PRP Records

Probable Primes Top 10000

(201620 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 ?
1(2^13372531+1)/34025533Ryan Propper09/2013
2(2^13347311+1)/34017941Ryan Propper09/2013
32^9092392+402912737083Engracio Esmenda / Five or Bust02/2011
4(2^7080247-1)/156822217506727/11283326312536321/96329405483303395932131318Gord Palameta10/2017
5(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
62^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
7(2^4834891-1)/1701881633/706596885755771455425Gord Palameta01/2017
82^4583176+21311379674Ben Maloney / Five or Bust09/2009
9(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
10(13^1199467+1)/141336138Paul Bourdelais12/2015
11(2^4194304+1026473)/31262611Tony Prest / Never Odd Or Even07/2017
12(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
13(14^1091401+1)/151250885Paul Bourdelais03/2014
14(16^1025393+1)/171234695Paul Bourdelais08/2014
15(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
16(106*23^800873-7)/111090573Curtis Bright05/2015
17(7^1264699-1)/61068794Paul Bourdelais01/2014
18(2^3464473-1)/6048745082991771042896Anand Nair10/2014
1910^999999+5934991000000Peter Kaiser02/2013
2010^999999-172473999999Patrick De Geest12/2016
212^2976221+2041857895932Makoto Morimoto09/2014
22(12^769543-1)/11830476Paul Bourdelais12/2014
23(64*10^779465-1)/81779465Serge Batalov09/2014
24(64*10^762811-1)/9762812Serge Batalov09/2014
25(10^718580+269)/9718580Serge Batalov12/2014
26(2^2327417-1)/23915387348002001700606Anand Nair08/2014
27(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
28(10^685224+89)/9685224Serge Batalov12/2014
29F(3244369)678033Henri Lifchitz09/2017
302^2249255+28433677094Ben Maloney / Five or Bust01/2009
31(10^675470+269)/9675470Serge Batalov12/2014
32Tau(151^56086)672156Nik Lygeros / Olivier Rozier / LR team10/2017
33(9^703393+1)/10671207Paul Bourdelais08/2015
34(15^551927+1)/16649116Paul Bourdelais07/2013
35(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
36Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
37(51*21^479149-1243)/4633542Curtis Bright11/2015
38Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
39(20^472709-1)/19615008Paul Bourdelais01/2015
40PIPrime(613373)613373Adrian Bondrescu05/2016
41(19^476929+1)/20609874Paul Bourdelais03/2015
42F(2904353)606974Henri Lifchitz07/2014
43(18^481147+1)/19603970Paul Bourdelais07/2011
44(15^505117-1)/14594063Paul Bourdelais01/2015
45(152^270217-1)/(152-1)589570Michael Stocker06/2015
46(3^1205459+1)/4575150Paul Bourdelais08/2015
472^1882800+384541566780Enzo Doria12/2017
48(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
492^1852265+1890425557588Enzo Doria11/2017
508^615997-7^615997556301Jean-Louis Charton07/2009
51Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
52((((((((((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
53(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
542^1730246+384439520856Enzo Doria09/2017
55(18^414269-1)/17520020Paul Bourdelais12/2014
56(20^393257+1)/21511638Paul Bourdelais12/2014
57(14^441697-1)/13506241Paul Bourdelais12/2014
583^1059503-2^1059503505512Mike Oakes04/2012
592^1670703+60293502932Enzo Doria11/2017
60(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
61(64*10^499210+53)/9499211Serge Batalov03/2015
62Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
63(2^1629469-1)/644908484660139264379223490496Gord Palameta11/2017
642^1617579+1889543486940Enzo Doria09/2017
65L(2316773)484177Serge Batalov06/2017
662^1595483+184133480289Enzo Doria07/2017
672^1585195+1888373477192Enzo Doria08/2017
68(2^1572882+5)/3473485Serge Batalov08/2015
69(6^608099-1)/5473193Paul Bourdelais05/2010
702^1567006+1888099471716Enzo Doria05/2017
712^1563067+1889813470531Enzo Doria08/2017
722^1549030+1887619466305Enzo Doria05/2017
73416^177481-415^177481464840Jean-Louis Charton12/2016
742^1518191+75353457022Ben Maloney / Five or Bust01/2009
752^1495434+1890439450171Enzo Doria12/2017
762^1493170+784129449489Enzo Doria08/2017
772^1489873+1888277448497Enzo Doria06/2017
