PRP Records

Probable Primes Top 10000

(46339 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 theses 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 (> 10000) Who ? When ?
12^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
22^4583176+21311379674Ben Maloney / Five or Bust09/2009
32^2249255+28433677094Ben Maloney / Five or Bust01/2009
48^615997-7^615997556301Jean-Louis Charton07/2009
52^1518191+75353457022Ben Maloney / Five or Bust01/2009
6138^196873-137^196873421285Jean-Louis Charton12/2009
7F(1968721)411439Henri Lifchitz11/2009
8(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
9F(1803059)376817Henri Lifchitz06/2009
102^1191375+8543358640Phil Moore06/2008
11(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
12F(1636007)341905Henri Lifchitz03/2009
13(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
148^336419-7^336419303817Jean-Louis Charton01/2008
15(2^986191+1)/3296873Vincent Diepeveen06/2008
162^983620+60451296100Phil Moore03/2008
1710^282493-9^282493282493Jean-Louis Charton03/2007
183^591827-2^591827282374Mike Oakes08/2009
19(10^270343-1)/9270343Maksym Voznyy07/2007
20F(1285607)268676Henri Lifchitz11/2008
213^485977-2^485977231870Mike Oakes09/2009
22Phi(180181,18)226176Andy Steward04/2007
23L(1051849)219824Renaud Lifchitz03/2009
24F(1049897)219416Henri Lifchitz10/2008
25(2^684127-1)/23765203727205933Jens K. Andersen04/2009
264^341233-3^341233205443Jean-Louis Charton01/2006
272^678561+678561204268Henri Lifchitz05/2006
28F(931517)194676Henri Lifchitz09/2008
29L(901657)188436Renaud Lifchitz11/2008
30(9^193247+1)/10184404Paul Bourdelais02/2010
31(2^148330+1)^4-2178608Cletus Emmanuel12/2003
325^246497-4^246497172295Jean-Louis Charton11/2008
332^566496+7170533Donovan Johnson07/2006
342^551542+19249166031Payam Samidoost08/2002
359^170099-8^170099162316Jean-Louis Charton05/2005
363^336353-2^336353160482Mike Oakes10/2007
378^173687-7^173687156855Jean-Louis Charton09/2004
382^505431-505431152150Henri Lifchitz04/2005
392^500899-500899150786Henri Lifchitz04/2005
402^481801-481801145037Henri Lifchitz03/2005
41L(692147)144651Henri Lifchitz10/2008
422^479844+3144448Donovan Johnson06/2006
43(5^201359-1)/4140744Paul Bourdelais12/2008
44555555*2^458524+1513138036Darren Bedwell08/2009
452^458465+2^32+1138012T. D. Noe06/2007
462^457822+105137819Donovan Johnson06/2006
47L(651821)136223Henri Lifchitz09/2008
48(5^193939+1)/6135557Paul Bourdelais12/2008
49L(637751)133283Henri Lifchitz09/2008
50L(631181)131910Henri Lifchitz09/2008
51L(616787)128901Henri Lifchitz09/2008
52F(604711)126377Henri Lifchitz02/2005
532^419637+29126324Henri Lifchitz02/2006
542^414032-5124637Henri Lifchitz07/2006
55F(593689)124074Henri Lifchitz01/2005
56(5^177337+1)/6123953Paul Bourdelais11/2008
57F(590041)123311Henri Lifchitz01/2005
58(2^406583-1)/813167122388Jens K. Andersen02/2009
593^256199-2^256199122238Mike Oakes06/2005
602^398877+105120074Donovan Johnson01/2006
61L(574219)120005Renaud Lifchitz03/2004
622^394034-3118617M. Frind & P. Underwood09/2002
6331^78759-30117459Theodore Burton02/2007
642^388180+93116854Donovan Johnson07/2008
652^384834+93115847Donovan Johnson07/2008
66569^41651-568^41651114754Jean-Louis Charton11/2009
67(2^374321+1)/3112682H.&R. Lifchitz12/2000
68L(532277)111240Renaud Lifchitz03/2004
694^184463-3^184463111058Jean-Louis Charton12/2004
70(2^365689+2^182845+1)/5110083Jean Penné11/2006
712^364982-5109871Henri Lifchitz04/2006
722^363120+3109311Donovan Johnson04/2006
73(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
742^354946-3106850M. Frind & P. Underwood08/2002
75(7^126037-1)/6106513Paul Bourdelais09/2008
766^135647-5^135647105554Jean-Louis Charton02/2009
77(4*10^103703-1)/3103704Serge Batalov08/2009
78(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
7943^63177-42103198Theodore Burton02/2007
802^341134+2533102692Henri Lifchitz09/2005
81(6^131891+1)/7102631Paul Bourdelais01/2010
822^340688-29102558Henri Lifchitz05/2005
832^338796+93101988Donovan Johnson06/2008
84lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
852^336958+79101435Lelio R Paula10/2009
