PRP Records

Probable Primes Top 10000

(288515 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(2^12503723-2^6251862+1)/53763995Ryan Propper + Sergey Batalov07/2020
8(2^10443557-1)/372893259948073143811GIMPS-fre_games07/2020
92^9092392+402912737083Engracio Esmenda / Five or Bust02/2011
10(17^1990523-1)/162449236Paul Bourdelais08/2020
11(11^2264611+1)/122358349Paul Bourdelais07/2021
12(2^7313983-1)/3054920802761932201714Oliver Kruse03/2018
13(2^7080247-1)/156822217506727/11283326312536321/96329405483303395932131318Gord Palameta10/2017
14(11^1868983-1)/101946345Paul Bourdelais06/2021
15(13^1503503-1)/121674817Paul Bourdelais04/2020
16(10^1600787+1)/111600786Paul Bourdelais05/2020
17(2^5243339-2^2621670+1)/51578402Ryan Propper + Sergey Batalov06/2020
18(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
192^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
20(2^4834891-1)/1701881633/706596885755771455425Gord Palameta01/2017
212^4583176+21311379674Ben Maloney / Five or Bust09/2009
22(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
23(13^1199467+1)/141336138Paul Bourdelais12/2015
24(5^1888279-1)/41319850Paul Bourdelais04/2018
25(5^1856147+1)/61297391Paul Bourdelais02/2019
26(20^984349-1)/191280667Paul Bourdelais09/2021
27(2^4194304+1026473)/31262611Tony Prest / Never Odd Or Even07/2017
28(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
29(14^1091401+1)/151250885Paul Bourdelais03/2014
30(16^1025393+1)/171234695Paul Bourdelais08/2014
31(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
32(3^2533963+1)/41209008Paul Bourdelais03/2020
332^3690839-18684071111054Enzo Doria03/2021
342^3668660+18888011104377Enzo Doria03/2020
35(106*23^800873-7)/111090573Curtis Bright05/2015
36(7^1264699-1)/61068794Paul Bourdelais01/2014
37(6^1365019-1)/51062191Paul Bourdelais12/2019
38(3^2215303-1)/21056968Paul Bourdelais02/2019
39(2^3464473-1)/6048745082991771042896Anand Nair10/2014
40(6^1313371+1)/71022001Paul Bourdelais01/2019
41(2^3352132+9)/51009092Tony Prest / Never Odd Or Even06/2018
42(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/674729942211009003Tony Prest / Never Odd Or Even08/2019
43(2^3351556+159)/5/7/7/2927/14552647/117615601/7068740758371008886Tony Prest / Never Odd Or Even08/2019
44(2^3350899+115)/3/3/11/4091008717Tony Prest / Never Odd Or Even04/2020
45(2^3350068+183)/953/157612311008461Tony Prest / Never Odd Or Even03/2020
46(2^3349565+57)/23/263/778931008311Tony Prest / Never Odd Or Even03/2020
47(2^3349080+137)/3/79/80604190991008162Tony Prest / Never Odd Or Even07/2020
48(2^3348456+23)/3/411007984Tony Prest / Never Odd Or Even01/2019
49(2^3348338+213)/71007950Tony Prest / Never Odd Or Even10/2018
50(2^3348184+123)/12491/3229442631007892Tony Prest / Never Odd Or Even01/2021
51(2^3348131+207)/5/11/41/43/12661193081/868684167491007862Tony Prest / Never Odd Or Even05/2021
52(2^3348111+245)/9721/215412555797/198704945240871007854Tony Prest / Never Odd Or Even05/2021
53(2^3347690+143)/3/7/167/5858771007746Tony Prest / Never Odd Or Even06/2020
54(2^3347613+103)/3/5/1948091007726Tony Prest / Never Odd Or Even02/2020
55(2^3346590+185)/3/31/83/2201765933/3262109845431007400Tony Prest / Never Odd Or Even04/2021
56(2^3346468+257)/3/7/13/71/108471007379Tony Prest / Never Odd Or Even05/2020
