PRP Records

Probable Primes Top 10000

(122749 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
9(7^1264699-1)/61068794Paul Bourdelais01/2014
1010^999999+5934991000000Peter Kaiser02/2013
11(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
122^2249255+28433677094Ben Maloney / Five or Bust01/2009
13(15^551927+1)/16649116Paul Bourdelais07/2013
14(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
15F(2904353)606974Henri Lifchitz07/2014
16(18^481147+1)/19603970Paul Bourdelais07/2011
17(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
188^615997-7^615997556301Jean-Louis Charton07/2009
19((((((((((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
203^1059503-2^1059503505512Mike Oakes04/2012
21(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
22(6^608099-1)/5473193Paul Bourdelais05/2010
232^1518191+75353457022Ben Maloney / Five or Bust01/2009
24(21^328129-1)/20433858Paul Bourdelais06/2014
25(17^348259+1)/18428514Paul Bourdelais05/2014
26(10^424861-7)/3424861Leonid Durman01/2012
27138^196873-137^196873421285Jean-Louis Charton12/2009
282^1398269+131595420921Makoto Morimoto10/2013
29(3^877843-1)/2418838Paul Bourdelais07/2010
30F(1968721)411439Henri Lifchitz11/2009
31(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
32(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
3315^328574+328574^15386434Serge Batalov05/2014
34(10^380976-7)/3380976Leonid Durman01/2012
352^1257787+1447761378632Makoto Morimoto10/2013
36F(1803059)376817Henri Lifchitz06/2009
372^1191375+8543358640Phil Moore06/2008
38(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
39(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
40F(1636007)341905Henri Lifchitz03/2009
41(11^327001+1)/12340536Paul Bourdelais09/2013
42(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
43(3^700897+1)/4334413Paul Bourdelais04/2010
442^1091469-379369328565Enzo Doria03/2014
452^1061095-1061095319422Henri Lifchitz10/2013
46(7^371669-1)/6314096Paul Bourdelais02/2010
47(11^293831-1)/10305993Paul Bourdelais03/2010
482^1015321-1015321305643Henri Lifchitz08/2013
492^1010751-107709304267Enzo Doria03/2014
50(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
518^336419-7^336419303817Jean-Louis Charton01/2008
5210^300476+3300477Ed Trice10/2012
53314738^9+9^314738300337Anatoly F. Selevich02/2011
547^355039-6^355039300043Jean-Louis Charton05/2011
55(2^986191+1)/3296873Vincent Diepeveen06/2008
562^983620+60451296100Phil Moore03/2008
572^970141-100363292042Enzo Doria02/2014
58(17^233689+1)/18287542Paul Bourdelais09/2013
59(11*2^948635-13)/15285568Renaud Lifchitz11/2011
6010^282493-9^282493282493Jean-Louis Charton03/2007
613^591827-2^591827282374Mike Oakes08/2009
62(21^210599+1)/22278457Paul Bourdelais08/2013
63757^96487-756^96487277796Jean-Louis Charton12/2012
64(5^396413-1)/4277081Paul Bourdelais06/2010
65(7*10^271757-61)/9271757Erik Branger03/2012
662^898762-251511270555Enzo Doria12/2013
67187322*10^270343-187321270349Danilo Nitsche09/2013
6848358*10^270343-48357270348Danilo Nitsche09/2013
69(10^270343-1)/9270343Maksym Voznyy07/2007
70F(1285607)268676Henri Lifchitz11/2008
71(10^268207+1)/11268206Paul Bourdelais02/2010
72(19^209359-1)/18267718Paul Bourdelais08/2010
7311^255426+255426^11265999Serge Batalov05/2014
74(7*10^260198-61)/9260198Erik Branger11/2011
752^859433+494711258716Makoto Morimoto10/2013
76(11*2^857159-13)/15258031Renaud Lifchitz08/2011
772^857016-633113257988Enzo Doria12/2013
782^853682-3911256984Enzo Doria05/2014
7911^246668-90256879Enzo Doria12/2012
8011^246167-90256357Enzo Doria12/2012
812^850700-569049256087Enzo Doria11/2013
822^848178-140291255328Enzo Doria01/2014
8311^243796-90253888Enzo Doria12/2012
8411^242579-60252620Enzo Doria10/2012
85tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
862^832244-403635250531Enzo Doria01/2014
