PRP Records

Probable Primes Top 10000

(124730 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(12^769543-1)/11830476Paul Bourdelais12/2014
15(64*10^779465-1)/81779465Serge Batalov09/2014
16(64*10^762811-1)/9762812Serge Batalov09/2014
17(10^718580+269)/9718580Serge Batalov12/2014
18(2^2327417-1)/23915387348002001700606Anand Nair08/2014
19(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
20(10^685224+89)/9685224Serge Batalov12/2014
212^2249255+28433677094Ben Maloney / Five or Bust01/2009
22(10^675470+269)/9675470Serge Batalov12/2014
23(15^551927+1)/16649116Paul Bourdelais07/2013
24(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
25(20^472709-1)/19615008Paul Bourdelais01/2015
26F(2904353)606974Henri Lifchitz07/2014
27(18^481147+1)/19603970Paul Bourdelais07/2011
28(15^505117-1)/14594063Paul Bourdelais01/2015
29(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
308^615997-7^615997556301Jean-Louis Charton07/2009
31((((((((((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
32(18^414269-1)/17520020Paul Bourdelais12/2014
33(20^393257+1)/21511638Paul Bourdelais12/2014
34(14^441697-1)/13506241Paul Bourdelais12/2014
353^1059503-2^1059503505512Mike Oakes04/2012
36(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
37(6^608099-1)/5473193Paul Bourdelais05/2010
382^1518191+75353457022Ben Maloney / Five or Bust01/2009
39(21^328129-1)/20433858Paul Bourdelais06/2014
40(17^348259+1)/18428514Paul Bourdelais05/2014
41(10^427912+89)/9427912Serge Batalov12/2014
42(10^424861-7)/3424861Leonid Durman01/2012
43138^196873-137^196873421285Jean-Louis Charton12/2009
442^1398269+131595420921Makoto Morimoto10/2013
45(3^877843-1)/2418838Paul Bourdelais07/2010
46(89*10^411590+1)/9411591Serge Batalov09/2014
47F(1968721)411439Henri Lifchitz11/2009
48(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
49(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
5015^328574+328574^15386434Serge Batalov05/2014
51(10^380976-7)/3380976Leonid Durman01/2012
522^1257787+1447761378632Makoto Morimoto10/2013
53F(1803059)376817Henri Lifchitz06/2009
54(64*10^360173-1)/243360173Serge Batalov09/2014
552^1191375+8543358640Phil Moore06/2008
56(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
57(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
58(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
59F(1636007)341905Henri Lifchitz03/2009
60(11^327001+1)/12340536Paul Bourdelais09/2013
61(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
62(3^700897+1)/4334413Paul Bourdelais04/2010
632^1091469-379369328565Enzo Doria03/2014
642^1061095-1061095319422Henri Lifchitz10/2013
65(7^371669-1)/6314096Paul Bourdelais02/2010
66(11^293831-1)/10305993Paul Bourdelais03/2010
672^1015321-1015321305643Henri Lifchitz08/2013
682^1010751-107709304267Enzo Doria03/2014
69(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
708^336419-7^336419303817Jean-Louis Charton01/2008
7110^300476+3300477Ed Trice10/2012
72314738^9+9^314738300337Anatoly F. Selevich02/2011
737^355039-6^355039300043Jean-Louis Charton05/2011
742^992525-114199298780Enzo Doria12/2014
75(2^986191+1)/3296873Vincent Diepeveen06/2008
762^984131-1828009296253Enzo Doria01/2015
772^983620+60451296100Phil Moore03/2008
782^970141-100363292042Enzo Doria02/2014
79(17^233689+1)/18287542Paul Bourdelais09/2013
80(11*2^948635-13)/15285568Renaud Lifchitz11/2011
812^948374-114137285490Enzo Doria01/2015
822^939881-114115282933Enzo Doria12/2014
8310^282493-9^282493282493Jean-Louis Charton03/2007
843^591827-2^591827282374Mike Oakes08/2009
85(5*10^280710+1)/3280711Serge Batalov10/2014
86(21^210599+1)/22278457Paul Bourdelais08/2013
87757^96487-756^96487277796Jean-Louis Charton12/2012
88(5^396413-1)/4277081Paul Bourdelais06/2010