782^1484671+1888463446931Enzo Doria06/2017
792^1482867+1886783446388Enzo Doria04/2017
802^1482148+284011446172Enzo Doria04/2017
812^1479356+1888291445331Enzo Doria06/2017
822^1461244+784531439879Enzo Doria10/2017
832^1443089+60227434414Enzo Doria10/2017
84(21^328129-1)/20433858Paul Bourdelais06/2014
852^1432308+1888801431168Enzo Doria10/2017
862^1425483+1886813429114Enzo Doria04/2017
87(17^348259+1)/18428514Paul Bourdelais05/2014
88(10^427912+89)/9427912Serge Batalov12/2014
892^1421089+1890167427791Enzo Doria09/2017
90(10^424861-7)/3424861Leonid Durman01/2012
912^1404213+184217422711Enzo Doria09/2017
922^1401872+1884385422006Enzo Doria04/2017
932^1401257+6077421821Enzo Doria09/2017
94138^196873-137^196873421285Jean-Louis Charton12/2009
952^1398269+131595420921Makoto Morimoto10/2013
962^1397071+684443420561Enzo Doria07/2017
97953^141023-952^141023420121Jean-Louis Charton10/2016
98(3^877843-1)/2418838Paul Bourdelais07/2010
992^1386320+184531417324Enzo Doria09/2017
1002^1382074+1883587416046Enzo Doria01/2017
1012^1379907+1885223415394Enzo Doria03/2017
1022^1375574+1886719414090Enzo Doria04/2017
1032^1373111+1884833413348Enzo Doria02/2017
1042^1368632+1889731412000Enzo Doria10/2017
105(89*10^411590+1)/9411591Serge Batalov09/2014
106F(1968721)411439Henri Lifchitz11/2009
1072^1366066+683749411227Enzo Doria02/2017
1082^1355790+1888939408134Enzo Doria07/2017
1092^1355635+1884203408087Enzo Doria01/2017
110(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
111Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
1122^1319770+1884949397291Enzo Doria06/2017
1132^1313062+1888849395272Enzo Doria08/2017
114(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
115(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
1162^1311618+783529394837Enzo Doria01/2017
1172^1308000+1883521393748Enzo Doria02/2017
118(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
119(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
120(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
121(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
122(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
123(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
1242^1303102+1866409392273Enzo Doria09/2017
1252^1302818+283429392188Enzo Doria01/2017
126(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
1272^1299181+1886867391093Enzo Doria04/2017
1282^1298304+1882891390829Enzo Doria01/2017
129(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
13015^328574+328574^15386434Serge Batalov05/2014
1312^1280078+1885099385342Enzo Doria08/2017
1322^1274941+1880717383796Enzo Doria10/2016
1332^1272632+383431383101Enzo Doria01/2017
1342^1271346+1889839382714Enzo Doria08/2017
135(10^380976-7)/3380976Leonid Durman01/2012
1362^1257787+1447761378632Makoto Morimoto10/2013
137(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
138F(1803059)376817Henri Lifchitz06/2009
1392^1234709+883127371685Enzo Doria12/2016
1402^1231466+283819370709Enzo Doria07/2017
1412^1220335+1881263367358Enzo Doria11/2016
1422^1216694+1884769366262Enzo Doria02/2017
1432^1215296+1885441365841Enzo Doria03/2017
1442^1214307+1888115365543Enzo Doria05/2017
1452^1207345+1882577363448Enzo Doria12/2016
1462^1207073+883727363366Enzo Doria03/2017
1473^761457-2363308Ryan Propper07/2015
1482^1200672+1880881361439Enzo Doria10/2016
149(64*10^360173-1)/243360173Serge Batalov09/2014
1502^1195093+1882577359759Enzo Doria12/2016
1512^1191375+8543358640Phil Moore06/2008
1522^1190972+1880191358519Enzo Doria11/2016
1532^1179836+1885021355167Enzo Doria02/2017
154numbpart(100000135540)352269Serge Batalov04/2017
155(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
1562^1168554+783529351770Enzo Doria01/2017
157(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
1582^1166152+1882411351047Enzo Doria12/2016
1592^1162154+1890207349844Enzo Doria08/2017
160(7*10^348724-61)/9348724Erik Branger09/2016
161(127^165601-1)/126348390Alexander Zhirkov09/2015
1622^1153083+1883693347113Enzo Doria04/2017
163(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
