PRP Records

Probable Primes Top 10000

(127409 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(15^551927+1)/16649116Paul Bourdelais07/2013
25(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
26(20^472709-1)/19615008Paul Bourdelais01/2015
27(19^476929+1)/20609874Paul Bourdelais03/2015
28F(2904353)606974Henri Lifchitz07/2014
29(18^481147+1)/19603970Paul Bourdelais07/2011
30(15^505117-1)/14594063Paul Bourdelais01/2015
31(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
328^615997-7^615997556301Jean-Louis Charton07/2009
33((((((((((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
34(18^414269-1)/17520020Paul Bourdelais12/2014
35(20^393257+1)/21511638Paul Bourdelais12/2014
36(14^441697-1)/13506241Paul Bourdelais12/2014
373^1059503-2^1059503505512Mike Oakes04/2012
38(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
39(64*10^499210+53)/9499211Serge Batalov03/2015
40Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
41(6^608099-1)/5473193Paul Bourdelais05/2010
422^1518191+75353457022Ben Maloney / Five or Bust01/2009
43(21^328129-1)/20433858Paul Bourdelais06/2014
44(17^348259+1)/18428514Paul Bourdelais05/2014
45(10^427912+89)/9427912Serge Batalov12/2014
46(10^424861-7)/3424861Leonid Durman01/2012
47138^196873-137^196873421285Jean-Louis Charton12/2009
482^1398269+131595420921Makoto Morimoto10/2013
49(3^877843-1)/2418838Paul Bourdelais07/2010
50(89*10^411590+1)/9411591Serge Batalov09/2014
51F(1968721)411439Henri Lifchitz11/2009
52(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
53(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
5415^328574+328574^15386434Serge Batalov05/2014
55(10^380976-7)/3380976Leonid Durman01/2012
562^1257787+1447761378632Makoto Morimoto10/2013
57F(1803059)376817Henri Lifchitz06/2009
58(64*10^360173-1)/243360173Serge Batalov09/2014
592^1191375+8543358640Phil Moore06/2008
60(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
61(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
62(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
63F(1636007)341905Henri Lifchitz03/2009
64(11^327001+1)/12340536Paul Bourdelais09/2013
65(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
66(3^700897+1)/4334413Paul Bourdelais04/2010
672^1104408-114539332460Enzo Doria03/2015
682^1091469-379369328565Enzo Doria03/2014
692^1072118-7321953322740Enzo Doria02/2015
702^1069293-1147195321890Enzo Doria05/2015
712^1065897-1147195320867Enzo Doria05/2015
722^1061095-1061095319422Henri Lifchitz10/2013
732^1052186-458165316740Enzo Doria03/2015
742^1046613-114685315062Enzo Doria04/2015
75(7^371669-1)/6314096Paul Bourdelais02/2010
762^1041153-114391313419Enzo Doria02/2015
772^1036020-114539311874Enzo Doria02/2015
78(11^293831-1)/10305993Paul Bourdelais03/2010
792^1015321-1015321305643Henri Lifchitz08/2013
802^1010751-107709304267Enzo Doria03/2014
81(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
828^336419-7^336419303817Jean-Louis Charton01/2008
8310^300476+3300477Ed Trice10/2012
84314738^9+9^314738300337Anatoly F. Selevich02/2011
857^355039-6^355039300043Jean-Louis Charton05/2011
862^996182-114431299881Enzo Doria02/2015
872^994791-114319299462Enzo Doria01/2015
882^992525-114199298780Enzo Doria12/2014
89(2^986191+1)/3296873Vincent Diepeveen06/2008
902^985217-114553296580Enzo Doria03/2015
912^984131-1828009296253Enzo Doria01/2015
922^983620+60451296100Phil Moore03/2008
932^972744-114419292826Enzo Doria03/2015
942^970141-100363292042Enzo Doria02/2014
95(17^233689+1)/18287542Paul Bourdelais09/2013
96(11*2^948635-13)/15285568Renaud Lifchitz11/2011