57(2^3345946+187)/7/31229571007223Tony Prest / Never Odd Or Even03/2019
582^3345603+631007127Tony Prest / Never Odd Or Even05/2018
59(2^3345474+255)/19/29/25571007082Tony Prest / Never Odd Or Even12/2019
60(2^3345080+247)/31/39671006965Tony Prest / Never Odd Or Even03/2019
61(2^3343888+209)/3/3/5/31/1791006606Tony Prest / Never Odd Or Even11/2019
62(2^3343774+115)/122391006573Tony Prest / Never Odd Or Even10/2018
63(2^3343633+105)/1371006532Tony Prest / Never Odd Or Even10/2018
64(2^3343714+149)/3/11/17/6047/23869/3993469/1713889507211006530Tony Prest / Never Odd Or Even01/2021
65(2^3343142+13)/587/212195573363/37759700667191006360Tony Prest / Never Odd Or Even05/2018
66(2^3342880+215)/3/7/157/239/8211006299Tony Prest / Never Odd Or Even04/2020
67(2^3342588+95)/3/619/13174671553/227610668471006196Tony Prest / Never Odd Or Even08/2018
6810^999999+5934991000000Peter Kaiser02/2013
6910^999999+308267*10^292000+11000000Sergey Batalov09/2021
70138159533888769035882147()973433052122012098003208^4096+11000000Anonymous11/2021
71138159533888769035882147()973433052122012098115876^4096+11000000Anonymous11/2021
7410^999999-172473999999Patrick De Geest12/2016
7210^999999-1087604*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
7310^999999-1022306*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
75(7^1178033+1)/8995553Paul Bourdelais01/2019
7610^995256+7995257Alfred Reich11/2021
772^3223639+74333970413Enzo Doria10/2021
782^3118435+73793938743Enzo Doria01/2021
792^3037438+1885789914360Enzo Doria05/2019
802^3032354+74209912830Enzo Doria01/2020
812^3018556+31908676Robert Price09/2019
82(3^1896463+1)/4904843Paul Bourdelais01/2020
83Tau(181^72558)900969Nik Lygeros / Olivier Rozier / LR team07/2018
842^2976221+2041857895932Makoto Morimoto09/2014
85(35^568453-1)/34877729Paul Bourdelais10/2021
86(2^2860553+1)/(3*1528891204123*11630352659013691)861084Gord Palameta03/2019
872^2843446+1885789855963Enzo Doria05/2019
88(12^769543-1)/11830476Paul Bourdelais12/2014
892^2740174+1884385824875Enzo Doria01/2019
90Tau(229^63498)824146Nik Lygeros / Olivier Rozier / LR team07/2020
91(9^860029+1)/10820676Paul Bourdelais09/2020
922^2723045+60227819719Enzo Doria01/2020
932^2711746+74179816317Enzo Doria11/2019
94(2^2687383+1)/(3*440088720954577)808968Gord Palameta03/2019
95(31^535571-1)/30798729Alexander Zhirkov08/2019
96(64*10^779465-1)/81779465Serge Batalov09/2014
97(64*10^762811-1)/9762812Serge Batalov09/2014
982^2515946+60529757376Enzo Doria10/2018
99(15^639833-1)/14752501Paul Bourdelais04/2019
1002^2442546+74209735280Enzo Doria03/2020
101(10^718580+269)/9718580Serge Batalov12/2014
102(2^2327417-1)/23915387348002001700606Anand Nair08/2014
103F(3340367)698096Henri Lifchitz03/2018
104(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
1052^2291342+73519689763Enzo Doria12/2018
106(10^685224+89)/9685224Serge Batalov12/2014
107F(3244369)678033Henri Lifchitz09/2017
1082^2249255+28433677094Ben Maloney / Five or Bust01/2009
109(10^675470+269)/9675470Serge Batalov12/2014
110Tau(151^56086)672156Nik Lygeros / Olivier Rozier / LR team10/2017
111(9^703393+1)/10671207Paul Bourdelais08/2015
112(121^320483+1)/122667496Paul Bourdelais08/2019
1132^2213586+71389666356Enzo Doria04/2018
1142^2205444+3663905Paul Bourdelais08/2020
