PRP Records

Probable Primes Top 10000

(129601 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 (> 20000) Who ? When ?
1(2^13372531+1)/34025533Ryan Propper09/2013
2(2^13347311+1)/34017941Ryan Propper09/2013
32^9092392+402912737083Engracio Esmenda / Five or Bust02/2011
42^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
52^4583176+21311379674Ben Maloney / Five or Bust09/2009
6(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
7(14^1091401+1)/151250885Paul Bourdelais03/2014
8(16^1025393+1)/171234695Paul Bourdelais08/2014
9(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
10(106*23^800873-7)/111090573Curtis Bright05/2015
11(7^1264699-1)/61068794Paul Bourdelais01/2014
12(2^3464473-1)/6048745082991771042896Anand Nair10/2014
1310^999999+5934991000000Peter Kaiser02/2013
142^2976221+2041857895932Makoto Morimoto09/2014
15(12^769543-1)/11830476Paul Bourdelais12/2014
16(64*10^779465-1)/81779465Serge Batalov09/2014
17(64*10^762811-1)/9762812Serge Batalov09/2014
18(10^718580+269)/9718580Serge Batalov12/2014
19(2^2327417-1)/23915387348002001700606Anand Nair08/2014
20(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
21(10^685224+89)/9685224Serge Batalov12/2014
222^2249255+28433677094Ben Maloney / Five or Bust01/2009
23(10^675470+269)/9675470Serge Batalov12/2014
24(9^703393+1)/10671207Paul Bourdelais08/2015
25(15^551927+1)/16649116Paul Bourdelais07/2013
26(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
27(20^472709-1)/19615008Paul Bourdelais01/2015
28(19^476929+1)/20609874Paul Bourdelais03/2015
29F(2904353)606974Henri Lifchitz07/2014
30(18^481147+1)/19603970Paul Bourdelais07/2011
31(15^505117-1)/14594063Paul Bourdelais01/2015
32(152^270217-1)/(152-1)589570Michael Stocker06/2015
33(3^1205459+1)/4575150Paul Bourdelais08/2015
34(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
358^615997-7^615997556301Jean-Louis Charton07/2009
36((((((((((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
37(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
38(18^414269-1)/17520020Paul Bourdelais12/2014
39(20^393257+1)/21511638Paul Bourdelais12/2014
40(14^441697-1)/13506241Paul Bourdelais12/2014
413^1059503-2^1059503505512Mike Oakes04/2012
42(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
43(64*10^499210+53)/9499211Serge Batalov03/2015
44Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
45(2^1572882+5)/3473485Serge Batalov08/2015
46(6^608099-1)/5473193Paul Bourdelais05/2010
472^1518191+75353457022Ben Maloney / Five or Bust01/2009
48(21^328129-1)/20433858Paul Bourdelais06/2014
49(17^348259+1)/18428514Paul Bourdelais05/2014
50(10^427912+89)/9427912Serge Batalov12/2014
51(10^424861-7)/3424861Leonid Durman01/2012
52138^196873-137^196873421285Jean-Louis Charton12/2009
532^1398269+131595420921Makoto Morimoto10/2013
54(3^877843-1)/2418838Paul Bourdelais07/2010
55(89*10^411590+1)/9411591Serge Batalov09/2014
56F(1968721)411439Henri Lifchitz11/2009
57(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
58(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
5915^328574+328574^15386434Serge Batalov05/2014
60(10^380976-7)/3380976Leonid Durman01/2012
612^1257787+1447761378632Makoto Morimoto10/2013
62F(1803059)376817Henri Lifchitz06/2009
633^761457-2363308Ryan Propper07/2015
64(64*10^360173-1)/243360173Serge Batalov09/2014
652^1191375+8543358640Phil Moore06/2008
66(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
67(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
68(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
69F(1636007)341905Henri Lifchitz03/2009
70(11^327001+1)/12340536Paul Bourdelais09/2013
71(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
72(3^700897+1)/4334413Paul Bourdelais04/2010
732^1104408-114539332460Enzo Doria03/2015
74(10^330906+71)/9330906Serge Batalov07/2015
752^1094740-1851539329550Enzo Doria08/2015
762^1091469-379369328565Enzo Doria03/2014
772^1072118-7321953322740Enzo Doria02/2015