972^948374-114137285490Enzo Doria01/2015
982^939881-114115282933Enzo Doria12/2014
9910^282493-9^282493282493Jean-Louis Charton03/2007
1003^591827-2^591827282374Mike Oakes08/2009
101Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
1022^936716-1835519281980Enzo Doria04/2015
103(5*10^280710+1)/3280711Serge Batalov10/2014
104(21^210599+1)/22278457Paul Bourdelais08/2013
105757^96487-756^96487277796Jean-Louis Charton12/2012
106(5^396413-1)/4277081Paul Bourdelais06/2010
1072^915576-114137275616Enzo Doria01/2015
1082^906594-113201272912Enzo Doria08/2014
109(7*10^271757-61)/9271757Erik Branger03/2012
1102^898762-251511270555Enzo Doria12/2013
111187322*10^270343-187321270349Danilo Nitsche09/2013
11248358*10^270343-48357270348Danilo Nitsche09/2013
113(10^270343-1)/9270343Maksym Voznyy07/2007
1142^896616-114179269909Enzo Doria12/2014
115F(1285607)268676Henri Lifchitz11/2008
116(10^268207+1)/11268206Paul Bourdelais02/2010
117(19^209359-1)/18267718Paul Bourdelais08/2010
11811^255426+255426^11265999Serge Batalov05/2014
1192^873288-269262886Yves Minet01/2015
1202^869601-163261776Yves Minet01/2015
1212^869035-114181261606Enzo Doria12/2014
1222^864899-113871260361Enzo Doria10/2014
123(7*10^260198-61)/9260198Erik Branger11/2011
1242^863621-113833259976Enzo Doria10/2014
1252^859433+494711258716Makoto Morimoto10/2013
126Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
127(11*2^857159-13)/15258031Renaud Lifchitz08/2011
1282^857016-633113257988Enzo Doria12/2013
1292^855732-113969257602Enzo Doria10/2014
1302^853682-3911256984Enzo Doria05/2014
13111^246668-90256879Enzo Doria12/2012
1322^851904-113939256449Enzo Doria10/2014
13311^246167-90256357Enzo Doria12/2012
1342^850700-569049256087Enzo Doria11/2013
13521^193601-20^193601255983Jean-Louis Charton02/2015
1362^849177-114025255628Enzo Doria12/2014
1372^848178-140291255328Enzo Doria01/2014
13824*29^174239+13361254809Curtis Bright04/2015
1392^845402-114761254492Enzo Doria05/2015
14011^243796-90253888Enzo Doria12/2012
14111^242579-60252620Enzo Doria10/2012
142tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
1432^832244-403635250531Enzo Doria01/2014
1442^831088-7200899250183Enzo Doria01/2015
1452^829589-113653249732Enzo Doria09/2014
14610^249010-21249010Serge Batalov12/2014
1472^824991-114121248348Enzo Doria12/2014
1482^824642-362727248242Enzo Doria12/2013
1492^824565-114265248219Enzo Doria01/2015
150(73*10^248145-1)/9248146Robert Price01/2015
1512^821590-114167247324Enzo Doria12/2014
1522^815111-113857245373Enzo Doria10/2014
153846^83761-845^83761245200Jean-Louis Charton12/2012
1542^814276-459029245122Enzo Doria04/2015
1552^811842-113675244389Enzo Doria09/2014
1562^808621-113809243420Enzo Doria09/2014
1572^805843-113611242583Enzo Doria08/2014
1582^804277-417933242112Enzo Doria01/2014
1592^803468-269039241868Enzo Doria10/2013
1603^506233-2241535Robert Price11/2013
1612^802025-25999241434Enzo Doria10/2013
162(3^505823+3^252912+1)/7241339Serge Batalov03/2014
1632^798973-26283240515Enzo Doria10/2013
1642^796910-26001239894Enzo Doria10/2013
165(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
166((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
1672^788844-114329237466Enzo Doria01/2015
16811^227092-90236492Enzo Doria11/2012
16919^184650-2236122Robert Price10/2014
1702^782634-113981235597Enzo Doria11/2014
1712^780408-113453234927Enzo Doria08/2014
1722^779593-1836559234681Enzo Doria05/2015
173(5^335429+1)/6234455Paul Bourdelais08/2010
1742^778395-113617234321Enzo Doria08/2014
1752^776060-114029233618Enzo Doria11/2014