872^824642-362727248242Enzo Doria12/2013
88846^83761-845^83761245200Jean-Louis Charton12/2012
892^804277-417933242112Enzo Doria01/2014
902^803468-269039241868Enzo Doria10/2013
913^506233-2241535Robert Price11/2013
922^802025-25999241434Enzo Doria10/2013
93(3^505823+3^252912+1)/7241339Serge Batalov03/2014
942^798973-26283240515Enzo Doria10/2013
952^796910-26001239894Enzo Doria10/2013
96(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
9711^227092-90236492Enzo Doria11/2012
98(5^335429+1)/6234455Paul Bourdelais08/2010
99(11^223999+1)/12233270Paul Bourdelais02/2010
10010^232599+192489232600Patrick De Geest12/2013
10110^232599-3232599Markus Tervooren10/2010
1025^332150-18188232163Enzo Doria06/2014
1033^485977-2^485977231870Mike Oakes09/2009
104(20^177967+1)/21231540Paul Bourdelais05/2013
105(3^483611-1)/2230741Paul Bourdelais02/2010
1062^762841-25905229639Enzo Doria10/2013
1072^756839+95849227832Makoto Morimoto10/2013
1082^756773-112723227812Enzo Doria07/2014
1092^751426-764321226202Enzo Doria12/2013
110(18^180181-1)/17226176Andy Steward04/2007
1112^750740-3225996Paul Bourdelais03/2012
112tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
113234178^9+9^234178223463Anatoly F. Selevich07/2011
11411^213654-180222498Enzo Doria01/2013
11510^221631+247617221632Patrick De Geest10/2013
11610^221631-9221631Alexander Gramolin02/2011
1172^733114-24555220690Enzo Doria09/2013
1182^731891-636259220322Enzo Doria12/2013
1192^731124-25539220091Enzo Doria09/2013
1202^730547-25581219917Enzo Doria09/2013
121L(1051849)219824Renaud Lifchitz03/2009
12211^210961-240219694Enzo Doria01/2013
123F(1049897)219416Henri Lifchitz10/2008
124tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
125277^88301-276^88301215674Jean-Louis Charton06/2012
126tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
12711^206081-10^206081214612Jean-Louis Charton10/2011
1282^712603-25357214515Enzo Doria09/2013
1292^710730-396765213952Enzo Doria09/2013
130227^89797+2211565Lelio R Paula08/2012
1312^702194-3211382Paul Bourdelais03/2012
1322^701449-25201211158Enzo Doria09/2013
1332^701189-25423211079Enzo Doria09/2013
1342^700400+9385210842Lelio R Paula01/2014
13511^202357-1140210734Enzo Doria12/2012
136(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
137(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
138(21^156217-1)/20206552Paul Bourdelais04/2010
1392^685578+3206380Paul Bourdelais04/2012
140326^81943-325^81943205941Jean-Louis Charton07/2012
141(2^684127-1)/23765203727205933Jens K. Andersen04/2009
1424^341233-3^341233205443Jean-Louis Charton01/2006
1432^681545+467205166Lelio R Paula11/2013
1442^678561+678561204268Henri Lifchitz05/2006
1452^674627-25161203083Enzo Doria09/2013
1465^289937-4^289937202658Jean-Louis Charton03/2013
1472^670539-25045201853Enzo Doria09/2013
1486^258413-5^258413201085Jean-Louis Charton03/2013
149(53*10^198529+1)/9198530Serge Batalov07/2010
150(18^157051-1)/17197141Paul Bourdelais03/2010
151(44*10^196684+1)/9196685Serge Batalov07/2010
1522^648619-24835195254Enzo Doria09/2013
1532^648190-24737195125Enzo Doria09/2013
15411^187185-90194934Enzo Doria09/2012
15515^165559-14^165559194713Jean-Louis Charton03/2011
156F(931517)194676Henri Lifchitz09/2008
157(5^277183+1)/6193742Paul Bourdelais07/2010
1582^642888-24965193529Enzo Doria09/2013
1592^641690-24737193168Enzo Doria09/2013
1602^640181+467192714Lelio R Paula08/2013
161(35*10^191073+1)/9191074Serge Batalov07/2010
1622^630108+781189682Lelio R Paula08/2013
163L(901657)188436Renaud Lifchitz11/2008
1642^624077-112723187866Enzo Doria07/2014
1652^622005-24091187243Enzo Doria08/2013
1662^620929-113203186919Enzo Doria07/2014
1672^620347-1777186744Lelio R Paula07/2013
16811^179143-4170186559Enzo Doria12/2012
169(5^266863+1)/6186529Paul Bourdelais07/2010
1702^617250+9385185811Lelio R Paula07/2013
