PRP Records

Probable Primes Top 10000

(253472 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(2^13372531+1)/34025533Ryan Propper09/2013
2(2^13347311+1)/34017941Ryan Propper09/2013
32^9092392+402912737083Engracio Esmenda / Five or Bust02/2011
4(2^7313983-1)/3054920802761932201714Oliver Kruse03/2018
5(2^7080247-1)/156822217506727/11283326312536321/96329405483303395932131318Gord Palameta10/2017
6(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
72^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
8(2^4834891-1)/1701881633/706596885755771455425Gord Palameta01/2017
92^4583176+21311379674Ben Maloney / Five or Bust09/2009
10(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
11(13^1199467+1)/141336138Paul Bourdelais12/2015
12(5^1888279-1)/41319850Paul Bourdelais04/2018
13(5^1856147+1)/61297391Paul Bourdelais02/2019
14(2^4194304+1026473)/31262611Tony Prest / Never Odd Or Even07/2017
15(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
16(14^1091401+1)/151250885Paul Bourdelais03/2014
17(16^1025393+1)/171234695Paul Bourdelais08/2014
18(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
19(106*23^800873-7)/111090573Curtis Bright05/2015
20(7^1264699-1)/61068794Paul Bourdelais01/2014
21(3^2215303-1)/21056968Paul Bourdelais02/2019
22(2^3464473-1)/6048745082991771042896Anand Nair10/2014
23(6^1313371+1)/71022001Paul Bourdelais01/2019
24(2^3352132+9)/51009092Tony Prest / Never Odd Or Even06/2018
25(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/674729942211009003Tony Prest / Never Odd Or Even08/2019
26(2^3351556+159)/5/7/7/2927/14552647/117615601/7068740758371008886Tony Prest / Never Odd Or Even08/2019
27(2^3348456+23)/3/411007984Tony Prest / Never Odd Or Even01/2019
28(2^3348338+213)/71007950Tony Prest / Never Odd Or Even10/2018
29(2^3345946+187)/7/31229571007223Tony Prest / Never Odd Or Even03/2019
302^3345603+631007127Tony Prest / Never Odd Or Even05/2018
31(2^3345080+247)/31/39671006965Tony Prest / Never Odd Or Even03/2019
32(2^3343774+115)/122391006573Tony Prest / Never Odd Or Even10/2018
33(2^3343633+105)/1371006532Tony Prest / Never Odd Or Even10/2018
34(2^3343142+13)/587/212195573363/37759700667191006360Tony Prest / Never Odd Or Even05/2018
35(2^3342588+95)/3/619/13174671553/227610668471006196Tony Prest / Never Odd Or Even08/2018
3610^999999+5934991000000Peter Kaiser02/2013
3710^999999-172473999999Patrick De Geest12/2016
38(7^1178033+1)/8995553Paul Bourdelais01/2019
392^3037438+1885789914360Enzo Doria05/2019
40Tau(181^72558)900969Nik Lygeros / Olivier Rozier / LR team07/2018
412^2976221+2041857895932Makoto Morimoto09/2014
42(2^2860553+1)/(3*1528891204123*11630352659013691)861084Gord Palameta03/2019
432^2843446+1885789855963Enzo Doria05/2019
44(12^769543-1)/11830476Paul Bourdelais12/2014
452^2740174+1884385824875Enzo Doria01/2019
46(2^2687383+1)/(3*440088720954577)808968Gord Palameta03/2019
47(64*10^779465-1)/81779465Serge Batalov09/2014
48(64*10^762811-1)/9762812Serge Batalov09/2014
492^2515946+60529757376Enzo Doria10/2018
50(15^639833-1)/14752501Paul Bourdelais04/2019
51(10^718580+269)/9718580Serge Batalov12/2014
52(2^2327417-1)/23915387348002001700606Anand Nair08/2014
53F(3340367)698096Henri Lifchitz03/2018
54(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
552^2291342+73519689763Enzo Doria12/2018
56(10^685224+89)/9685224Serge Batalov12/2014
57F(3244369)678033Henri Lifchitz09/2017
582^2249255+28433677094Ben Maloney / Five or Bust01/2009
59(10^675470+269)/9675470Serge Batalov12/2014
60Tau(151^56086)672156Nik Lygeros / Olivier Rozier / LR team10/2017
61(9^703393+1)/10671207Paul Bourdelais08/2015
62(121^320483+1)/122667496Paul Bourdelais08/2019
632^2213586+71389666356Enzo Doria04/2018
642^2187054+1886719658369Enzo Doria11/2018
65(15^551927+1)/16649116Paul Bourdelais07/2013
662^2153756+72181648346Enzo Doria04/2018
67(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
68Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
692^2119239+684443637955Enzo Doria11/2018
70(51*21^479149-1243)/4633542Curtis Bright11/2015
712^2099459+71663632001Enzo Doria07/2018
72Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
732^2097791+60563631499Enzo Doria04/2018
742^2083766+73519627277Enzo Doria01/2019