782^1069293-1147195321890Enzo Doria05/2015
792^1065897-1147195320867Enzo Doria05/2015
802^1061095-1061095319422Henri Lifchitz10/2013
812^1052186-458165316740Enzo Doria03/2015
822^1046613-114685315062Enzo Doria04/2015
832^1045625-459373314765Enzo Doria06/2015
84(7^371669-1)/6314096Paul Bourdelais02/2010
852^1041153-114391313419Enzo Doria02/2015
862^1036020-114539311874Enzo Doria02/2015
87(11^293831-1)/10305993Paul Bourdelais03/2010
882^1015321-1015321305643Henri Lifchitz08/2013
892^1010751-107709304267Enzo Doria03/2014
90(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
918^336419-7^336419303817Jean-Louis Charton01/2008
92(2^1007838+5)/3303389Serge Batalov08/2015
9310^300476+3300477Ed Trice10/2012
94314738^9+9^314738300337Anatoly F. Selevich02/2011
957^355039-6^355039300043Jean-Louis Charton05/2011
962^996182-114431299881Enzo Doria02/2015
972^994791-114319299462Enzo Doria01/2015
982^992525-114199298780Enzo Doria12/2014
99(2^986191+1)/3296873Vincent Diepeveen06/2008
1002^985217-114553296580Enzo Doria03/2015
1012^984131-1828009296253Enzo Doria01/2015
1022^983620+60451296100Phil Moore03/2008
1032^972744-114419292826Enzo Doria03/2015
1042^970141-100363292042Enzo Doria02/2014
105(17^233689+1)/18287542Paul Bourdelais09/2013
106(11*2^948635-13)/15285568Renaud Lifchitz11/2011
1072^948374-114137285490Enzo Doria01/2015
1082^939881-114115282933Enzo Doria12/2014
10910^282493-9^282493282493Jean-Louis Charton03/2007
1103^591827-2^591827282374Mike Oakes08/2009
111Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
1122^936716-1835519281980Enzo Doria04/2015
113(5*10^280710+1)/3280711Serge Batalov10/2014
114(10^279978+11)/3279978Serge Batalov07/2015
1152^925330-1301278553Yves Minet06/2015
116(21^210599+1)/22278457Paul Bourdelais08/2013
117757^96487-756^96487277796Jean-Louis Charton12/2012
118(5^396413-1)/4277081Paul Bourdelais06/2010
1192^915576-114137275616Enzo Doria01/2015
1202^906594-113201272912Enzo Doria08/2014
121(7*10^271757-61)/9271757Erik Branger03/2012
1222^899121-115033270663Enzo Doria07/2015
1232^898762-251511270555Enzo Doria12/2013
124187322*10^270343-187321270349Danilo Nitsche09/2013
12548358*10^270343-48357270348Danilo Nitsche09/2013
126(10^270343-1)/9270343Maksym Voznyy07/2007
1272^897849-115273270280Enzo Doria07/2015
1282^896616-114179269909Enzo Doria12/2014
1292^894673-39343269324Enzo Doria08/2015
130F(1285607)268676Henri Lifchitz11/2008
131(10^268207+1)/11268206Paul Bourdelais02/2010
1322^890122-351401267954Enzo Doria07/2015
133(19^209359-1)/18267718Paul Bourdelais08/2010
13411^255426+255426^11265999Serge Batalov05/2014
1352^883462-343421265949Enzo Doria07/2015
1362^883333-291583265910Enzo Doria07/2015
1372^875748-461129263627Enzo Doria07/2015
1382^875101-350083263432Enzo Doria08/2015
1392^873288-269262886Yves Minet01/2015
1402^869601-163261776Yves Minet01/2015
1412^869035-114181261606Enzo Doria12/2014
1422^864899-113871260361Enzo Doria10/2014
143(7*10^260198-61)/9260198Erik Branger11/2011
1442^863621-113833259976Enzo Doria10/2014
1452^859433+494711258716Makoto Morimoto10/2013
146Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
147(11*2^857159-13)/15258031Renaud Lifchitz08/2011
1482^857016-633113257988Enzo Doria12/2013
1492^855732-113969257602Enzo Doria10/2014
1502^853682-3911256984Enzo Doria05/2014
15111^246668-90256879Enzo Doria12/2012
1522^851904-113939256449Enzo Doria10/2014
15311^246167-90256357Enzo Doria12/2012
1542^850700-569049256087Enzo Doria11/2013
15521^193601-20^193601255983Jean-Louis Charton02/2015
1562^849177-114025255628Enzo Doria12/2014
1572^848178-140291255328Enzo Doria01/2014
15824*29^174239+13361254809Curtis Bright04/2015
1592^845402-114761254492Enzo Doria05/2015
16011^243796-90253888Enzo Doria12/2012
1612^840358-462491252973Enzo Doria08/2015
16211^242579-60252620Enzo Doria10/2012
1632^837536-311039252124Enzo Doria06/2015
16421^190632-2252058Robert Price07/2015
165tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
