PRP Records

Probable Primes Top 10000

(294613 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 (> 50000) Who ? When ?
1(10^8177207-1)/98177207Ryan Propper + Sergey Batalov05/2021
2(10^5794777-1)/95794777Ryan Propper + Sergey Batalov04/2021
3(2^15135397+1)/34556209Ryan Propper06/2021
4(3^8530117-1)/24069900Ryan Propper11/2023
52^13380298-274027872Jeff Gilchrist /Diepeveen-Reix-Underwood-Gilchrist03/2021
6(2^13372531+1)/34025533Ryan Propper09/2013
7(2^13347311+1)/34017941Ryan Propper09/2013
8(2^12720787-1)/1119429257/175573124547437977/84809998784211069913829294Anonymous10/2022
9(3^7973131-1)/23804150Ryan Propper11/2023
10(2^12588091-1)/320754643488972821695394248013789365Eden Avidan / Naegi Makoto05/2023
11(2^12503723-2^6251862+1)/53763995Ryan Propper + Sergey Batalov07/2020
12(5^5154509-1)/43602847Ryan Propper02/2024
13(5^4939471-1)/43452542Ryan Propper01/2024
14(2^10443557-1)/372893259948073143811GIMPS-fre_games07/2020
152^9092392+402912737083Engracio Esmenda / Five or Bust02/2011
16(6^3360347-1)/52614858Ryan Propper10/2023
17(17^1990523-1)/162449236Paul Bourdelais08/2020
18(35963^524288+1)/22388581Ryan Propper08/2022
19(11^2264611+1)/122358349Paul Bourdelais07/2021
20(5^3300593-1)/42307015Anonymous02/2022
21(3^4694803+2^4694803)/52239990Ryan Propper12/2023
22(2^7313983-1)/3054920802761932201714Oliver Kruse03/2018
23(3^4571447+2^4571447)/52181134Ryan Propper12/2023
244532794^3+3^45327942162693Ryan Propper10/2023
25(2^7080247-1)/156822217506727/11283326312536321/96329405483303395932131318Gord Palameta10/2017
26360834^356345+356345^3608342003304Ryan Propper02/2024
27(11^1868983-1)/101946345Paul Bourdelais06/2021
28(36^1145393+1)/371782577Paul Bourdelais11/2023
291343238^19+19^13432381717671Ryan Propper05/2023
30(3^3598867-1)/21717096Ryan Propper12/2021
31(13^1503503-1)/121674817Paul Bourdelais04/2020
32(10^1600787+1)/111600786Paul Bourdelais05/2020
33(18^1270141-1)/171594372Paul Bourdelais12/2021
34(14^1385203+1)/151587619Paul Bourdelais02/2022
35(2^5243339-2^2621670+1)/51578402Ryan Propper + Sergey Batalov06/2020
36(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
372^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
38(2^4834891-1)/1701881633/706596885755771455425Gord Palameta01/2017
39300102^59935+59935^3001021433792Ryan Propper05/2023
40(187503^262144+1)/21382288Ryan Propper08/2022
412^4583176+21311379674Ben Maloney / Five or Bust09/2009
42F(6530879)1364873Ryan Propper08/2022
43(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
44(13^1199467+1)/141336138Paul Bourdelais12/2015
45(5^1888279-1)/41319850Paul Bourdelais04/2018
46(5^1856147+1)/61297391Paul Bourdelais02/2019
47(3^2704981-1)/21290604Ryan Propper12/2021
48(20^984349-1)/191280667Paul Bourdelais09/2021
491139148^13+13^11391481268947Ryan Propper07/2023
50(2^4194304+1026473)/31262611Tony Prest / Never Odd Or Even07/2017
51(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
52(14^1091401+1)/151250885Paul Bourdelais03/2014
53(16^1025393+1)/171234695Paul Bourdelais08/2014
5411^1181716+11817161230631Kellen Shenton07/2023
55(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
56(3^2533963+1)/41209008Paul Bourdelais03/2020
57L(5466311)1142392Ryan Propper08/2022
58(34^735439+1)/351126308Paul Bourdelais10/2023
59(67*10^1116676+23)/91116677Ryan Propper + Sergey Batalov01/2023
602^3690839-18684071111054Enzo Doria03/2021
612^3678448+3845411107324Enzo Doria03/2022
622^3668660+18888011104377Enzo Doria03/2020
63(106*23^800873-7)/111090573Curtis Bright05/2015
64(7^1264699-1)/61068794Paul Bourdelais01/2014
