PRP Records

Probable Primes Top 10000

(169946 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
4(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
52^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
62^4583176+21311379674Ben Maloney / Five or Bust09/2009
7(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
8(13^1199467+1)/141336138Paul Bourdelais12/2015
9(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
10(14^1091401+1)/151250885Paul Bourdelais03/2014
11(16^1025393+1)/171234695Paul Bourdelais08/2014
12(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
13(106*23^800873-7)/111090573Curtis Bright05/2015
14(7^1264699-1)/61068794Paul Bourdelais01/2014
15(2^3464473-1)/6048745082991771042896Anand Nair10/2014
1610^999999+5934991000000Peter Kaiser02/2013
172^2976221+2041857895932Makoto Morimoto09/2014
18(12^769543-1)/11830476Paul Bourdelais12/2014
19(64*10^779465-1)/81779465Serge Batalov09/2014
20(64*10^762811-1)/9762812Serge Batalov09/2014
21(10^718580+269)/9718580Serge Batalov12/2014
22(2^2327417-1)/23915387348002001700606Anand Nair08/2014
23(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
24(10^685224+89)/9685224Serge Batalov12/2014
252^2249255+28433677094Ben Maloney / Five or Bust01/2009
26(10^675470+269)/9675470Serge Batalov12/2014
27(9^703393+1)/10671207Paul Bourdelais08/2015
28(15^551927+1)/16649116Paul Bourdelais07/2013
29(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
30Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
31(51*21^479149-1243)/4633542Curtis Bright11/2015
32Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
33(20^472709-1)/19615008Paul Bourdelais01/2015
34PIPrime(613373)613373Adrian Bondrescu05/2016
35(19^476929+1)/20609874Paul Bourdelais03/2015
36F(2904353)606974Henri Lifchitz07/2014
37(18^481147+1)/19603970Paul Bourdelais07/2011
38(15^505117-1)/14594063Paul Bourdelais01/2015
39(152^270217-1)/(152-1)589570Michael Stocker06/2015
40(3^1205459+1)/4575150Paul Bourdelais08/2015
41(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
428^615997-7^615997556301Jean-Louis Charton07/2009
43Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
44((((((((((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
45(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
46(18^414269-1)/17520020Paul Bourdelais12/2014
47(20^393257+1)/21511638Paul Bourdelais12/2014
48(14^441697-1)/13506241Paul Bourdelais12/2014
493^1059503-2^1059503505512Mike Oakes04/2012
50(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
51(64*10^499210+53)/9499211Serge Batalov03/2015
52Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
53(2^1572882+5)/3473485Serge Batalov08/2015
54(6^608099-1)/5473193Paul Bourdelais05/2010
552^1518191+75353457022Ben Maloney / Five or Bust01/2009
56(21^328129-1)/20433858Paul Bourdelais06/2014
57(17^348259+1)/18428514Paul Bourdelais05/2014
58(10^427912+89)/9427912Serge Batalov12/2014
59(10^424861-7)/3424861Leonid Durman01/2012
60138^196873-137^196873421285Jean-Louis Charton12/2009
612^1398269+131595420921Makoto Morimoto10/2013
62953^141023-952^141023420121Jean-Louis Charton10/2016
63(3^877843-1)/2418838Paul Bourdelais07/2010
64(89*10^411590+1)/9411591Serge Batalov09/2014
65F(1968721)411439Henri Lifchitz11/2009
66(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
67Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
68(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
6915^328574+328574^15386434Serge Batalov05/2014
702^1274941+1880717383796Enzo Doria10/2016
71(10^380976-7)/3380976Leonid Durman01/2012
722^1257787+1447761378632Makoto Morimoto10/2013
73F(1803059)376817Henri Lifchitz06/2009
742^1220335+1881263367358Enzo Doria11/2016
753^761457-2363308Ryan Propper07/2015
762^1200672+1880881361439Enzo Doria10/2016
77(64*10^360173-1)/243360173Serge Batalov09/2014
782^1191375+8543358640Phil Moore06/2008
792^1190972+1880191358519Enzo Doria11/2016