1662^832511-461197250611Enzo Doria07/2015
1672^832244-403635250531Enzo Doria01/2014
1682^831088-7200899250183Enzo Doria01/2015
1692^830956-1349250143Yves Minet07/2015
1702^829589-113653249732Enzo Doria09/2014
17110^249010-21249010Serge Batalov12/2014
1722^824991-114121248348Enzo Doria12/2014
1732^824642-362727248242Enzo Doria12/2013
1742^824565-114265248219Enzo Doria01/2015
175(73*10^248145-1)/9248146Robert Price01/2015
1762^821590-114167247324Enzo Doria12/2014
1772^817160-350369245990Enzo Doria06/2015
1782^815111-113857245373Enzo Doria10/2014
179846^83761-845^83761245200Jean-Louis Charton12/2012
1802^814276-459029245122Enzo Doria04/2015
1812^811842-113675244389Enzo Doria09/2014
1822^808621-113809243420Enzo Doria09/2014
1832^805843-113611242583Enzo Doria08/2014
1842^805745-459763242554Enzo Doria05/2015
1852^804277-417933242112Enzo Doria01/2014
1862^803468-269039241868Enzo Doria10/2013
1873^506233-2241535Robert Price11/2013
1882^802025-25999241434Enzo Doria10/2013
189(3^505823+3^252912+1)/7241339Serge Batalov03/2014
1902^798973-26283240515Enzo Doria10/2013
1912^796910-26001239894Enzo Doria10/2013
1922^796002-1852211239621Enzo Doria08/2015
1932^795075-1852057239342Enzo Doria08/2015
1942^792988-344429238714Enzo Doria08/2015
1952^792663-1844797238616Enzo Doria06/2015
1962^792605-291943238598Enzo Doria07/2015
197(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
198((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
1992^788844-114329237466Enzo Doria01/2015
20011^227092-90236492Enzo Doria11/2012
20119^184650-2236122Robert Price10/2014
2022^782634-113981235597Enzo Doria11/2014
2032^780408-113453234927Enzo Doria08/2014
2042^779593-1836559234681Enzo Doria05/2015
205(5^335429+1)/6234455Paul Bourdelais08/2010
2062^778395-113617234321Enzo Doria08/2014
2072^776060-114029233618Enzo Doria11/2014
208(11^223999+1)/12233270Paul Bourdelais02/2010
20921^176191-20^176191232964Jean-Louis Charton01/2015
2102^773679-113425232901Enzo Doria08/2014
21110^232599+192489232600Patrick De Geest12/2013
21210^232599-3232599Markus Tervooren10/2010
2132^772552-458879232562Enzo Doria04/2015
2145^332150-18188232163Enzo Doria06/2014
2153^485977-2^485977231870Mike Oakes09/2009
2162^770082-114161231818Enzo Doria01/2015
217(20^177967+1)/21231540Paul Bourdelais05/2013
218(3^483611-1)/2230741Paul Bourdelais02/2010
219(10^230706+179)/9230706Serge Batalov12/2014
2202^764348-113697230092Enzo Doria09/2014
2212^762841-25905229639Enzo Doria10/2013
2222^761117-113569229120Enzo Doria08/2014
2232^756839+95849227832Makoto Morimoto10/2013
2242^756773-112723227812Enzo Doria07/2014
2252^755097-114193227307Enzo Doria12/2014
2262^751426-764321226202Enzo Doria12/2013
227(18^180181-1)/17226176Andy Steward04/2007
2282^750740-3225996Paul Bourdelais03/2012
2292^750525-113743225931Enzo Doria09/2014
230(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
231tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
2322^746653-291583224765Enzo Doria07/2015
2332^746461-114043224708Enzo Doria11/2014
2342^745098-350471224297Enzo Doria06/2015
235(154*10^224061-1)/9224063Serge Batalov12/2014
2362^744211-1845787224030Enzo Doria07/2015
237234178^9+9^234178223463Anatoly F. Selevich07/2011
2382^741651-461197223260Enzo Doria07/2015
2392^741362-1845251223173Enzo Doria07/2015
24011^213654-180222498Enzo Doria01/2013
241(10^221654+179)/9221654Serge Batalov12/2014
24210^221631+247617221632Patrick De Geest10/2013
24310^221631-9221631Alexander Gramolin02/2011
2442^735970-1839821221550Enzo Doria06/2015
2452^733114-24555220690Enzo Doria09/2013
2462^731891-636259220322Enzo Doria12/2013
2472^731124-25539220091Enzo Doria09/2013
2482^730972-462029220045Enzo Doria07/2015
2492^730547-25581219917Enzo Doria09/2013
250L(1051849)219824Renaud Lifchitz03/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 02 2015 22:04 (Time in France)

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