PRP Records

Probable Primes Top 10000

(123637 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(7^1264699-1)/61068794Paul Bourdelais01/2014
11(2^3464473-1)/6048745082991771042896Anand Nair10/2014
1210^999999+5934991000000Peter Kaiser02/2013
132^2976221+2041857895932Makoto Morimoto09/2014
14(64*10^779465-1)/81779465Serge Batalov09/2014
15(64*10^762811-1)/9762812Serge Batalov09/2014
16(2^2327417-1)/23915387348002001700606Anand Nair08/2014
17(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
182^2249255+28433677094Ben Maloney / Five or Bust01/2009
19(15^551927+1)/16649116Paul Bourdelais07/2013
20(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
21F(2904353)606974Henri Lifchitz07/2014
22(18^481147+1)/19603970Paul Bourdelais07/2011
23(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
248^615997-7^615997556301Jean-Louis Charton07/2009
25((((((((((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
263^1059503-2^1059503505512Mike Oakes04/2012
27(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
28(6^608099-1)/5473193Paul Bourdelais05/2010
292^1518191+75353457022Ben Maloney / Five or Bust01/2009
30(21^328129-1)/20433858Paul Bourdelais06/2014
31(17^348259+1)/18428514Paul Bourdelais05/2014
32(10^424861-7)/3424861Leonid Durman01/2012
33138^196873-137^196873421285Jean-Louis Charton12/2009
342^1398269+131595420921Makoto Morimoto10/2013
35(3^877843-1)/2418838Paul Bourdelais07/2010
36(89*10^411590+1)/9411591Serge Batalov09/2014
37F(1968721)411439Henri Lifchitz11/2009
38(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
39(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
4015^328574+328574^15386434Serge Batalov05/2014
41(10^380976-7)/3380976Leonid Durman01/2012
422^1257787+1447761378632Makoto Morimoto10/2013
43F(1803059)376817Henri Lifchitz06/2009
44(64*10^360173-1)/243360173Serge Batalov09/2014
452^1191375+8543358640Phil Moore06/2008
46(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
47(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
48F(1636007)341905Henri Lifchitz03/2009
49(11^327001+1)/12340536Paul Bourdelais09/2013
50(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
51(3^700897+1)/4334413Paul Bourdelais04/2010
522^1091469-379369328565Enzo Doria03/2014
532^1061095-1061095319422Henri Lifchitz10/2013
54(7^371669-1)/6314096Paul Bourdelais02/2010
55(11^293831-1)/10305993Paul Bourdelais03/2010
562^1015321-1015321305643Henri Lifchitz08/2013
572^1010751-107709304267Enzo Doria03/2014
58(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
598^336419-7^336419303817Jean-Louis Charton01/2008
6010^300476+3300477Ed Trice10/2012
61314738^9+9^314738300337Anatoly F. Selevich02/2011
627^355039-6^355039300043Jean-Louis Charton05/2011
63(2^986191+1)/3296873Vincent Diepeveen06/2008
642^983620+60451296100Phil Moore03/2008
652^970141-100363292042Enzo Doria02/2014
66(17^233689+1)/18287542Paul Bourdelais09/2013
67(11*2^948635-13)/15285568Renaud Lifchitz11/2011
6810^282493-9^282493282493Jean-Louis Charton03/2007
693^591827-2^591827282374Mike Oakes08/2009
70(21^210599+1)/22278457Paul Bourdelais08/2013
71757^96487-756^96487277796Jean-Louis Charton12/2012
72(5^396413-1)/4277081Paul Bourdelais06/2010
732^906594-113201272912Enzo Doria08/2014
74(7*10^271757-61)/9271757Erik Branger03/2012
752^898762-251511270555Enzo Doria12/2013
76187322*10^270343-187321270349Danilo Nitsche09/2013
7748358*10^270343-48357270348Danilo Nitsche09/2013
78(10^270343-1)/9270343Maksym Voznyy07/2007
79F(1285607)268676Henri Lifchitz11/2008
80(10^268207+1)/11268206Paul Bourdelais02/2010
81(19^209359-1)/18267718Paul Bourdelais08/2010
8211^255426+255426^11265999Serge Batalov05/2014
832^864899-113871260361Enzo Doria10/2014
84(7*10^260198-61)/9260198Erik Branger11/2011
852^863621-113833259976Enzo Doria10/2014