80(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
81(10^352237-1)/90380699499072573352221Robert Price07/2016
82(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
83(7*10^348724-61)/9348724Erik Branger09/2016
84(127^165601-1)/126348390Alexander Zhirkov09/2015
85(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
862^1145882+80779344945Enzo Doria09/2016
87F(1636007)341905Henri Lifchitz03/2009
882^1133678+782569341272Enzo Doria11/2016
89(11^327001+1)/12340536Paul Bourdelais09/2013
90(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
91Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
922^1124549+143807338523Enzo Doria10/2016
932^1114517+1880087335504Enzo Doria10/2016
94(3^700897+1)/4334413Paul Bourdelais04/2010
952^1104408-114539332460Enzo Doria03/2015
962^1101921+82085331712Enzo Doria10/2016
97(10^330906+71)/9330906Serge Batalov07/2015
982^1098346+482899330636Enzo Doria11/2016
992^1095679+1878713329833Enzo Doria09/2016
1002^1094740-1851539329550Enzo Doria08/2015
1012^1091469-379369328565Enzo Doria03/2014
1022^1085750+582349326844Enzo Doria11/2016
1032^1078242+1881649324584Enzo Doria11/2016
1042^1077737+1880117324432Enzo Doria10/2016
1052^1075425+1880117323736Enzo Doria10/2016
1062^1072118-7321953322740Enzo Doria02/2015
1072^1070539+1880633322265Enzo Doria10/2016
1082^1069293-1147195321890Enzo Doria05/2015
1092^1065968+1880941320889Enzo Doria10/2016
1102^1065897-1147195320867Enzo Doria05/2015
1112^1063427+1882103320124Enzo Doria12/2016
1122^1061095-1061095319422Henri Lifchitz10/2013
1132^1060363+782753319202Enzo Doria11/2016
1142^1053965+1879667317276Enzo Doria10/2016
1152^1052186-458165316740Enzo Doria03/2015
1162^1046613-114685315062Enzo Doria04/2015
1172^1045625-459373314765Enzo Doria06/2015
118(7*10^314564-61)/9314564Erik Branger09/2016
119(7^371669-1)/6314096Paul Bourdelais02/2010
1202^1041153-114391313419Enzo Doria02/2015
1212^1038871+1866983312732Enzo Doria04/2016
1222^1037647+1881263312363Enzo Doria11/2016
1232^1037226+1879699312237Enzo Doria10/2016
1242^1036867+1865843312129Enzo Doria02/2016
1252^1036020-114539311874Enzo Doria02/2015
1262^1030352+1870021310167Enzo Doria06/2016
1272^1030046+1882843310075Enzo Doria11/2016
128(11^293831-1)/10305993Paul Bourdelais03/2010
1292^1015321-1015321305643Henri Lifchitz08/2013
1302^1014224-2791229305312Enzo Doria01/2016
1312^1010751-107709304267Enzo Doria03/2014
132(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
1332^1009577+1869587303913Enzo Doria06/2016
1348^336419-7^336419303817Jean-Louis Charton01/2008
1352^1008301+1869377303529Enzo Doria06/2016
136(2^1007838+5)/3303389Serge Batalov08/2015
1372^1004929+1877567302514Enzo Doria08/2016
1382^1003494+1874899302082Enzo Doria06/2016
1392^1003046+60529301947Enzo Doria04/2016
1402^1000647+1881353301225Enzo Doria11/2016
1412^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
1422^999646+1874029300924Enzo Doria06/2016
14310^300476+3300477Ed Trice10/2012
14410^300476-530913300476Patrick De Geest03/2016
1452^998053+1879667300444Enzo Doria09/2016
146314738^9+9^314738300337Anatoly F. Selevich02/2011
1477^355039-6^355039300043Jean-Louis Charton05/2011
1482^996182-114431299881Enzo Doria02/2015
1492^995214-2788361299590Enzo Doria12/2015
1502^994791-114319299462Enzo Doria01/2015
1512^994490-1863791299372Enzo Doria01/2016
1522^992711-2788807298836Enzo Doria12/2015
1532^992525-114199298780Enzo Doria12/2014
154(2^986191+1)/3296873Vincent Diepeveen06/2008
1552^985217-114553296580Enzo Doria03/2015
1562^984131-1828009296253Enzo Doria01/2015
1572^983620+60451296100Phil Moore03/2008
1582^982721-2683295829Yves Minet02/2016
1592^981298-2788421295401Enzo Doria12/2015
1602^981163-2790967295360Enzo Doria12/2015
1612^979594+1865839294888Enzo Doria02/2016
1622^974441+1878407293336Enzo Doria08/2016
1632^974180+1876831293258Enzo Doria07/2016
1642^972744-114419292826Enzo Doria03/2015
165CopelandErdos(292447)292447Mark Rodenkirch12/2015