75(20^472709-1)/19615008Paul Bourdelais01/2015
76PIPrime(613373)613373Adrian Bondrescu05/2016
77(19^476929+1)/20609874Paul Bourdelais03/2015
782^2019811+1867211608024Enzo Doria04/2018
79F(2904353)606974Henri Lifchitz07/2014
802^2014720+71893606492Enzo Doria04/2018
81(18^481147+1)/19603970Paul Bourdelais07/2011
82(15^505117-1)/14594063Paul Bourdelais01/2015
83(152^270217-1)/(152-1)589570Michael Stocker06/2015
842^1950002+1867369587010Enzo Doria02/2018
85(3^1205459+1)/4575150Paul Bourdelais08/2015
862^1882800+384541566780Enzo Doria12/2017
87(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
882^1882474+71389566682Enzo Doria04/2018
89(6^727496-11)/5566102Paul Bourdelais08/2019
902^1852265+1890425557588Enzo Doria11/2017
918^615997-7^615997556301Jean-Louis Charton07/2009
92Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
93((((((((((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
94(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
952^1787167+71963537991Enzo Doria12/2018
96(12^495953+1)/13535223Paul Bourdelais11/2018
972^1773644+72511533921Enzo Doria10/2018
98(11559^131072+1)/2532535Serge Batalov04/2018
99(21^394579+1)/22521719Paul Bourdelais10/2018
1002^1730246+384439520856Enzo Doria09/2017
101(18^414269-1)/17520020Paul Bourdelais12/2014
102(20^393257+1)/21511638Paul Bourdelais12/2014
103(14^441697-1)/13506241Paul Bourdelais12/2014
1043^1059503-2^1059503505512Mike Oakes04/2012
1052^1670703+60293502932Enzo Doria11/2017
106(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
107(64*10^499210+53)/9499211Serge Batalov03/2015
108Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
10929^339887-28^339887497051Jean-Louis Charton05/2019
110(2^1629469-1)/644908484660139264379223490496Gord Palameta11/2017
1112^1617579+1889543486940Enzo Doria09/2017
112L(2316773)484177Serge Batalov06/2017
1132^1595483+184133480289Enzo Doria07/2017
1142^1594947+3480127Paul Bourdelais07/2019
1152^1585195+1888373477192Enzo Doria08/2017
1162^1575391+71483474240Enzo Doria04/2018
117(2^1572882+5)/3473485Serge Batalov08/2015
118(6^608099-1)/5473193Paul Bourdelais05/2010
1192^1567006+1888099471716Enzo Doria05/2017
1202^1563067+1889813470531Enzo Doria08/2017
1212^1549797+60197466536Enzo Doria02/2018
1222^1549030+1887619466305Enzo Doria05/2017
123416^177481-415^177481464840Jean-Louis Charton12/2016
1242^1522569+71657458339Enzo Doria04/2018
1252^1518191+75353457022Ben Maloney / Five or Bust01/2009
1262^1506029+1890167453360Enzo Doria02/2018
127(34^294277+1)/35450678Paul Bourdelais06/2018
1282^1495434+1890439450171Enzo Doria12/2017
1292^1493170+784129449489Enzo Doria08/2017
1302^1489873+1888277448497Enzo Doria06/2017
1312^1484671+1888463446931Enzo Doria06/2017
1322^1482867+1886783446388Enzo Doria04/2017
1332^1482148+284011446172Enzo Doria04/2017
1342^1479356+1888291445331Enzo Doria06/2017
1352^1461244+784531439879Enzo Doria10/2017
1362^1443089+60227434414Enzo Doria10/2017
137(21^328129-1)/20433858Paul Bourdelais06/2014
1382^1434400+3431798Paul Bourdelais06/2019
1392^1432308+1888801431168Enzo Doria10/2017
140(2^1430131+1)/(3*356468732537*36519993971459)430487Gord Palameta12/2018
1412^1425483+1886813429114Enzo Doria04/2017
142(17^348259+1)/18428514Paul Bourdelais05/2014
143(10^427912+89)/9427912Serge Batalov12/2014
1442^1421089+1890167427791Enzo Doria09/2017
145(10^424861-7)/3424861Leonid Durman01/2012
1462^1404213+184217422711Enzo Doria09/2017
1472^1401872+1884385422006Enzo Doria04/2017
1482^1401257+6077421821Enzo Doria09/2017
149138^196873-137^196873421285Jean-Louis Charton12/2009
1502^1398269+131595420921Makoto Morimoto10/2013
1512^1397071+684443420561Enzo Doria07/2017
152953^141023-952^141023420121Jean-Louis Charton10/2016
153(3^877843-1)/2418838Paul Bourdelais07/2010
1542^1386321+60299417325Enzo Doria02/2018
1552^1386320+184531417324Enzo Doria09/2017
1562^1382074+1883587416046Enzo Doria01/2017
1572^1379907+1885223415394Enzo Doria03/2017
1582^1375574+1886719414090Enzo Doria04/2017
1592^1373111+1884833413348Enzo Doria02/2017
1602^1368632+1889731412000Enzo Doria10/2017
161(89*10^411590+1)/9411591Serge Batalov09/2014
162F(1968721)411439Henri Lifchitz11/2009
1632^1366066+683749411227Enzo Doria02/2017
1642^1355790+1888939408134Enzo Doria07/2017