65(6^1365019-1)/51062191Paul Bourdelais12/2019
662^3511529-151057076Stefano Morozzi06/2023
67(3^2215303-1)/21056968Paul Bourdelais02/2019
682^3480081-91047609Stefano Morozzi05/2023
6910^1043372+71043373Alfred Reich12/2021
70(2^3464473-1)/6048745082991771042896Anand Nair10/2014
71202628^128217+128217^2026281035013Ryan Propper12/2023
72202688^125163+125163^2026881033198Ryan Propper12/2023
73201868^129567+129567^2018681032050Ryan Propper11/2023
74202168^126585+126585^2021681031539Ryan Propper11/2023
75202336^124213+124213^2023361030734Ryan Propper11/2023
76201754^125605+125605^2017541028746Ryan Propper10/2023
77(6^1313371+1)/71022001Paul Bourdelais01/2019
78200307^126128+126128^2003071021729Ryan Propper10/2023
79200026^126791+126791^2000261020751Ryan Propper09/2023
80200068^125561+125561^2000681020118Ryan Propper09/2023
81(2^3352132+9)/51009092Tony Prest / Never Odd Or Even06/2018
82(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/674729942211009003Tony Prest / Never Odd Or Even08/2019
83(2^3351556+159)/5/7/7/2927/14552647/117615601/7068740758371008886Tony Prest / Never Odd Or Even08/2019
84(2^3351346+113)/3/548533/39539021/946508381271008831Tony Prest / Never Odd Or Even11/2022
85(2^3350899+115)/3/3/11/4091008717Tony Prest / Never Odd Or Even04/2020
86(2^3350068+183)/953/157612311008461Tony Prest / Never Odd Or Even03/2020
87(2^3349565+57)/23/263/778931008311Tony Prest / Never Odd Or Even03/2020
88(2^3349080+137)/3/79/80604190991008162Tony Prest / Never Odd Or Even07/2020
89(2^3349027+183)/23/1277/11638321/50448485271008137Tony Prest / Never Odd Or Even09/2022
90(2^3348456+23)/3/411007984Tony Prest / Never Odd Or Even01/2019
91(2^3348338+213)/71007950Tony Prest / Never Odd Or Even10/2018
92(2^3348184+123)/12491/3229442631007892Tony Prest / Never Odd Or Even01/2021
93(2^3348131+207)/5/11/41/43/12661193081/868684167491007862Tony Prest / Never Odd Or Even05/2021
94(2^3348111+245)/9721/215412555797/198704945240871007854Tony Prest / Never Odd Or Even05/2021
95(2^3347690+143)/3/7/167/5858771007746Tony Prest / Never Odd Or Even06/2020
96(2^3347613+103)/3/5/1948091007726Tony Prest / Never Odd Or Even02/2020
97(2^3347274+143)/3/3/3/234786457/34840035575691007608Tony Prest / Never Odd Or Even07/2022
98(2^3346590+185)/3/31/83/2201765933/3262109845431007400Tony Prest / Never Odd Or Even04/2021
99(2^3346468+257)/3/7/13/71/108471007379Tony Prest / Never Odd Or Even05/2020
100L(4819961)1007313Ryan Propper07/2022
101(2^3346066+139)/168803/71205272050631007249Tony Prest / Never Odd Or Even05/2023
102(2^3345946+187)/7/31229571007223Tony Prest / Never Odd Or Even03/2019
1032^3345603+631007127Tony Prest / Never Odd Or Even05/2018
104(2^3345474+255)/19/29/25571007082Tony Prest / Never Odd Or Even12/2019
105(2^3345364+43)/53/79/109/2389/10889/168383091007035Tony Prest / Never Odd Or Even07/2022
106(2^3345080+247)/31/39671006965Tony Prest / Never Odd Or Even03/2019
107(2^3343888+209)/3/3/5/31/1791006606Tony Prest / Never Odd Or Even11/2019
108(2^3343774+115)/122391006573Tony Prest / Never Odd Or Even10/2018
109(2^3343633+105)/1371006532Tony Prest / Never Odd Or Even10/2018
110(2^3343714+149)/3/11/17/6047/23869/3993469/1713889507211006530Tony Prest / Never Odd Or Even01/2021
111(2^3343629+183)/5/35107/2154259/282128297091006511Tony Prest / Never Odd Or Even05/2022
112(2^3343142+13)/587/212195573363/37759700667191006360Tony Prest / Never Odd Or Even05/2018
113(2^3342880+215)/3/7/157/239/8211006299Tony Prest / Never Odd Or Even04/2020
114(2^3342804+51)/13/13/43/2069/1491731006272Tony Prest / Never Odd Or Even01/2023