1662^970911+1873373292274Enzo Doria07/2016
1672^970141-100363292042Enzo Doria02/2014
1682^969945+1874717291983Enzo Doria06/2016
1692^969384+1880701291814Enzo Doria10/2016
1702^962194+60139289650Enzo Doria02/2016
1712^959307-1861507288781Enzo Doria11/2015
1722^957192-1864049288144Enzo Doria01/2016
1732^956446+1875199287919Enzo Doria06/2016
174(17^233689+1)/18287542Paul Bourdelais09/2013
1752^954001+1875257287183Enzo Doria07/2016
1762^952268+1878601286662Enzo Doria09/2016
1772^950801+81557286220Enzo Doria08/2016
178(11*2^948635-13)/15285568Renaud Lifchitz11/2011
1792^948510+782569285530Enzo Doria10/2016
1802^948374-114137285490Enzo Doria01/2015
1812^947739+1872923285298Enzo Doria06/2016
1822^942533+82067283731Enzo Doria09/2016
1832^940950+1874989283255Enzo Doria06/2016
1842^940426-2786141283097Enzo Doria11/2015
1852^939881-114115282933Enzo Doria12/2014
18610^282493-9^282493282493Jean-Louis Charton03/2007
1873^591827-2^591827282374Mike Oakes08/2009
188Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
1892^936716-1835519281980Enzo Doria04/2015
1902^936588+79411281942Enzo Doria06/2016
1912^936047+1877423281779Enzo Doria08/2016
1922^935713+1869377281678Enzo Doria05/2016
1932^933082+1877059280886Enzo Doria08/2016
194(5*10^280710+1)/3280711Serge Batalov10/2014
195(10^279978+11)/3279978Serge Batalov07/2015
1962^929524-1864829279815Enzo Doria01/2016
1972^929152+60181279703Enzo Doria02/2016
1982^928621-2787883279543Enzo Doria11/2015
1992^925330-1301278553Yves Minet06/2015
200(21^210599+1)/22278457Paul Bourdelais08/2013
2012^923261-69175277930Enzo Doria11/2015
202757^96487-756^96487277796Jean-Louis Charton12/2012
203((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
204(5^396413-1)/4277081Paul Bourdelais06/2010
2052^920318+2792299277044Enzo Doria02/2016
2062^918596-2786939276525Enzo Doria11/2015
2072^916639+60563275936Enzo Doria04/2016
2082^916385-2786383275860Enzo Doria11/2015
2092^915928+82081275722Enzo Doria09/2016
2102^915576-114137275616Enzo Doria01/2015
2112^914828+1876741275391Enzo Doria07/2016
2122^914757-2203275370Yves Minet12/2015
2132^911900+1871245274510Enzo Doria05/2016
2142^909988-1862249273934Enzo Doria12/2015
2152^909297+1879157273726Enzo Doria08/2016
2162^909257-1864423273714Enzo Doria01/2016
2172^908579-1861747273510Enzo Doria12/2015
2182^907635-2791597273226Enzo Doria01/2016
2192^906594-113201272912Enzo Doria08/2014
2202^904773+1872167272364Enzo Doria06/2016
2212^904149-1862473272176Enzo Doria12/2015
222(7*10^271757-61)/9271757Erik Branger03/2012
2232^902497+1880117271679Enzo Doria09/2016
2242^901858+77689271487Enzo Doria06/2016
2252^901372+1875301271341Enzo Doria06/2016
2262^899121-115033270663Enzo Doria07/2015
2272^898900+883021270596Enzo Doria12/2016
2282^898762-251511270555Enzo Doria12/2013
2292^898589+47270503Lelio R Paula03/2016
230187322*10^270343-187321270349Danilo Nitsche09/2013
23148358*10^270343-48357270348Danilo Nitsche09/2013
232(10^270343-1)/9270343Maksym Voznyy07/2007
2332^897849-115273270280Enzo Doria07/2015
2342^896616-114179269909Enzo Doria12/2014
2352^894673-39343269324Enzo Doria08/2015
236F(1285607)268676Henri Lifchitz11/2008
2372^892112+187663268553Enzo Doria08/2016
238(10^268207+1)/11268206Paul Bourdelais02/2010
2392^890957-69583268205Enzo Doria12/2015
2402^890122-351401267954Enzo Doria07/2015
241(19^209359-1)/18267718Paul Bourdelais08/2010
2422^886324+77791266811Enzo Doria06/2016
2432^884714+1880527266326Enzo Doria10/2016
24411^255426+255426^11265999Serge Batalov05/2014
2452^883462-343421265949Enzo Doria07/2015
2462^883442+1875019265943Enzo Doria06/2016
2472^883333-291583265910Enzo Doria07/2015
2482^879530-2788031264765Enzo Doria12/2015
2492^878118+2793079264340Enzo Doria02/2016
2502^875748-461129263627Enzo Doria07/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 04 2016 08:41 (Time in France)

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