176(11^223999+1)/12233270Paul Bourdelais02/2010
17721^176191-20^176191232964Jean-Louis Charton01/2015
1782^773679-113425232901Enzo Doria08/2014
17910^232599+192489232600Patrick De Geest12/2013
18010^232599-3232599Markus Tervooren10/2010
1812^772552-458879232562Enzo Doria04/2015
1825^332150-18188232163Enzo Doria06/2014
1833^485977-2^485977231870Mike Oakes09/2009
1842^770082-114161231818Enzo Doria01/2015
185(20^177967+1)/21231540Paul Bourdelais05/2013
186(3^483611-1)/2230741Paul Bourdelais02/2010
187(10^230706+179)/9230706Serge Batalov12/2014
1882^764348-113697230092Enzo Doria09/2014
1892^762841-25905229639Enzo Doria10/2013
1902^761117-113569229120Enzo Doria08/2014
1912^756839+95849227832Makoto Morimoto10/2013
1922^756773-112723227812Enzo Doria07/2014
1932^755097-114193227307Enzo Doria12/2014
1942^751426-764321226202Enzo Doria12/2013
195(18^180181-1)/17226176Andy Steward04/2007
1962^750740-3225996Paul Bourdelais03/2012
1972^750525-113743225931Enzo Doria09/2014
198(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
199tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
2002^746461-114043224708Enzo Doria11/2014
201(154*10^224061-1)/9224063Serge Batalov12/2014
202234178^9+9^234178223463Anatoly F. Selevich07/2011
20311^213654-180222498Enzo Doria01/2013
204(10^221654+179)/9221654Serge Batalov12/2014
20510^221631+247617221632Patrick De Geest10/2013
20610^221631-9221631Alexander Gramolin02/2011
2072^733114-24555220690Enzo Doria09/2013
2082^731891-636259220322Enzo Doria12/2013
2092^731124-25539220091Enzo Doria09/2013
2102^730547-25581219917Enzo Doria09/2013
211L(1051849)219824Renaud Lifchitz03/2009
21211^210961-240219694Enzo Doria01/2013
2132^729611-113437219635Enzo Doria08/2014
214F(1049897)219416Henri Lifchitz10/2008
21533^144412+2219292Robert Price04/2015
2162^727729-114073219069Enzo Doria12/2014
217(109*10^217360-1)/9217362Serge Batalov12/2014
218tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
2192^718756-114107216368Enzo Doria12/2014
220277^88301-276^88301215674Jean-Louis Charton06/2012
221227^91413-40215372Enzo Doria04/2015
222tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
22311^206081-10^206081214612Jean-Louis Charton10/2011
2242^712603-25357214515Enzo Doria09/2013
2252^710730-396765213952Enzo Doria09/2013
2262^708468-114329213271Enzo Doria02/2015
227(163*10^212779-1)/9212781Serge Batalov12/2014
2282^704577-113871212099Enzo Doria10/2014
229(10^211610-91)/9211610Serge Batalov12/2014
230227^89797+2211565Lelio R Paula08/2012
2312^702194-3211382Paul Bourdelais03/2012
2322^701968-113873211314Enzo Doria10/2014
2332^701713-113779211237Enzo Doria09/2014
2342^701449-25201211158Enzo Doria09/2013
2352^701189-25423211079Enzo Doria09/2013
2362^701162-459161211071Enzo Doria05/2015
2372^700400+9385210842Lelio R Paula01/2014
23811^202357-1140210734Enzo Doria12/2012
239(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
240(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
2412^689122-114521207447Enzo Doria04/2015
242(21^156217-1)/20206552Paul Bourdelais04/2010
2432^685578+3206380Paul Bourdelais04/2012
244326^81943-325^81943205941Jean-Louis Charton07/2012
245(2^684127-1)/23765203727205933Jens K. Andersen04/2009
2464^341233-3^341233205443Jean-Louis Charton01/2006
2472^681545+467205166Lelio R Paula11/2013
2482^678561+678561204268Henri Lifchitz05/2006
2492^678101-114043204129Enzo Doria11/2014
2502^676306-114713203589Enzo Doria04/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 29 2015 20:07 (Time in France)

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