115(2^3342732+41)/3/7/285138001393791006248Tony Prest / Never Odd Or Even03/2023
116(2^3342588+95)/3/619/13174671553/227610668471006196Tony Prest / Never Odd Or Even08/2018
117194968^136197+136197^1949681000999Hans Havermann12/2023
118191319^170462+170462^1913191000910Hans Havermann07/2023
119197180^119151+119151^1971801000905Hans Havermann08/2023
120202818^85523+85523^2028181000316Gabor Levai08/2023
121(2^3322799+505)/31000262Stefano Morozzi08/2022
122218767^37314+37314^2187671000175Gabor Levai03/2023
1232^3322077+6591000045Stefano Morozzi04/2022
124211185^54364+54364^2111851000027Gabor Levai05/2022
13010^999999+5934991000000Peter Kaiser02/2013
12510^999999+308267*10^292000+11000000Sergey Batalov09/2021
126138159533888769035882147()973433052122012098003208^4096+11000000Anonymous11/2021
127138159533888769035882147()973433052122012098115876^4096+11000000Anonymous11/2021
128190880568043619196745858()064791100275825910782112^2048+11000000Anonymous05/2023
129190880568043619196745858()064791100275825910980374^2048+11000000Anonymous05/2023
13110^999999-172473999999Patrick De Geest12/2016
13210^999999-1087604*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
13310^999999-1022306*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
134(7^1178033+1)/8995553Paul Bourdelais01/2019
13510^995256+7995257Alfred Reich11/2021
136F(4740217)990647Ryan Propper07/2022
137(3^2052329+2^2052329)/5979210Ryan Propper12/2023
1382^3223639+74333970413Enzo Doria10/2021
1392^3118435+73793938743Enzo Doria01/2021
1402^3037438+1885789914360Enzo Doria05/2019
1412^3032354+74209912830Enzo Doria01/2020
1422^3018556+31908676Robert Price09/2019
143(3^1896463+1)/4904843Paul Bourdelais01/2020
144Tau(181^72558)900969Nik Lygeros / Olivier Rozier / LR team07/2018
1452^2976221+2041857895932Makoto Morimoto09/2014
1461839730^3+3^1839730877775Ryan Propper06/2023
147(35^568453-1)/34877729Paul Bourdelais10/2021
148L(4161629)869730Ryan Propper07/2022
149(2^2860553+1)/(3*1528891204123*11630352659013691)861084Gord Palameta03/2019
1502^2843446+1885789855963Enzo Doria05/2019
1513^1753088+2836436Paul Bourdelais03/2022
152(12^769543-1)/11830476Paul Bourdelais12/2014
1532^2740174+1884385824875Enzo Doria01/2019
154Tau(229^63498)824146Nik Lygeros / Olivier Rozier / LR team07/2020
155(168326^157609-1)/(168326^397-1)821614Ryan Propper11/2023
156(9^860029+1)/10820676Paul Bourdelais09/2020
1572^2723045+60227819719Enzo Doria01/2020
1582^2711746+74179816317Enzo Doria11/2019
159(2^2687383+1)/(3*440088720954577)808968Gord Palameta03/2019
160684614^15+15^684614805169Ryan Propper05/2023
161(31^535571-1)/30798729Alexander Zhirkov08/2019
162(9^835391-7^835391)/2797166Jon Grantham07/2023
163(64*10^779465-1)/81779465Serge Batalov09/2014
164(8^854149-3^854149)/5771373Jon Grantham08/2023
165(64*10^762811-1)/9762812Serge Batalov09/2014
1662^2515946+60529757376Enzo Doria10/2018
167(15^639833-1)/14752501Paul Bourdelais04/2019
1682^2442546+74209735280Enzo Doria03/2020
169(110212^143641-1)/(110212^379-1)722361Ryan Propper11/2023
170(79^379703+1)/80720533Paul Bourdelais10/2023
171(10^718580+269)/9718580Serge Batalov12/2014
172(7^846913-2^846913)/5715724Jon Grantham08/2023
173(99^357779+1)/100713995Paul Bourdelais02/2022
174558232^19+19^558232713842Ryan Propper05/2023
175(26^501409+1)/27709479Paul Bourdelais10/2023
176(81^370421+1)/82706942Paul Bourdelais12/2021
177(2^2327417-1)/23915387348002001700606Anand Nair08/2014
178F(3340367)698096Henri Lifchitz03/2018
179(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
180(7^817519-3^817519)/4690884Jon Grantham08/2023