1642^1145882+80779344945Enzo Doria09/2016
1652^1136462+1887289342110Enzo Doria05/2017
166F(1636007)341905Henri Lifchitz03/2009
1672^1133678+782569341272Enzo Doria11/2016
168(11^327001+1)/12340536Paul Bourdelais09/2013
169(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
170Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
1712^1125446+1885099338794Enzo Doria08/2017
1722^1124549+143807338523Enzo Doria10/2016
1732^1121187+1886783337511Enzo Doria04/2017
1742^1116184+1883521336005Enzo Doria02/2017
1752^1114517+1880087335504Enzo Doria10/2016
176(3^700897+1)/4334413Paul Bourdelais04/2010
1772^1104408-114539332460Enzo Doria03/2015
1782^1101921+82085331712Enzo Doria10/2016
1792^1100655+683513331331Enzo Doria01/2017
180(10^330906+71)/9330906Serge Batalov07/2015
1812^1098346+482899330636Enzo Doria11/2016
1822^1095679+1878713329833Enzo Doria09/2016
1832^1094740-1851539329550Enzo Doria08/2015
1842^1091469-379369328565Enzo Doria03/2014
1852^1085750+582349326844Enzo Doria11/2016
1862^1083596+483061326195Enzo Doria12/2016
1872^1082908+583561325988Enzo Doria05/2017
1882^1078242+1881649324584Enzo Doria11/2016
1892^1077737+1880117324432Enzo Doria10/2016
1902^1075425+1880117323736Enzo Doria10/2016
1912^1072146+1886869322749Enzo Doria04/2017
1922^1072118-7321953322740Enzo Doria02/2015
1932^1071026+1886869322411Enzo Doria04/2017
1942^1070539+1880633322265Enzo Doria10/2016
1952^1069293-1147195321890Enzo Doria05/2015
1962^1065968+1880941320889Enzo Doria10/2016
1972^1065897-1147195320867Enzo Doria05/2015
1982^1063427+1882103320124Enzo Doria12/2016
1992^1061095-1061095319422Henri Lifchitz10/2013
2002^1060950+653119319378Enzo Doria12/2016
2012^1060363+782753319202Enzo Doria11/2016
2022^1054736+483061317508Enzo Doria12/2016
2032^1053965+1879667317276Enzo Doria10/2016
2042^1052186-458165316740Enzo Doria03/2015
2052^1046613-114685315062Enzo Doria04/2015
2062^1045625-459373314765Enzo Doria06/2015
207(7*10^314564-61)/9314564Erik Branger09/2016
208(7^371669-1)/6314096Paul Bourdelais02/2010
2092^1041944+283051313657Enzo Doria12/2016
2102^1041153-114391313419Enzo Doria02/2015
2112^1038871+1866983312732Enzo Doria04/2016
2122^1037647+1881263312363Enzo Doria11/2016
2132^1037226+1879699312237Enzo Doria10/2016
2142^1036867+1865843312129Enzo Doria02/2016
2152^1036020-114539311874Enzo Doria02/2015
2162^1032240+1883431310736Enzo Doria01/2017
2172^1030352+1870021310167Enzo Doria06/2016
2182^1030046+1882843310075Enzo Doria11/2016
219(11^293831-1)/10305993Paul Bourdelais03/2010
2202^1015321-1015321305643Henri Lifchitz08/2013
2212^1014224-2791229305312Enzo Doria01/2016
2222^1010751-107709304267Enzo Doria03/2014
223(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
2242^1009577+1869587303913Enzo Doria06/2016
2258^336419-7^336419303817Jean-Louis Charton01/2008
2262^1008301+1869377303529Enzo Doria06/2016
227(2^1007838+5)/3303389Serge Batalov08/2015
2282^1005326+383059302634Enzo Doria12/2016
2292^1004929+1877567302514Enzo Doria08/2016
2302^1003494+1874899302082Enzo Doria06/2016
2312^1003046+60529301947Enzo Doria04/2016
2322^1000647+1881353301225Enzo Doria11/2016
2332^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
2342^999646+1874029300924Enzo Doria06/2016
23510^300476+3300477Ed Trice10/2012
23610^300476-530913300476Patrick De Geest03/2016
2372^998053+1879667300444Enzo Doria09/2016
238314738^9+9^314738300337Anatoly F. Selevich02/2011
2397^355039-6^355039300043Jean-Louis Charton05/2011
240numbpart(72526161452)299999Serge Batalov04/2017
2412^996182-114431299881Enzo Doria02/2015
2422^995214-2788361299590Enzo Doria12/2015
2432^994791-114319299462Enzo Doria01/2015
2442^994490-1863791299372Enzo Doria01/2016
2452^993322+1885729299020Enzo Doria03/2017
2462^992711-2788807298836Enzo Doria12/2015
2472^992525-114199298780Enzo Doria12/2014
2482^992329+1884707298721Enzo Doria02/2017
249(2^986191+1)/3296873Vincent Diepeveen06/2008
2502^985217-114553296580Enzo Doria03/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 21 2018 09:45 (Time in France)

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