862^336942+169101430Lelio R Paula10/2009
872^335858+153101104Lelio R Paula10/2009
882^335586+169101022Lelio R Paula10/2009
892^334524+145100702Lelio R Paula07/2009
904832563059*2^333333+30029100353Donovan Johnson01/2008
91(2^333227-2^166614+1)/5100311Jean Penné11/2006
9217^81417-16100180Theodore Burton11/2005
9325206!+p(4114)100001Henri Lifchitz09/2005
9425206!-p(5447)100001Henri Lifchitz10/2005
9525206!-p(12402)100001Henri Lifchitz04/2006
9625206!-p(16290)100001Henri Lifchitz09/2006
9725206!-p(19647)100001Henri Lifchitz02/2007
982^332194+11473100001Henri Lifchitz03/2007
9910^100000+342909100001Milton L. Brown12/2007
10110^99999+309403100000Daniel Heuer01/2004
10010^100000-260199100000Patrick De Geest01/2010
10210^99999-5951199999Patrick De Geest07/2009
10348^58543-47^5854398425Jean-Louis Charton11/2005
10413^87557-12^8755797534Jean-Louis Charton12/2008
10561^54517-60^5451797331Jean-Louis Charton09/2005
106GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
107(28*10^96743+71)/996744Serge Batalov12/2008
10814^83869-13^8386996125Jean-Louis Charton01/2009
1092^317024+9395434Donovan Johnson06/2008
110(23*10^95326+1)/395327Serge Batalov05/2009
1112^316140-595168Henri Lifchitz02/2006
112(1000547^15749+1)/100054894492Faysal YAtim12/2008
1132^311471+31146993763Renaud Lifchitz01/2003
114(2^311027-2^155514+1)/593628Jean Penné11/2006
115(1000907^15583+1)/100090893499Faysal YAtim04/2009
1163^195430-293244Theodore Burton02/2007
11741^57783-4093192Theodore Burton02/2007
1182^308809+3796792961Phil Moore03/2008
119L(443609)92709Renaud Lifchitz11/2003
1202^307407-307407^292539Henri Lifchitz05/2005
1212^307125-4978992454Henri Lifchitz08/2005
122(2^305867-2^152934+1)/592075Jean Penné11/2006
1232^305676+9392018Donovan Johnson06/2008
124(7*10^91856-61)/991856Erik Branger12/2009
1252^304015+6413391518David Broadhurst06/2002
1262^303224+253391280Henri Lifchitz05/2005
1277*10^91215+391216Erik Branger11/2009
1282^302949+8191197Henri Lifchitz02/2007
1292^302505+8191064Henri Lifchitz02/2007
1302^301683-301683^290816Henri Lifchitz05/2005
131F(433781)90655Henri Lifchitz09/2003
13210^90000+886990001Patrick De Geest12/2009
13410^89999+8293990000Dirk Augustin04/2007
13310^90000-14034390000Patrick De Geest12/2009
13510^89999-19489189999Patrick De Geest11/2009
136(7^106187+1)/889738Paul Bourdelais04/2008
1374^148663-3^14866389505Jean-Louis Charton11/2005
1382^296016+8189110Henri Lifchitz02/2007
13931^59713-3089054Theodore Burton02/2007
14019^69025-1888266Theodore Burton01/2006
1412^292929+4387788181Donovan Johnson04/2005
1426^113177-5^11317788069Jean-Louis Charton01/2009
14391382^9+9^9138287201Andrey Kulsha11/2004
144(10^86453-1)/986453Lew Baxter10/2000
1452^284133-385533M. Frind & P. Underwood07/2002
14619834^19834+894785235Henri Lifchitz11/2004
147((1+sqrt(3)+sqrt(2))^79357-1)*((1+sqrt(3)-sqrt(2))^79357-1)*((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(384849Mike Oakes04/2009
1482^280852+9768184545Yves Minet08/2004
149(141584^16384+1)/6553784390Syoichiro Yamada06/2008
150(2*10^84239+1)/384239Serge Batalov07/2009
1512^276587-93783261Yves Minet10/2009
152F(397379)83047Henri Lifchitz08/2003
1532^275259+8182862Henri Lifchitz01/2007
1543^173191-2^17319182634Mike Oakes02/2004
15511^79133-1082409Theodore Burton11/2005
156(2^271549-1)/23874968248781734Jens K. Andersen02/2009
157(2^271211-1)/61396149515981631Jens K. Andersen02/2009
158(2^269987+1)/381274H.&R. Lifchitz10/2000
159(23*10^81214+1)/381215Serge Batalov06/2009
1602^269490-362381125Yves Minet10/2009
161L(387433)80969Renaud Lifchitz11/2003
162134^37987-133^3798780803Jean-Louis Charton12/2005
1632^268079-192780700Yves Minet10/2009
164(2^267017+1)/380380H.&R. Lifchitz09/2000
16510^80000+8573180001Patrick De Geest10/2009
16610^80000-716980000Patrick De Geest09/2009
16710^79999+2239980000Patrick De Geest09/2009
16810^79999-7487379999Patrick De Geest09/2009
16947^47667-4679704Theodore Burton02/2007
17019^61980-1879258Theodore Burton12/2005
1714^131497-3^13149779170Jean-Louis Charton05/2004
172lucasU(486,25,29457)-5*lucasU(486,25,29456)79137Mike Oakes05/2009