862^859433+494711258716Makoto Morimoto10/2013
87(11*2^857159-13)/15258031Renaud Lifchitz08/2011
882^857016-633113257988Enzo Doria12/2013
892^853682-3911256984Enzo Doria05/2014
9011^246668-90256879Enzo Doria12/2012
9111^246167-90256357Enzo Doria12/2012
922^850700-569049256087Enzo Doria11/2013
932^848178-140291255328Enzo Doria01/2014
9411^243796-90253888Enzo Doria12/2012
9511^242579-60252620Enzo Doria10/2012
96tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
972^832244-403635250531Enzo Doria01/2014
982^829589-113653249732Enzo Doria09/2014
992^824642-362727248242Enzo Doria12/2013
1002^815111-113857245373Enzo Doria10/2014
101846^83761-845^83761245200Jean-Louis Charton12/2012
1022^811842-113675244389Enzo Doria09/2014
1032^808621-113809243420Enzo Doria09/2014
1042^805843-113611242583Enzo Doria08/2014
1052^804277-417933242112Enzo Doria01/2014
1062^803468-269039241868Enzo Doria10/2013
1073^506233-2241535Robert Price11/2013
1082^802025-25999241434Enzo Doria10/2013
109(3^505823+3^252912+1)/7241339Serge Batalov03/2014
1102^798973-26283240515Enzo Doria10/2013
1112^796910-26001239894Enzo Doria10/2013
112(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
11311^227092-90236492Enzo Doria11/2012
1142^780408-113453234927Enzo Doria08/2014
115(5^335429+1)/6234455Paul Bourdelais08/2010
1162^778395-113617234321Enzo Doria08/2014
117(11^223999+1)/12233270Paul Bourdelais02/2010
1182^773679-113425232901Enzo Doria08/2014
11910^232599+192489232600Patrick De Geest12/2013
12010^232599-3232599Markus Tervooren10/2010
1215^332150-18188232163Enzo Doria06/2014
1223^485977-2^485977231870Mike Oakes09/2009
123(20^177967+1)/21231540Paul Bourdelais05/2013
124(3^483611-1)/2230741Paul Bourdelais02/2010
1252^764348-113697230092Enzo Doria09/2014
1262^762841-25905229639Enzo Doria10/2013
1272^761117-113569229120Enzo Doria08/2014
1282^756839+95849227832Makoto Morimoto10/2013
1292^756773-112723227812Enzo Doria07/2014
1302^751426-764321226202Enzo Doria12/2013
131(18^180181-1)/17226176Andy Steward04/2007
1322^750740-3225996Paul Bourdelais03/2012
1332^750525-113743225931Enzo Doria09/2014
134(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
135tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
136234178^9+9^234178223463Anatoly F. Selevich07/2011
13711^213654-180222498Enzo Doria01/2013
13810^221631+247617221632Patrick De Geest10/2013
13910^221631-9221631Alexander Gramolin02/2011
1402^733114-24555220690Enzo Doria09/2013
1412^731891-636259220322Enzo Doria12/2013
1422^731124-25539220091Enzo Doria09/2013
1432^730547-25581219917Enzo Doria09/2013
144L(1051849)219824Renaud Lifchitz03/2009
14511^210961-240219694Enzo Doria01/2013
1462^729611-113437219635Enzo Doria08/2014
147F(1049897)219416Henri Lifchitz10/2008
148tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
149277^88301-276^88301215674Jean-Louis Charton06/2012
150tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
15111^206081-10^206081214612Jean-Louis Charton10/2011
1522^712603-25357214515Enzo Doria09/2013
1532^710730-396765213952Enzo Doria09/2013
1542^704577-113871212099Enzo Doria10/2014
155227^89797+2211565Lelio R Paula08/2012
1562^702194-3211382Paul Bourdelais03/2012
1572^701968-113873211314Enzo Doria10/2014
1582^701713-113779211237Enzo Doria09/2014
1592^701449-25201211158Enzo Doria09/2013
1602^701189-25423211079Enzo Doria09/2013
1612^700400+9385210842Lelio R Paula01/2014
16211^202357-1140210734Enzo Doria12/2012
163(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
164(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
165(21^156217-1)/20206552Paul Bourdelais04/2010
1662^685578+3206380Paul Bourdelais04/2012
167326^81943-325^81943205941Jean-Louis Charton07/2012
168(2^684127-1)/23765203727205933Jens K. Andersen04/2009
1694^341233-3^341233205443Jean-Louis Charton01/2006
1702^681545+467205166Lelio R Paula11/2013