1152^2191232+105659627Stefano Morozzi10/2021
1162^2187054+1886719658369Enzo Doria11/2018
117(6^840316-11)/5653893Paul Bourdelais06/2020
118(15^551927+1)/16649116Paul Bourdelais07/2013
1192^2153756+72181648346Enzo Doria04/2018
120(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
121Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
1222^2119239+684443637955Enzo Doria11/2018
1232^2117699+89637491Stefano Morozzi10/2021
1242^2107382+105634385Stefano Morozzi10/2021
125(51*21^479149-1243)/4633542Curtis Bright11/2015
1262^2099459+71663632001Enzo Doria07/2018
127Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
1282^2097791+60563631499Enzo Doria04/2018
1292^2086750-3628175Paul Bourdelais05/2020
1302^2083766+73519627277Enzo Doria01/2019
131(20^472709-1)/19615008Paul Bourdelais01/2015
132PIPrime(613373)613373Adrian Bondrescu05/2016
13311^586020-2610277Paul Bourdelais11/2021
134(19^476929+1)/20609874Paul Bourdelais03/2015
1352^2019811+1867211608024Enzo Doria04/2018
136F(2904353)606974Henri Lifchitz07/2014
1372^2014720+71893606492Enzo Doria04/2018
138(18^481147+1)/19603970Paul Bourdelais07/2011
139(15^505117-1)/14594063Paul Bourdelais01/2015
140(152^270217-1)/(152-1)589570Michael Stocker06/2015
1412^1950002+1867369587010Enzo Doria02/2018
1422^1940812+3584243Paul Bourdelais06/2020
1432^1923104+153578912Stefano Morozzi07/2021
144(3^1205459+1)/4575150Paul Bourdelais08/2015
1452^1882800+384541566780Enzo Doria12/2017
146(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
1472^1882474+71389566682Enzo Doria04/2018
148(6^727496-11)/5566102Paul Bourdelais08/2019
1492^1875552+3564598Paul Bourdelais04/2020
1503^1180181-2563090Jorge Coveiro05/2020
1512^1852265+1890425557588Enzo Doria11/2017
1525^797390-2557352Paul Bourdelais03/2021
1538^615997-7^615997556301Jean-Louis Charton07/2009
154Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
155((((((((((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
156(42^337081-1)/41547165Paul Bourdelais09/2021
157(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
15810^538640-3538640Paul Bourdelais01/2021
1592^1787167+71963537991Enzo Doria12/2018
160(12^495953+1)/13535223Paul Bourdelais11/2018
1612^1773644+72511533921Enzo Doria10/2018
162(11559^131072+1)/2532535Serge Batalov04/2018
1632^1762004-3530417Paul Bourdelais04/2020
164(21^394579+1)/22521719Paul Bourdelais10/2018
1652^1730246+384439520856Enzo Doria09/2017
166(18^414269-1)/17520020Paul Bourdelais12/2014
16720^396120-3515365Paul Bourdelais01/2021
168(20^393257+1)/21511638Paul Bourdelais12/2014
16910^509546+3509547Paul Bourdelais01/2021
170(14^441697-1)/13506241Paul Bourdelais12/2014
1713^1059503-2^1059503505512Mike Oakes04/2012
1722^1670703+60293502932Enzo Doria11/2017
173(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
174100207^99856+99856^100207500973Gabor Levai11/2021
175100263^98600+98600^100263500702Gabor Levai09/2021
1762^1661176+336631500064Tony Prest / Never Odd Or Even09/2019
177(85^259159-1)/84500025Paul Bourdelais11/2021
1782^1660973+368139500003Tony Prest / Never Odd Or Even08/2020
1792^1660964-382425500000Tony Prest / Never Odd Or Even05/2020
180(87^257689-1)/86499791Paul Bourdelais01/2021
181(64*10^499210+53)/9499211Serge Batalov03/2015
182Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