892^915576-114137275616Enzo Doria01/2015
902^906594-113201272912Enzo Doria08/2014
91(7*10^271757-61)/9271757Erik Branger03/2012
922^898762-251511270555Enzo Doria12/2013
93187322*10^270343-187321270349Danilo Nitsche09/2013
9448358*10^270343-48357270348Danilo Nitsche09/2013
95(10^270343-1)/9270343Maksym Voznyy07/2007
962^896616-114179269909Enzo Doria12/2014
97F(1285607)268676Henri Lifchitz11/2008
98(10^268207+1)/11268206Paul Bourdelais02/2010
99(19^209359-1)/18267718Paul Bourdelais08/2010
10011^255426+255426^11265999Serge Batalov05/2014
1012^873288-269262886Yves Minet01/2015
1022^869601-163261776Yves Minet01/2015
1032^869035-114181261606Enzo Doria12/2014
1042^864899-113871260361Enzo Doria10/2014
105(7*10^260198-61)/9260198Erik Branger11/2011
1062^863621-113833259976Enzo Doria10/2014
1072^859433+494711258716Makoto Morimoto10/2013
108(11*2^857159-13)/15258031Renaud Lifchitz08/2011
1092^857016-633113257988Enzo Doria12/2013
1102^855732-113969257602Enzo Doria10/2014
1112^853682-3911256984Enzo Doria05/2014
11211^246668-90256879Enzo Doria12/2012
1132^851904-113939256449Enzo Doria10/2014
11411^246167-90256357Enzo Doria12/2012
1152^850700-569049256087Enzo Doria11/2013
1162^849177-114025255628Enzo Doria12/2014
1172^848178-140291255328Enzo Doria01/2014
11811^243796-90253888Enzo Doria12/2012
11911^242579-60252620Enzo Doria10/2012
120tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
1212^832244-403635250531Enzo Doria01/2014
1222^829589-113653249732Enzo Doria09/2014
12310^249010-21249010Serge Batalov12/2014
1242^824991-114121248348Enzo Doria12/2014
1252^824642-362727248242Enzo Doria12/2013
1262^824565-114265248219Enzo Doria01/2015
127(73*10^248145-1)/9248146Robert Price01/2015
1282^821590-114167247324Enzo Doria12/2014
1292^815111-113857245373Enzo Doria10/2014
130846^83761-845^83761245200Jean-Louis Charton12/2012
1312^811842-113675244389Enzo Doria09/2014
1322^808621-113809243420Enzo Doria09/2014
1332^805843-113611242583Enzo Doria08/2014
1342^804277-417933242112Enzo Doria01/2014
1352^803468-269039241868Enzo Doria10/2013
1363^506233-2241535Robert Price11/2013
1372^802025-25999241434Enzo Doria10/2013
138(3^505823+3^252912+1)/7241339Serge Batalov03/2014
1392^798973-26283240515Enzo Doria10/2013
1402^796910-26001239894Enzo Doria10/2013
141(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
14211^227092-90236492Enzo Doria11/2012
14319^184650-2236122Robert Price10/2014
1442^782634-113981235597Enzo Doria11/2014
1452^780408-113453234927Enzo Doria08/2014
146(5^335429+1)/6234455Paul Bourdelais08/2010
1472^778395-113617234321Enzo Doria08/2014
1482^776060-114029233618Enzo Doria11/2014
149(11^223999+1)/12233270Paul Bourdelais02/2010
15021^176191-20^176191232964Jean-Louis Charton01/2015
1512^773679-113425232901Enzo Doria08/2014
15210^232599+192489232600Patrick De Geest12/2013
15310^232599-3232599Markus Tervooren10/2010
1545^332150-18188232163Enzo Doria06/2014
1553^485977-2^485977231870Mike Oakes09/2009
1562^770082-114161231818Enzo Doria01/2015
157(20^177967+1)/21231540Paul Bourdelais05/2013
158(3^483611-1)/2230741Paul Bourdelais02/2010
159(10^230706+179)/9230706Serge Batalov12/2014
1602^764348-113697230092Enzo Doria09/2014
1612^762841-25905229639Enzo Doria10/2013
1622^761117-113569229120Enzo Doria08/2014
1632^756839+95849227832Makoto Morimoto10/2013
1642^756773-112723227812Enzo Doria07/2014
1652^755097-114193227307Enzo Doria12/2014
1662^751426-764321226202Enzo Doria12/2013
167(18^180181-1)/17226176Andy Steward04/2007
1682^750740-3225996Paul Bourdelais03/2012
1692^750525-113743225931Enzo Doria09/2014
170(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
171tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
1722^746461-114043224708Enzo Doria11/2014