1731000001^13159-1000000^1315978953Jean-Louis Charton10/2003
1742^261856+9876533178827Jason Earls01/2009
1752^261507-228778722Yves Minet04/2009
176L(376121)+F(376122)78605Henri Lifchitz01/2007
177lucasU(2403,1,23229)-lucasU(2403,1,23228)78529Mike Oakes05/2009
17814*10^78362+108978364Jens K. Andersen11/2007
1797^92511-678181Theodore Burton11/2005
180PIPrime(78073)78073Eric W. Weisstein07/2006
181(2^257869+1)/(3*18645362967379)77613Henri Lifchitz04/2005
182(14^67421-1)/1377272Paul Bourdelais09/2008
1832^256391-1155*25639177182Henri Lifchitz03/2005
184lucasU(1107,1,25297)-lucasU(1107,1,25296)77005Mike Oakes05/2009
185(223^32768+1)/13107476945Lelio R Paula02/2009
186(10^76537-1)/9/6612796976529Jens K. Andersen04/2009
187Phi(76537,10)/6612796976529Maksym Voznyy01/2010
1887^90291-676305Theodore Burton11/2005
18914*10^75798+108975800Jens K. Andersen11/2007
19012^70067-11^7006775615Jean-Louis Charton11/2006
1918^83663-7^8366375556Jean-Louis Charton01/2004
1922*F(358297)-174880Henri Lifchitz12/2009
19319401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
194(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
1952^247165-374405M. Frind & P. Underwood07/2002
196(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
1972^246618+42774240Henri Lifchitz02/2005
19819255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
1999998*2^245696+373966Donovan Johnson10/2004
2002^244618-229773638Yves Minet10/2009
2017^86689-6^8668973261Predrag Minovic09/2004
2026^93812+573000Wojciech Florek03/2006
2032^242150+1765972895Lelio R Paula11/2009
204F(348307)/2056289086590809372776Donovan Johnson07/2007
205(3^152287+1)/472659Paul Bourdelais04/2008
2062^241004-372550M. Frind & P. Underwood07/2002
207lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
208lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
209L(344293)71953Renaud Lifchitz09/2003
2102^238568+9876533171817Jason Earls01/2009
211lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
2122^238144+9876533171689Jason Earls01/2009
2132^238081+1155*23808171670Henri Lifchitz02/2005
214((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
2152^237407-978771467Lelio R Paula11/2009
2162^236911-114771318Yves Minet10/2009
217-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
2182^235326+370841Donovan Johnson02/2006
219r(35414,90)*1000+91170831Patrick De Geest07/2004
220(2^235099-2^117550+1)/570772Jean Penné11/2006
2212^234133-316370482Yves Minet04/2009
22219471^16428-270467Faysal YAtim09/2005
223(19775^16384+1)/270388Henri Lifchitz03/2007
22410^70000+8048770001Milton L. Brown05/2006
22510^69999+13485770000Patrick De Geest02/2007
22610^70000-927370000Patrick De Geest08/2009
22710^69999-8825169999Patrick De Geest08/2009
2282^228944+8168920Henri Lifchitz01/2007
229lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
2308^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
2312^228271-22827168717Henri Lifchitz11/2004
2322*F(328450)-168642Henri Lifchitz12/2009
233(14^59693-1)/1368415Paul Bourdelais06/2008
2342^227115-780768369Lelio R Paula10/2009
2352^225536-2967894Henri Lifchitz05/2005
236(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
2372^224815-4978967677Henri Lifchitz04/2005
238((1+sqrt(7)+sqrt(6))^45863-1)*((1+sqrt(7)-sqrt(6))^45863-1)*((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(767653Mike Oakes05/2009
239(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
2402^222943+2967113Henri Lifchitz08/2005
241(13*10^67038-31)/967039Serge Batalov11/2008
24210^66949-9^6694966949Jean-Louis Charton12/2005
243(2^221891-2^110946+1)/566796Jean Penné11/2006
244(2^221509-1)/29239188166673Jens K. Andersen02/2009
245(5*10^66394-17)/366395Serge Batalov05/2009
2462^219812-314966171Yves Minet10/2009
2472^219653+15015*21965366123Henri Lifchitz04/2005
2482^219304+45424566018Henri Lifchitz03/2007
249Pell-LucasQ(172243)/265931Eric W. Weisstein01/2007
2502*F(314335)-165693Henri Lifchitz12/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 07 2010 23:29 (Time in France)

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