1652^1355635+1884203408087Enzo Doria01/2017
166(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
1672^1347744-3405712Paul Bourdelais07/2019
168Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
1692^1319770+1884949397291Enzo Doria06/2017
1702^1313062+1888849395272Enzo Doria08/2017
171(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
172(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
1732^1311618+783529394837Enzo Doria01/2017
1742^1308000+1883521393748Enzo Doria02/2017
175(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
176(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
177(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
178(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
179(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
180(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
1812^1303102+1866409392273Enzo Doria09/2017
1822^1302818+283429392188Enzo Doria01/2017
183(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
1842^1299181+1886867391093Enzo Doria04/2017
1852^1298304+1882891390829Enzo Doria01/2017
186(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
18715^328574+328574^15386434Serge Batalov05/2014
1882^1280078+1885099385342Enzo Doria08/2017
1892^1274941+1880717383796Enzo Doria10/2016
1902^1272632+383431383101Enzo Doria01/2017
1912^1271346+1889839382714Enzo Doria08/2017
192(10^380976-7)/3380976Leonid Durman01/2012
1932^1257787+1447761378632Makoto Morimoto10/2013
194(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
195F(1803059)376817Henri Lifchitz06/2009
1962^1234709+883127371685Enzo Doria12/2016
1972^1231466+283819370709Enzo Doria07/2017
1982^1220335+1881263367358Enzo Doria11/2016
1992^1216694+1884769366262Enzo Doria02/2017
2002^1215889-3366020Paul Bourdelais06/2019
2012^1215296+1885441365841Enzo Doria03/2017
2022^1214307+1888115365543Enzo Doria05/2017
2032^1213815+3365395Paul Bourdelais06/2019
2042^1207345+1882577363448Enzo Doria12/2016
2052^1207073+883727363366Enzo Doria03/2017
2063^761457-2363308Ryan Propper07/2015
2072^1200672+1880881361439Enzo Doria10/2016
208(64*10^360173-1)/243360173Serge Batalov09/2014
2092^1195093+1882577359759Enzo Doria12/2016
210(6^461108-11)/5358812Paul Bourdelais04/2019
2112^1191375+8543358640Phil Moore06/2008
2122^1190972+1880191358519Enzo Doria11/2016
2132^1179836+1885021355167Enzo Doria02/2017
214numbpart(100000135540)352269Serge Batalov04/2017
215(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
2162^1168554+783529351770Enzo Doria01/2017
217(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
2182^1166152+1882411351047Enzo Doria12/2016
2192^1162154+1890207349844Enzo Doria08/2017
220(7*10^348724-61)/9348724Erik Branger09/2016
221(127^165601-1)/126348390Alexander Zhirkov09/2015
2222^1153083+1883693347113Enzo Doria04/2017
223(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
2242^1145882+80779344945Enzo Doria09/2016
2252^1136462+1887289342110Enzo Doria05/2017
226F(1636007)341905Henri Lifchitz03/2009
2272^1133678+782569341272Enzo Doria11/2016
228(11^327001+1)/12340536Paul Bourdelais09/2013
229(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
230Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
2312^1126380-3339075Paul Bourdelais06/2019
2322^1125446+1885099338794Enzo Doria08/2017
2332^1124549+143807338523Enzo Doria10/2016
2342^1121187+1886783337511Enzo Doria04/2017
2352^1116184+1883521336005Enzo Doria02/2017
2362^1114517+1880087335504Enzo Doria10/2016
237(3^700897+1)/4334413Paul Bourdelais04/2010
2382^1104408-114539332460Enzo Doria03/2015
2392^1101921+82085331712Enzo Doria10/2016
2402^1100655+683513331331Enzo Doria01/2017
241(10^330906+71)/9330906Serge Batalov07/2015
2422^1098346+482899330636Enzo Doria11/2016
2432^1095679+1878713329833Enzo Doria09/2016
2442^1094740-1851539329550Enzo Doria08/2015
2452^1091469-379369328565Enzo Doria03/2014
2462^1085750+582349326844Enzo Doria11/2016
2472^1083596+483061326195Enzo Doria12/2016
248(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
2492^1082908+583561325988Enzo Doria05/2017
25030^220411-29^220411325574Jean-Louis Charton10/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 22 2019 21:56 (Time in France)

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