18329^339887-28^339887497051Jean-Louis Charton05/2019
184(2^1629469-1)/644908484660139264379223490496Gord Palameta11/2017
18510^487291+7487292Alfred Reich06/2021
1862^1617579+1889543486940Enzo Doria09/2017
187L(2316773)484177Serge Batalov06/2017
188(57^275669-1)/56484039Paul Bourdelais04/2021
18910^480684-3480684Paul Bourdelais01/2021
1902^1595483+184133480289Enzo Doria07/2017
1912^1594947+3480127Paul Bourdelais07/2019
192(94^241993-1)/93477482Paul Bourdelais09/2020
1932^1585195+1888373477192Enzo Doria08/2017
194(33^313553+1)/34476134Paul Bourdelais02/2021
1953^994536+16474515Robert Price10/2020
1962^1575391+71483474240Enzo Doria04/2018
197(2^1572882+5)/3473485Serge Batalov08/2015
198(6^608099-1)/5473193Paul Bourdelais05/2010
1993^989124+16471933Robert Price10/2020
2002^1567006+1888099471716Enzo Doria05/2017
2012^1563067+1889813470531Enzo Doria08/2017
2022^1549797+60197466536Enzo Doria02/2018
2032^1549030+1887619466305Enzo Doria05/2017
204416^177481-415^177481464840Jean-Louis Charton12/2016
205(78^245183-1)/77463908Paul Bourdelais02/2021
2062^1522569+71657458339Enzo Doria04/2018
2072^1518191+75353457022Ben Maloney / Five or Bust01/2009
2086^584279-5454658Paul Bourdelais02/2021
209(52^264697-1)/51454220Paul Bourdelais10/2021
2102^1506029+1890167453360Enzo Doria02/2018
211(34^294277+1)/35450678Paul Bourdelais06/2018
2122^1495434+1890439450171Enzo Doria12/2017
2132^1493170+784129449489Enzo Doria08/2017
2142^1489873+1888277448497Enzo Doria06/2017
2152^1484671+1888463446931Enzo Doria06/2017
2162^1482867+1886783446388Enzo Doria04/2017
2172^1482148+284011446172Enzo Doria04/2017
2182^1479356+1888291445331Enzo Doria06/2017
21914^384558+3440753Paul Bourdelais01/2021
2202^1461244+784531439879Enzo Doria10/2017
221(67^239053+1)/68436527Paul Bourdelais09/2021
222(80^228419+1)/81434701Paul Bourdelais02/2021
2232^1443089+60227434414Enzo Doria10/2017
224(21^328129-1)/20433858Paul Bourdelais06/2014
225(35^280979+1)/36433850Paul Bourdelais09/2021
2262^1434400+3431798Paul Bourdelais06/2019
2272^1432308+1888801431168Enzo Doria10/2017
228(2^1430131+1)/(3*356468732537*36519993971459)430487Gord Palameta12/2018
2292^1425483+1886813429114Enzo Doria04/2017
230(63^238481+1)/64429107Paul Bourdelais12/2020
231(17^348259+1)/18428514Paul Bourdelais05/2014
232(10^427912+89)/9427912Serge Batalov12/2014
2332^1421089+1890167427791Enzo Doria09/2017
23420^326600+3424917Paul Bourdelais01/2021
235(10^424861-7)/3424861Leonid Durman01/2012
2362^1404213+184217422711Enzo Doria09/2017
2372^1401872+1884385422006Enzo Doria04/2017
2382^1401257+6077421821Enzo Doria09/2017
239138^196873-137^196873421285Jean-Louis Charton12/2009
2402^1398269+131595420921Makoto Morimoto10/2013
2412^1397071+684443420561Enzo Doria07/2017
242953^141023-952^141023420121Jean-Louis Charton10/2016
243(3^877843-1)/2418838Paul Bourdelais07/2010
2442^1386321+60299417325Enzo Doria02/2018
2452^1386320+184531417324Enzo Doria09/2017
2462^1382074+1883587416046Enzo Doria01/2017
2472^1379907+1885223415394Enzo Doria03/2017
2482^1375574+1886719414090Enzo Doria04/2017
2492^1373111+1884833413348Enzo Doria02/2017
2502^1368632+1889731412000Enzo Doria10/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 01 2021 22:29 (Time in France)

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