PRP Records

Probable Primes Top 10000

(156000 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(13^1199467+1)/141336138Paul Bourdelais12/2015
8(14^1091401+1)/151250885Paul Bourdelais03/2014
9(16^1025393+1)/171234695Paul Bourdelais08/2014
10(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
11(106*23^800873-7)/111090573Curtis Bright05/2015
12(7^1264699-1)/61068794Paul Bourdelais01/2014
13(2^3464473-1)/6048745082991771042896Anand Nair10/2014
1410^999999+5934991000000Peter Kaiser02/2013
152^2976221+2041857895932Makoto Morimoto09/2014
16(12^769543-1)/11830476Paul Bourdelais12/2014
17(64*10^779465-1)/81779465Serge Batalov09/2014
18(64*10^762811-1)/9762812Serge Batalov09/2014
19(10^718580+269)/9718580Serge Batalov12/2014
20(2^2327417-1)/23915387348002001700606Anand Nair08/2014
21(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
22(10^685224+89)/9685224Serge Batalov12/2014
232^2249255+28433677094Ben Maloney / Five or Bust01/2009
24(10^675470+269)/9675470Serge Batalov12/2014
25(9^703393+1)/10671207Paul Bourdelais08/2015
26(15^551927+1)/16649116Paul Bourdelais07/2013
27(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
28Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
29(51*21^479149-1243)/4633542Curtis Bright11/2015
30Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
31(20^472709-1)/19615008Paul Bourdelais01/2015
32(19^476929+1)/20609874Paul Bourdelais03/2015
33F(2904353)606974Henri Lifchitz07/2014
34(18^481147+1)/19603970Paul Bourdelais07/2011
35(15^505117-1)/14594063Paul Bourdelais01/2015
36(152^270217-1)/(152-1)589570Michael Stocker06/2015
37(3^1205459+1)/4575150Paul Bourdelais08/2015
38(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
398^615997-7^615997556301Jean-Louis Charton07/2009
40Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
41((((((((((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
42(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
43(18^414269-1)/17520020Paul Bourdelais12/2014
44(20^393257+1)/21511638Paul Bourdelais12/2014
45(14^441697-1)/13506241Paul Bourdelais12/2014
463^1059503-2^1059503505512Mike Oakes04/2012
47(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
48(64*10^499210+53)/9499211Serge Batalov03/2015
49Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
50(2^1572882+5)/3473485Serge Batalov08/2015
51(6^608099-1)/5473193Paul Bourdelais05/2010
522^1518191+75353457022Ben Maloney / Five or Bust01/2009
53(21^328129-1)/20433858Paul Bourdelais06/2014
54(17^348259+1)/18428514Paul Bourdelais05/2014
55(10^427912+89)/9427912Serge Batalov12/2014
56(10^424861-7)/3424861Leonid Durman01/2012
57138^196873-137^196873421285Jean-Louis Charton12/2009
582^1398269+131595420921Makoto Morimoto10/2013
59(3^877843-1)/2418838Paul Bourdelais07/2010
60(89*10^411590+1)/9411591Serge Batalov09/2014
61F(1968721)411439Henri Lifchitz11/2009
62(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
63Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
64(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
6515^328574+328574^15386434Serge Batalov05/2014
66(10^380976-7)/3380976Leonid Durman01/2012
672^1257787+1447761378632Makoto Morimoto10/2013
68F(1803059)376817Henri Lifchitz06/2009
693^761457-2363308Ryan Propper07/2015
70(64*10^360173-1)/243360173Serge Batalov09/2014
712^1191375+8543358640Phil Moore06/2008
72(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
73(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
74(127^165601-1)/126348390Alexander Zhirkov09/2015
75(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
76F(1636007)341905Henri Lifchitz03/2009
77(11^327001+1)/12340536Paul Bourdelais09/2013
78(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
79Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
80(3^700897+1)/4334413Paul Bourdelais04/2010