173(154*10^224061-1)/9224063Serge Batalov12/2014
174234178^9+9^234178223463Anatoly F. Selevich07/2011
17511^213654-180222498Enzo Doria01/2013
176(10^221654+179)/9221654Serge Batalov12/2014
17710^221631+247617221632Patrick De Geest10/2013
17810^221631-9221631Alexander Gramolin02/2011
1792^733114-24555220690Enzo Doria09/2013
1802^731891-636259220322Enzo Doria12/2013
1812^731124-25539220091Enzo Doria09/2013
1822^730547-25581219917Enzo Doria09/2013
183L(1051849)219824Renaud Lifchitz03/2009
18411^210961-240219694Enzo Doria01/2013
1852^729611-113437219635Enzo Doria08/2014
186F(1049897)219416Henri Lifchitz10/2008
1872^727729-114073219069Enzo Doria12/2014
188(109*10^217360-1)/9217362Serge Batalov12/2014
189tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
1902^718756-114107216368Enzo Doria12/2014
191277^88301-276^88301215674Jean-Louis Charton06/2012
192tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
19311^206081-10^206081214612Jean-Louis Charton10/2011
1942^712603-25357214515Enzo Doria09/2013
1952^710730-396765213952Enzo Doria09/2013
196(163*10^212779-1)/9212781Serge Batalov12/2014
1972^704577-113871212099Enzo Doria10/2014
198(10^211610-91)/9211610Serge Batalov12/2014
199227^89797+2211565Lelio R Paula08/2012
2002^702194-3211382Paul Bourdelais03/2012
2012^701968-113873211314Enzo Doria10/2014
2022^701713-113779211237Enzo Doria09/2014
2032^701449-25201211158Enzo Doria09/2013
2042^701189-25423211079Enzo Doria09/2013
2052^700400+9385210842Lelio R Paula01/2014
20611^202357-1140210734Enzo Doria12/2012
207(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
208(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
209(21^156217-1)/20206552Paul Bourdelais04/2010
2102^685578+3206380Paul Bourdelais04/2012
211326^81943-325^81943205941Jean-Louis Charton07/2012
212(2^684127-1)/23765203727205933Jens K. Andersen04/2009
2134^341233-3^341233205443Jean-Louis Charton01/2006
2142^681545+467205166Lelio R Paula11/2013
2152^678561+678561204268Henri Lifchitz05/2006
2162^678101-114043204129Enzo Doria11/2014
2172^674627-25161203083Enzo Doria09/2013
2185^289937-4^289937202658Jean-Louis Charton03/2013
2192^670539-25045201853Enzo Doria09/2013
2202^669854-113501201647Enzo Doria08/2014
221(145*10^201504-1)/9201506Serge Batalov12/2014
2226^258413-5^258413201085Jean-Louis Charton03/2013
223(172*10^200746-1)/9200748Serge Batalov12/2014
224(10^200001+149)/3200001Serge Batalov12/2014
225(53*10^198529+1)/9198530Serge Batalov07/2010
226(18^157051-1)/17197141Paul Bourdelais03/2010
227(44*10^196684+1)/9196685Serge Batalov07/2010
228(103*10^195478-1)/3195480Serge Batalov12/2014
2292^648619-24835195254Enzo Doria09/2013
2302^648190-24737195125Enzo Doria09/2013
23111^187185-90194934Enzo Doria09/2012
23215^165559-14^165559194713Jean-Louis Charton03/2011
233F(931517)194676Henri Lifchitz09/2008
234(112*10^194150-1)/3194152Serge Batalov12/2014
235(5^277183+1)/6193742Paul Bourdelais07/2010
2362^642888-24965193529Enzo Doria09/2013
2372^641690-24737193168Enzo Doria09/2013
2382^640181+467192714Lelio R Paula08/2013
2392^638490-113507192205Enzo Doria08/2014
2402^636158-113627191503Enzo Doria08/2014
241(35*10^191073+1)/9191074Serge Batalov07/2010
2422^633088-113879190579Enzo Doria10/2014
2432^630108+781189682Lelio R Paula08/2013
244(10^189385-61)/3189385Serge Batalov12/2014
245L(901657)188436Renaud Lifchitz11/2008
246(10^188164+359)/9188164Serge Batalov12/2014
2472^624481-113611187988Enzo Doria08/2014
2482^624077-112723187866Enzo Doria07/2014
2492^623714-114035187757Enzo Doria11/2014
2502^622005-24091187243Enzo Doria08/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 24 2015 17:23 (Time in France)

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