1712^678561+678561204268Henri Lifchitz05/2006
1722^674627-25161203083Enzo Doria09/2013
1735^289937-4^289937202658Jean-Louis Charton03/2013
1742^670539-25045201853Enzo Doria09/2013
1752^669854-113501201647Enzo Doria08/2014
1766^258413-5^258413201085Jean-Louis Charton03/2013
177(53*10^198529+1)/9198530Serge Batalov07/2010
178(18^157051-1)/17197141Paul Bourdelais03/2010
179(44*10^196684+1)/9196685Serge Batalov07/2010
1802^648619-24835195254Enzo Doria09/2013
1812^648190-24737195125Enzo Doria09/2013
18211^187185-90194934Enzo Doria09/2012
18315^165559-14^165559194713Jean-Louis Charton03/2011
184F(931517)194676Henri Lifchitz09/2008
185(5^277183+1)/6193742Paul Bourdelais07/2010
1862^642888-24965193529Enzo Doria09/2013
1872^641690-24737193168Enzo Doria09/2013
1882^640181+467192714Lelio R Paula08/2013
1892^638490-113507192205Enzo Doria08/2014
1902^636158-113627191503Enzo Doria08/2014
191(35*10^191073+1)/9191074Serge Batalov07/2010
1922^633088-113879190579Enzo Doria10/2014
1932^630108+781189682Lelio R Paula08/2013
194L(901657)188436Renaud Lifchitz11/2008
1952^624481-113611187988Enzo Doria08/2014
1962^624077-112723187866Enzo Doria07/2014
1972^622005-24091187243Enzo Doria08/2013
1982^620929-113203186919Enzo Doria07/2014
1992^620347-1777186744Lelio R Paula07/2013
20011^179143-4170186559Enzo Doria12/2012
201(5^266863+1)/6186529Paul Bourdelais07/2010
2022^617250+9385185811Lelio R Paula07/2013
203(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
2045^265007-4^265007185232Jean-Louis Charton02/2013
205(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840185052Serge Batalov07/2013
206(9^193247+1)/10184404Paul Bourdelais02/2010
2072^611628-24537184119Enzo Doria08/2013
2082^610401+1277183750Lelio R Paula07/2013
20911^176176-240183469Enzo Doria11/2012
2102^606560-357182593Enzo Doria05/2014
211(20^140053+1)/21182212Paul Bourdelais04/2010
2122^605174-112751182176Enzo Doria06/2014
21311^174145-360181354Enzo Doria10/2012
2142^602351-396765181326Enzo Doria08/2013
2152^601957-113833181208Enzo Doria09/2014
21666^99581-65^99581181193Robert Price09/2013
2172^601023-113851180926Enzo Doria10/2014
2182^599702-369885180529Enzo Doria11/2013
219Gamma-Prime(179849)179849Eric W. Weisstein06/2011
2203^375887-112696179344Enzo Doria07/2014
221(2^148330+1)^4-2178608Cletus Emmanuel12/2003
222(18^142031-1)/17178287Paul Bourdelais03/2010
2232^590762-396765177838Enzo Doria08/2013
224ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
2252^588912-113519177281Enzo Doria08/2014
2262^587560-113699176874Enzo Doria09/2014
2275^252763-12862176674Enzo Doria05/2014
2282^585832-112799176354Enzo Doria07/2014
22910^175608+2971175609Mike Oakes05/2010
23010^175608-55829175608Patrick De Geest09/2013
2312^582860-23829175459Enzo Doria08/2013
2322^582670-23913175402Enzo Doria08/2013
2332^578583-113917174171Enzo Doria10/2014
234(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
2359^180804+2172531Robert Price08/2014
2363^361608+2172531Robert Price08/2014
2375^246497-4^246497172295Jean-Louis Charton11/2008
238(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
23911^164009-270170798Enzo Doria10/2012
2403^357706-112358170670Enzo Doria07/2014
241TheodorusPrime(170657)170657Eric W. Weisstein08/2013
2422^566496+7170533Donovan Johnson07/2006
243(7^201653+1)/8170416Paul Bourdelais02/2010
2442^558125-113661168013Enzo Doria09/2014
245393^64747-392^64747167980Jean-Louis Charton08/2012
246589^60089-588^60089166454Jean-Louis Charton09/2012
24711^159756-2424166369Mike Oakes06/2010
2482^552649-361275166364Enzo Doria05/2014
2492^552628-113669166358Enzo Doria09/2014
2502^551542+19249166031Payam Samidoost08/2002


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 21 2014 09:43 (Time in France)

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