812^1104408-114539332460Enzo Doria03/2015
82(10^330906+71)/9330906Serge Batalov07/2015
832^1094740-1851539329550Enzo Doria08/2015
842^1091469-379369328565Enzo Doria03/2014
852^1072118-7321953322740Enzo Doria02/2015
862^1069293-1147195321890Enzo Doria05/2015
872^1065897-1147195320867Enzo Doria05/2015
882^1061095-1061095319422Henri Lifchitz10/2013
892^1052186-458165316740Enzo Doria03/2015
902^1046613-114685315062Enzo Doria04/2015
912^1045625-459373314765Enzo Doria06/2015
92(7^371669-1)/6314096Paul Bourdelais02/2010
932^1041153-114391313419Enzo Doria02/2015
942^1038871+1866983312732Enzo Doria04/2016
952^1036867+1865843312129Enzo Doria02/2016
962^1036020-114539311874Enzo Doria02/2015
97(11^293831-1)/10305993Paul Bourdelais03/2010
982^1015321-1015321305643Henri Lifchitz08/2013
992^1014224-2791229305312Enzo Doria01/2016
1002^1010751-107709304267Enzo Doria03/2014
101(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
1028^336419-7^336419303817Jean-Louis Charton01/2008
103(2^1007838+5)/3303389Serge Batalov08/2015
1042^1003046+60529301947Enzo Doria04/2016
1052^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
10610^300476+3300477Ed Trice10/2012
10710^300476-530913300476Patrick De Geest03/2016
108314738^9+9^314738300337Anatoly F. Selevich02/2011
1097^355039-6^355039300043Jean-Louis Charton05/2011
1102^996182-114431299881Enzo Doria02/2015
1112^995214-2788361299590Enzo Doria12/2015
1122^994791-114319299462Enzo Doria01/2015
1132^994490-1863791299372Enzo Doria01/2016
1142^992711-2788807298836Enzo Doria12/2015
1152^992525-114199298780Enzo Doria12/2014
116(2^986191+1)/3296873Vincent Diepeveen06/2008
1172^985217-114553296580Enzo Doria03/2015
1182^984131-1828009296253Enzo Doria01/2015
1192^983620+60451296100Phil Moore03/2008
1202^982721-2683295829Yves Minet02/2016
1212^981298-2788421295401Enzo Doria12/2015
1222^981163-2790967295360Enzo Doria12/2015
1232^979594+1865839294888Enzo Doria02/2016
1242^972744-114419292826Enzo Doria03/2015
125CopelandErdos(292447)292447Mark Rodenkirch12/2015
1262^970141-100363292042Enzo Doria02/2014
1272^962194+60139289650Enzo Doria02/2016
1282^959307-1861507288781Enzo Doria11/2015
1292^957192-1864049288144Enzo Doria01/2016
130(17^233689+1)/18287542Paul Bourdelais09/2013
131(11*2^948635-13)/15285568Renaud Lifchitz11/2011
1322^948374-114137285490Enzo Doria01/2015
1332^940426-2786141283097Enzo Doria11/2015
1342^939881-114115282933Enzo Doria12/2014
13510^282493-9^282493282493Jean-Louis Charton03/2007
1363^591827-2^591827282374Mike Oakes08/2009
137Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
1382^936716-1835519281980Enzo Doria04/2015
139(5*10^280710+1)/3280711Serge Batalov10/2014
140(10^279978+11)/3279978Serge Batalov07/2015
1412^929524-1864829279815Enzo Doria01/2016
1422^929152+60181279703Enzo Doria02/2016
1432^928621-2787883279543Enzo Doria11/2015
1442^925330-1301278553Yves Minet06/2015
145(21^210599+1)/22278457Paul Bourdelais08/2013
1462^923261-69175277930Enzo Doria11/2015
147757^96487-756^96487277796Jean-Louis Charton12/2012
148(5^396413-1)/4277081Paul Bourdelais06/2010
1492^920318+2792299277044Enzo Doria02/2016
1502^918596-2786939276525Enzo Doria11/2015
1512^916639+60563275936Enzo Doria04/2016
1522^916385-2786383275860Enzo Doria11/2015
1532^915576-114137275616Enzo Doria01/2015
1542^914757-2203275370Yves Minet12/2015
1552^909988-1862249273934Enzo Doria12/2015
1562^909257-1864423273714Enzo Doria01/2016
1572^908579-1861747273510Enzo Doria12/2015
1582^907635-2791597273226Enzo Doria01/2016
1592^906594-113201272912Enzo Doria08/2014
1602^904149-1862473272176Enzo Doria12/2015
161(7*10^271757-61)/9271757Erik Branger03/2012
1622^899121-115033270663Enzo Doria07/2015
1632^898762-251511270555Enzo Doria12/2013
1642^898589+47270503Lelio R Paula03/2016
165187322*10^270343-187321270349Danilo Nitsche09/2013
