6047/23869/3993469/1713889507211006530Tony Prest / Never Odd Or Even01/2021
57(2^3343142+13)/587/212195573363/37759700667191006360Tony Prest / Never Odd Or Even05/2018
58(2^3342880+215)/3/7/157/239/8211006299Tony Prest / Never Odd Or Even04/2020
59(2^3342588+95)/3/619/13174671553/227610668471006196Tony Prest / Never Odd Or Even08/2018
6010^999999+5934991000000Peter Kaiser02/2013
6110^999999-172473999999Patrick De Geest12/2016
62(7^1178033+1)/8995553Paul Bourdelais01/2019
632^3118435+73793938743Enzo Doria01/2021
642^3037438+1885789914360Enzo Doria05/2019
652^3032354+74209912830Enzo Doria01/2020
662^3018556+31908676Robert Price09/2019
67(3^1896463+1)/4904843Paul Bourdelais01/2020
68Tau(181^72558)900969Nik Lygeros / Olivier Rozier / LR team07/2018
692^2976221+2041857895932Makoto Morimoto09/2014
70(2^2860553+1)/(3*1528891204123*11630352659013691)861084Gord Palameta03/2019
712^2843446+1885789855963Enzo Doria05/2019
72(12^769543-1)/11830476Paul Bourdelais12/2014
732^2740174+1884385824875Enzo Doria01/2019
74Tau(229^63498)824146Nik Lygeros / Olivier Rozier / LR team07/2020
75(9^860029+1)/10820676Paul Bourdelais09/2020
762^2723045+60227819719Enzo Doria01/2020
772^2711746+74179816317Enzo Doria11/2019
78(2^2687383+1)/(3*440088720954577)808968Gord Palameta03/2019
79(31^535571-1)/30798729Alexander Zhirkov08/2019
80(64*10^779465-1)/81779465Serge Batalov09/2014
81(64*10^762811-1)/9762812Serge Batalov09/2014
822^2515946+60529757376Enzo Doria10/2018
83(15^639833-1)/14752501Paul Bourdelais04/2019
842^2442546+74209735280Enzo Doria03/2020
85(10^718580+269)/9718580Serge Batalov12/2014
86(2^2327417-1)/23915387348002001700606Anand Nair08/2014
87F(3340367)698096Henri Lifchitz03/2018
88(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
892^2291342+73519689763Enzo Doria12/2018
90(10^685224+89)/9685224Serge Batalov12/2014
91F(3244369)678033Henri Lifchitz09/2017
922^2249255+28433677094Ben Maloney / Five or Bust01/2009
93(10^675470+269)/9675470Serge Batalov12/2014
94Tau(151^56086)672156Nik Lygeros / Olivier Rozier / LR team10/2017
95(9^703393+1)/10671207Paul Bourdelais08/2015
96(121^320483+1)/122667496Paul Bourdelais08/2019
972^2213586+71389666356Enzo Doria04/2018
982^2205444+3663905Paul Bourdelais08/2020
992^2187054+1886719658369Enzo Doria11/2018
100(6^840316-11)/5653893Paul Bourdelais06/2020
101(15^551927+1)/16649116Paul Bourdelais07/2013
1022^2153756+72181648346Enzo Doria04/2018
103(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
104Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
1052^2119239+684443637955Enzo Doria11/2018
106(51*21^479149-1243)/4633542Curtis Bright11/2015
1072^2099459+71663632001Enzo Doria07/2018
108Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
1092^2097791+60563631499Enzo Doria04/2018
1102^2086750-3628175Paul Bourdelais05/2020
1112^2083766+73519627277Enzo Doria01/2019
112(20^472709-1)/19615008Paul Bourdelais01/2015
113PIPrime(613373)613373Adrian Bondrescu05/2016
114(19^476929+1)/20609874Paul Bourdelais03/2015
1152^2019811+1867211608024Enzo Doria04/2018
116F(2904353)606974Henri Lifchitz07/2014
1172^2014720+71893606492Enzo Doria04/2018
118(18^481147+1)/19603970Paul Bourdelais07/2011
119(15^505117-1)/14594063Paul Bourdelais01/2015
120(152^270217-1)/(152-1)589570Michael Stocker06/2015
1212^1950002+1867369587010Enzo Doria02/2018
1222^1940812+3584243Paul Bourdelais06/2020
123(3^1205459+1)/4575150Paul Bourdelais08/2015
1242^1882800+384541566780Enzo Doria12/2017
125(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
1262^1882474+71389566682Enzo Doria04/2018
127(6^727496-11)/5566102Paul Bourdelais08/2019
1282^1875552+3564598Paul Bourdelais04/2020
1293^1180181-2563090Jorge Coveiro05/2020
1302^1852265+1890425557588Enzo Doria11/2017
1315^797390-2557352Paul Bourdelais03/2021
1328^615997-7^615997556301Jean-Louis Charton07/2009
133Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
134((((((((((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
135(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
13610^538640-3538640Paul Bourdelais01/2021
1372^1787167+71963537991Enzo Doria12/2018
138(12^495953+1)/13535223Paul Bourdelais11/2018
1392^1773644+72511533921Enzo Doria10/2018
140(11559^131072+1)/2532535Serge Batalov04/2018
1412^1762004-3530417Paul Bourdelais04/2020
142(21^394579+1)/22521719Paul Bourdelais10/2018
1432^1730246+384439520856Enzo Doria09/2017
144(18^414269-1)/17520020Paul Bourdelais12/2014
14520^396120-3515365Paul Bourdelais01/2021
146(20^393257+1)/21511638Paul Bourdelais12/2014
14710^509546+3509547Paul Bourdelais01/2021
148(14^441697-1)/13506241Paul Bourdelais12/2014
1493^1059503-2^1059503505512Mike Oakes04/2012
1502^1670703+60293502932Enzo Doria11/2017
151(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
1522^1661176+336631500064Tony Prest / Never Odd Or Even09/2019