171(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
1725^265007-4^265007185232Jean-Louis Charton02/2013
173(((((((((((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
174(9^193247+1)/10184404Paul Bourdelais02/2010
1752^611628-24537184119Enzo Doria08/2013
1762^610401+1277183750Lelio R Paula07/2013
17711^176176-240183469Enzo Doria11/2012
1782^606560-357182593Enzo Doria05/2014
179(20^140053+1)/21182212Paul Bourdelais04/2010
1802^605174-112751182176Enzo Doria06/2014
18111^174145-360181354Enzo Doria10/2012
1822^602351-396765181326Enzo Doria08/2013
18366^99581-65^99581181193Robert Price09/2013
1842^599702-369885180529Enzo Doria11/2013
185Gamma-Prime(179849)179849Eric W. Weisstein06/2011
1863^375887-112696179344Enzo Doria07/2014
187(2^148330+1)^4-2178608Cletus Emmanuel12/2003
188(18^142031-1)/17178287Paul Bourdelais03/2010
1892^590762-396765177838Enzo Doria08/2013
190ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
1915^252763-12862176674Enzo Doria05/2014
1922^585832-112799176354Enzo Doria07/2014
19310^175608+2971175609Mike Oakes05/2010
19410^175608-55829175608Patrick De Geest09/2013
1952^582860-23829175459Enzo Doria08/2013
1962^582670-23913175402Enzo Doria08/2013
197(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
1985^246497-4^246497172295Jean-Louis Charton11/2008
199(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
20011^164009-270170798Enzo Doria10/2012
2013^357706-112358170670Enzo Doria07/2014
202TheodorusPrime(170657)170657Eric W. Weisstein08/2013
2032^566496+7170533Donovan Johnson07/2006
204(7^201653+1)/8170416Paul Bourdelais02/2010
205393^64747-392^64747167980Jean-Louis Charton08/2012
206589^60089-588^60089166454Jean-Louis Charton09/2012
20711^159756-2424166369Mike Oakes06/2010
2082^552649-361275166364Enzo Doria05/2014
2092^551542+19249166031Payam Samidoost08/2002
2102^551535-23821166029Enzo Doria08/2013
2112^551507-23557166021Enzo Doria08/2013
2122^550000-23625165567Enzo Doria08/2013
213-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
21411^158160-60164707Enzo Doria07/2012
215919^54919-918^54919162743Jean-Louis Charton01/2013
2163^340694-112960162553Enzo Doria07/2014
2179^170099-8^170099162316Jean-Louis Charton05/2005
2182^538473-112723162097Enzo Doria06/2014
2192^538104+1531161986Lelio R Paula01/2013
2202^537815-22737161899Enzo Doria07/2013
2212^536569-22881161524Enzo Doria07/2013
2222^535205-23295161113Enzo Doria08/2013
2232^534359-23229160859Enzo Doria08/2013
22467^88037-66^88037160763Robert Price10/2013
2252^533665-23335160650Enzo Doria08/2013
2263^336353-2^336353160482Mike Oakes10/2007
2272^528000-23307158944Enzo Doria08/2013
228(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
2292^527553-23401158810Enzo Doria08/2013
23011^152420-210158730Enzo Doria09/2012
2312^526849-113233158598Enzo Doria07/2014
2322^526375-23115158455Enzo Doria08/2013
2332^526028-112793158351Enzo Doria07/2014
2342^525690-9221158249Lelio R Paula01/2013
2352^524515-23245157895Enzo Doria08/2013
2362^524499-109087157890Enzo Doria04/2014
2372^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
238(46^94841+1)/47157696Robert Price01/2014
2392^521348-23397156942Enzo Doria08/2013
2408^173687-7^173687156855Jean-Louis Charton09/2004
241(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
24253^90679-52^90679156356Robert Price01/2013
2432^517698+4429155843Lelio R Paula01/2013
2442^517543-113257155796Enzo Doria07/2014
24531^104309-30^104309155563Henri Lifchitz08/2013
2462^515644-113247155225Enzo Doria07/2014
247EPrime(155025)155025Eric W. Weisstein10/2010
2482^513306-113201154521Enzo Doria07/2014
2492^511077-112723153850Enzo Doria06/2014
25069^83653-68^83653153826Robert Price12/2013


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 01 2014 14:03 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!