1812^2291342+73519689763Enzo Doria12/2018
182(10^685224+89)/9685224Serge Batalov12/2014
183(65^375017-1)/64679872Paul Bourdelais10/2023
184F(3244369)678033Henri Lifchitz09/2017
1852^2249255+28433677094Ben Maloney / Five or Bust01/2009
186(10^675470+269)/9675470Serge Batalov12/2014
187Tau(151^56086)672156Nik Lygeros / Olivier Rozier / LR team10/2017
188(9^703393+1)/10671207Paul Bourdelais08/2015
189(121^320483+1)/122667496Paul Bourdelais08/2019
190(10^666903-7)/3666903Rytis Slatkevicius01/2023
1912^2213586+71389666356Enzo Doria04/2018
192(9614^167281-1)/(9614^409-1)664636Ryan Propper11/2023
1932^2205444+3663905Paul Bourdelais08/2020
194(41*13^592198+27)/4659677Eric Chen11/2023
1952^2191232+105659627Stefano Morozzi10/2021
1962^2187054+1886719658369Enzo Doria11/2018
197(6^840316-11)/5653893Paul Bourdelais06/2020
198(15^551927+1)/16649116Paul Bourdelais07/2013
1992^2153756+72181648346Enzo Doria04/2018
200(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
201Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
2022^2119239+684443637955Enzo Doria11/2018
2032^2117699+89637491Stefano Morozzi10/2021
204(5*10^636570+31)/9636570Rytis Slatkevicius02/2023
2052^2114495+20753636527Enzo Doria08/2023
2062^2107382+105634385Stefano Morozzi10/2021
207(51*21^479149-1243)/4633542Curtis Bright11/2015
2082^2099459+71663632001Enzo Doria07/2018
209(10^631715+53)/9631715Rytis Slatkevicius01/2023
210Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
2112^2097791+60563631499Enzo Doria04/2018
2122^2086750-3628175Paul Bourdelais05/2020
2132^2083766+73519627277Enzo Doria01/2019
214(16105^146689-1)/(16105^383-1)615504Ryan Propper11/2023
215(20^472709-1)/19615008Paul Bourdelais01/2015
216PIPrime(613373)613373Adrian Bondrescu05/2016
217124452^80465+80465^124452610513Ryan Propper10/2023
21811^586020-2610277Paul Bourdelais11/2021
219(19^476929+1)/20609874Paul Bourdelais03/2015
220(7^720497-2^720497)/5608890Jon Grantham08/2023
2212^2019811+1867211608024Enzo Doria04/2018
222F(2904353)606974Henri Lifchitz07/2014
2232^2014720+71893606492Enzo Doria04/2018
224(5^866029-3^866029)/2605328Jon Grantham08/2023
225L(2894561)604928Ryan Propper06/2022
226(18^481147+1)/19603970Paul Bourdelais07/2011
227200^262144+119^262144603202Kellen Shenton08/2022
228(83467^121801-1)/(83467^349-1)597728Ryan Propper11/2023
229(61448^124609-1)/(61448^353-1)595001Ryan Propper11/2023
230(15^505117-1)/14594063Paul Bourdelais01/2015
23181^310721-80^310721593007Paul Bourdelais07/2023
232(152^270217-1)/(152-1)589570Michael Stocker06/2015
233Phi(177147,94259)587458Anonymous09/2022
2342^1950002+1867369587010Enzo Doria02/2018
235116265^111218+111218^116265586694Ryan Propper10/2023
2362^1940812+3584243Paul Bourdelais06/2020
2371933695^2+2^1933695582101Ryan Propper05/2023
238(5^832151-2^832151)/3581649Jon Grantham08/2023
239(129810^113569-1)/(129810^337-1)578991Ryan Propper11/2023
2402^1923104+153578912Stefano Morozzi07/2021
241116761^87652+87652^116761577122Ryan Propper10/2023
242116395^87994+87994^116395575510Ryan Propper10/2023
243(3^1205459+1)/4575150Paul Bourdelais08/2015
244(160972^109561-1)/(160972^331-1)568734Ryan Propper11/2023
245(37015^124609-1)/(37015^353-1)567649Ryan Propper11/2023
2462^1882800+384541566780Enzo Doria12/2017
247(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
2482^1882474+71389566682Enzo Doria04/2018
249(6^727496-11)/5566102Paul Bourdelais08/2019
2502^1875552+3564598Paul Bourdelais04/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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