1532^1660973+368139500003Tony Prest / Never Odd Or Even08/2020
1542^1660964-382425500000Tony Prest / Never Odd Or Even05/2020
155(87^257689-1)/86499791Paul Bourdelais01/2021
156(64*10^499210+53)/9499211Serge Batalov03/2015
157Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
15829^339887-28^339887497051Jean-Louis Charton05/2019
159(2^1629469-1)/644908484660139264379223490496Gord Palameta11/2017
1602^1617579+1889543486940Enzo Doria09/2017
161L(2316773)484177Serge Batalov06/2017
16210^480684-3480684Paul Bourdelais01/2021
1632^1595483+184133480289Enzo Doria07/2017
1642^1594947+3480127Paul Bourdelais07/2019
165(94^241993-1)/93477482Paul Bourdelais09/2020
1662^1585195+1888373477192Enzo Doria08/2017
167(33^313553+1)/34476134Paul Bourdelais02/2021
1683^994536+16474515Robert Price10/2020
1692^1575391+71483474240Enzo Doria04/2018
170(2^1572882+5)/3473485Serge Batalov08/2015
171(6^608099-1)/5473193Paul Bourdelais05/2010
1723^989124+16471933Robert Price10/2020
1732^1567006+1888099471716Enzo Doria05/2017
1742^1563067+1889813470531Enzo Doria08/2017
1752^1549797+60197466536Enzo Doria02/2018
1762^1549030+1887619466305Enzo Doria05/2017
177416^177481-415^177481464840Jean-Louis Charton12/2016
178(78^245183-1)/77463908Paul Bourdelais02/2021
1792^1522569+71657458339Enzo Doria04/2018
1802^1518191+75353457022Ben Maloney / Five or Bust01/2009
1816^584279-5454658Paul Bourdelais02/2021
1822^1506029+1890167453360Enzo Doria02/2018
183(34^294277+1)/35450678Paul Bourdelais06/2018
1842^1495434+1890439450171Enzo Doria12/2017
1852^1493170+784129449489Enzo Doria08/2017
1862^1489873+1888277448497Enzo Doria06/2017
1872^1484671+1888463446931Enzo Doria06/2017
1882^1482867+1886783446388Enzo Doria04/2017
1892^1482148+284011446172Enzo Doria04/2017
1902^1479356+1888291445331Enzo Doria06/2017
19114^384558+3440753Paul Bourdelais01/2021
1922^1461244+784531439879Enzo Doria10/2017
193(80^228419+1)/81434701Paul Bourdelais02/2021
1942^1443089+60227434414Enzo Doria10/2017
195(21^328129-1)/20433858Paul Bourdelais06/2014
1962^1434400+3431798Paul Bourdelais06/2019
1972^1432308+1888801431168Enzo Doria10/2017
198(2^1430131+1)/(3*356468732537*36519993971459)430487Gord Palameta12/2018
1992^1425483+1886813429114Enzo Doria04/2017
200(63^238481+1)/64429107Paul Bourdelais12/2020
201(17^348259+1)/18428514Paul Bourdelais05/2014
202(10^427912+89)/9427912Serge Batalov12/2014
2032^1421089+1890167427791Enzo Doria09/2017
20420^326600+3424917Paul Bourdelais01/2021
205(10^424861-7)/3424861Leonid Durman01/2012
2062^1404213+184217422711Enzo Doria09/2017
2072^1401872+1884385422006Enzo Doria04/2017
2082^1401257+6077421821Enzo Doria09/2017
209138^196873-137^196873421285Jean-Louis Charton12/2009
2102^1398269+131595420921Makoto Morimoto10/2013
2112^1397071+684443420561Enzo Doria07/2017
212953^141023-952^141023420121Jean-Louis Charton10/2016
213(3^877843-1)/2418838Paul Bourdelais07/2010
2142^1386321+60299417325Enzo Doria02/2018
2152^1386320+184531417324Enzo Doria09/2017
2162^1382074+1883587416046Enzo Doria01/2017
2172^1379907+1885223415394Enzo Doria03/2017
2182^1375574+1886719414090Enzo Doria04/2017
2192^1373111+1884833413348Enzo Doria02/2017
2202^1368632+1889731412000Enzo Doria10/2017
221(89*10^411590+1)/9411591Serge Batalov09/2014
222F(1968721)411439Henri Lifchitz11/2009
2232^1366066+683749411227Enzo Doria02/2017
2242^1355790+1888939408134Enzo Doria07/2017
2252^1355635+1884203408087Enzo Doria01/2017
226(88^208739+1)/89405888Paul Bourdelais12/2020
227(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
2282^1347744-3405712Paul Bourdelais07/2019
22910^400000+1415223400001Patrick De Geest10/2020
23010^400000-339233400000Patrick De Geest10/2020
231Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
2322^1319770+1884949397291Enzo Doria06/2017
2332^1313062+1888849395272Enzo Doria08/2017
234(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
235(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
2362^1311618+783529394837Enzo Doria01/2017
2372^1308000+1883521393748Enzo Doria02/2017
238(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
239(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
240(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
241(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
242(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
243(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
2442^1303102+1866409392273Enzo Doria09/2017
2452^1302818+283429392188Enzo Doria01/2017
246(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
2472^1299181+1886867391093Enzo Doria04/2017
248(37^249341-1)/36391016Paul Bourdelais08/2020
2492^1298304+1882891390829Enzo Doria01/2017
250(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 11 2021 15:05 (Time in France)

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