16648358*10^270343-48357270348Danilo Nitsche09/2013
167(10^270343-1)/9270343Maksym Voznyy07/2007
1682^897849-115273270280Enzo Doria07/2015
1692^896616-114179269909Enzo Doria12/2014
1702^894673-39343269324Enzo Doria08/2015
171F(1285607)268676Henri Lifchitz11/2008
172(10^268207+1)/11268206Paul Bourdelais02/2010
1732^890957-69583268205Enzo Doria12/2015
1742^890122-351401267954Enzo Doria07/2015
175(19^209359-1)/18267718Paul Bourdelais08/2010
17611^255426+255426^11265999Serge Batalov05/2014
1772^883462-343421265949Enzo Doria07/2015
1782^883333-291583265910Enzo Doria07/2015
1792^879530-2788031264765Enzo Doria12/2015
1802^878118+2793079264340Enzo Doria02/2016
1812^875748-461129263627Enzo Doria07/2015
1822^875181-2789923263456Enzo Doria12/2015
1832^875101-350083263432Enzo Doria08/2015
1842^874073+2792957263123Enzo Doria02/2016
1852^873288-269262886Yves Minet01/2015
1862^869601-163261776Yves Minet01/2015
1872^869035-114181261606Enzo Doria12/2014
1882^864899-113871260361Enzo Doria10/2014
189(7*10^260198-61)/9260198Erik Branger11/2011
1902^864298-2788421260180Enzo Doria12/2015
1912^864039-2791357260102Enzo Doria01/2016
1922^863621-113833259976Enzo Doria10/2014
1932^862837+75767259740Enzo Doria05/2016
1942^861516-1854029259343Enzo Doria09/2015
1952^860975-1853977259180Enzo Doria09/2015
1962^860625-1858843259074Enzo Doria10/2015
1972^859433+494711258716Makoto Morimoto10/2013
198Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
199(11*2^857159-13)/15258031Renaud Lifchitz08/2011
2002^857016-633113257988Enzo Doria12/2013
2012^855732-113969257602Enzo Doria10/2014
2022^853682-3911256984Enzo Doria05/2014
20311^246668-90256879Enzo Doria12/2012
2042^851904-113939256449Enzo Doria10/2014
20511^246167-90256357Enzo Doria12/2012
2062^850700-569049256087Enzo Doria11/2013
20721^193601-20^193601255983Jean-Louis Charton02/2015
2082^849177-114025255628Enzo Doria12/2014
2092^848178-140291255328Enzo Doria01/2014
2102^847622-2441255160Yves Minet02/2016
21124*29^174239+13361254809Curtis Bright04/2015
2122^845610-1868591254554Enzo Doria04/2016
2132^845402-114761254492Enzo Doria05/2015
2142^844334-2792441254170Enzo Doria02/2016
21511^243796-90253888Enzo Doria12/2012
2162^842123-59197253505Enzo Doria10/2015
2172^840358-462491252973Enzo Doria08/2015
21811^242579-60252620Enzo Doria10/2012
21945^152659+2252378Robert Price09/2015
2202^837725+1869377252181Enzo Doria05/2016
2212^837536-311039252124Enzo Doria06/2015
22221^190632-2252058Robert Price07/2015
2232^836656-2787929251859Enzo Doria11/2015
224tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
2252^832511-461197250611Enzo Doria07/2015
2262^832244-403635250531Enzo Doria01/2014
2272^831088-7200899250183Enzo Doria01/2015
2282^830956-1349250143Yves Minet07/2015
2292^829589-113653249732Enzo Doria09/2014
2302^828064-2785619249273Enzo Doria10/2015
2312^827602+60409249134Enzo Doria03/2016
23210^249010+348861249011Patrick De Geest04/2016
23310^249010-21249010Serge Batalov12/2014
2342^824991-114121248348Enzo Doria12/2014
2352^824642-362727248242Enzo Doria12/2013
2362^824565-114265248219Enzo Doria01/2015
237(73*10^248145-1)/9248146Robert Price01/2015
2382^821590-114167247324Enzo Doria12/2014
2392^821512-2790659247300Enzo Doria12/2015
2402^819463-59197246683Enzo Doria10/2015
2412^817160-350369245990Enzo Doria06/2015
2422^815111-113857245373Enzo Doria10/2014
243846^83761-845^83761245200Jean-Louis Charton12/2012
2442^814356-2790449245146Enzo Doria12/2015
2452^814276-459029245122Enzo Doria04/2015
2462^811842-113675244389Enzo Doria09/2014
2472^811132-2787929244176Enzo Doria11/2015
2482^809746-2790971243758Enzo Doria01/2016
2492^808621-113809243420Enzo Doria09/2014
2502^805843-113611242583Enzo Doria08/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 06 2016 18:27 (Time in France)

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