PRP Records

Probable Primes Top 10000

(295260 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
27360339^356572+356572^3603392000656Ryan Propper05/2024
28(11^1868983-1)/101946345Paul Bourdelais06/2021
29(36^1145393+1)/371782577Paul Bourdelais11/2023
301343238^19+19^13432381717671Ryan Propper05/2023
31(3^3598867-1)/21717096Ryan Propper12/2021
32(13^1503503-1)/121674817Paul Bourdelais04/2020
33Mills(3,30,6,80,12,450,894,3636,70756,97220,66768,300840,1623568,8436308)1665461Ryan Propper + Sergey Batalov05/2024
34(10^1600787+1)/111600786Paul Bourdelais05/2020
35(18^1270141-1)/171594372Paul Bourdelais12/2021
36(14^1385203+1)/151587619Paul Bourdelais02/2022
37(2^5243339-2^2621670+1)/51578402Ryan Propper + Sergey Batalov06/2020
38(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
392^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
40(2^4834891-1)/1701881633/706596885755771455425Gord Palameta01/2017
41300102^59935+59935^3001021433792Ryan Propper05/2023
42(187503^262144+1)/21382288Ryan Propper08/2022
432^4583176+21311379674Ben Maloney / Five or Bust09/2009
44F(6530879)1364873Ryan Propper08/2022
45(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
46(13^1199467+1)/141336138Paul Bourdelais12/2015
47(5^1888279-1)/41319850Paul Bourdelais04/2018
48(5^1856147+1)/61297391Paul Bourdelais02/2019
49(3^2704981-1)/21290604Ryan Propper12/2021
50(20^984349-1)/191280667Paul Bourdelais09/2021
51(3^2674381+1)/41276004Paul Bourdelais03/2024
521139148^13+13^11391481268947Ryan Propper07/2023
53(2^4194304+1026473)/31262611Tony Prest / Never Odd Or Even07/2017
54(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
55(14^1091401+1)/151250885Paul Bourdelais03/2014
56(16^1025393+1)/171234695Paul Bourdelais08/2014
5711^1181716+11817161230631Kellen Shenton07/2023
58(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
59(3^2533963+1)/41209008Paul Bourdelais03/2020
60L(5466311)1142392Ryan Propper08/2022
61(34^735439+1)/351126308Paul Bourdelais10/2023
62(67*10^1116676+23)/91116677Ryan Propper + Sergey Batalov01/2023
632^3690839-18684071111054Enzo Doria03/2021
642^3678448+3845411107324Enzo Doria03/2022
652^3668660+18888011104377Enzo Doria03/2020
66(106*23^800873-7)/111090573Curtis Bright05/2015
67(7^1264699-1)/61068794Paul Bourdelais01/2014
68(6^1365019-1)/51062191Paul Bourdelais12/2019
692^3511529-151057076Stefano Morozzi06/2023
70(3^2215303-1)/21056968Paul Bourdelais02/2019
712^3480081-91047609Stefano Morozzi05/2023
7210^1043372+71043373Alfred Reich12/2021
73(2^3464473-1)/6048745082991771042896Anand Nair10/2014
74202628^128217+128217^2026281035013Ryan Propper12/2023
75202688^125163+125163^2026881033198Ryan Propper12/2023
76201868^129567+129567^2018681032050Ryan Propper11/2023
77202168^126585+126585^2021681031539Ryan Propper11/2023
78202336^124213+124213^2023361030734Ryan Propper11/2023
79201754^125605+125605^2017541028746Ryan Propper10/2023
80(6^1313371+1)/71022001Paul Bourdelais01/2019
81200307^126128+126128^2003071021729Ryan Propper10/2023
82193143^193143+214^2141020931Ryan Propper + Sergey Batalov05/2024
83200026^126791+126791^2000261020751Ryan Propper09/2023
84200068^125561+125561^2000681020118Ryan Propper09/2023
85192223^192223+166^1661015669Ryan Propper + Sergey Batalov05/2024
86(2^3352132+9)/51009092Tony Prest / Never Odd Or Even06/2018
87(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/674729942211009003Tony Prest / Never Odd Or Even08/2019
88(2^3351556+159)/5/7/7/2927/14552647/117615601/7068740758371008886Tony Prest / Never Odd Or Even08/2019
89(2^3351346+113)/3/548533/39539021/946508381271008831Tony Prest / Never Odd Or Even11/2022
90(2^3350899+115)/3/3/11/4091008717Tony Prest / Never Odd Or Even04/2020
91(2^3350068+183)/953/157612311008461Tony Prest / Never Odd Or Even03/2020
92(2^3349565+57)/23/263/778931008311Tony Prest / Never Odd Or Even03/2020
93(2^3349080+137)/3/79/80604190991008162Tony Prest / Never Odd Or Even07/2020
94(2^3349027+183)/23/1277/11638321/50448485271008137Tony Prest / Never Odd Or Even09/2022
95(2^3348456+23)/3/411007984Tony Prest / Never Odd Or Even01/2019
96(2^3348338+213)/71007950Tony Prest / Never Odd Or Even10/2018
97(2^3348184+123)/12491/3229442631007892Tony Prest / Never Odd Or Even01/2021
98(2^3348131+207)/5/11/41/43/12661193081/868684167491007862Tony Prest / Never Odd Or Even05/2021
99(2^3348111+245)/9721/215412555797/198704945240871007854Tony Prest / Never Odd Or Even05/2021
100(2^3347690+143)/3/7/167/5858771007746Tony Prest / Never Odd Or Even06/2020
101(2^3347613+103)/3/5/1948091007726Tony Prest / Never Odd Or Even02/2020
102(2^3347274+143)/3/3/3/234786457/34840035575691007608Tony Prest / Never Odd Or Even07/2022
103(2^3346590+185)/3/31/83/2201765933/3262109845431007400Tony Prest / Never Odd Or Even04/2021
104(2^3346468+257)/3/7/13/71/108471007379Tony Prest / Never Odd Or Even05/2020
105L(4819961)1007313Ryan Propper07/2022
106(2^3346066+139)/168803/71205272050631007249Tony Prest / Never Odd Or Even05/2023
107(2^3345946+187)/7/31229571007223Tony Prest / Never Odd Or Even03/2019
1082^3345603+631007127Tony Prest / Never Odd Or Even05/2018
109(2^3345474+255)/19/29/25571007082Tony Prest / Never Odd Or Even12/2019
110(2^3345364+43)/53/79/109/2389/10889/168383091007035Tony Prest / Never Odd Or Even07/2022
111(2^3345080+247)/31/39671006965Tony Prest / Never Odd Or Even03/2019
112(2^3343888+209)/3/3/5/31/1791006606Tony Prest / Never Odd Or Even11/2019
113(2^3343774+115)/122391006573Tony Prest / Never Odd Or Even10/2018
114(2^3343633+105)/1371006532Tony Prest / Never Odd Or Even10/2018
115(2^3343714+149)/3/11/17/6047/23869/3993469/1713889507211006530Tony Prest / Never Odd Or Even01/2021
116(2^3343629+183)/5/35107/2154259/282128297091006511Tony Prest / Never Odd Or Even05/2022
117(2^3343142+13)/587/212195573363/37759700667191006360Tony Prest / Never Odd Or Even05/2018
118(2^3342880+215)/3/7/157/239/8211006299Tony Prest / Never Odd Or Even04/2020
119(2^3342804+51)/13/13/43/2069/1491731006272Tony Prest / Never Odd Or Even01/2023
120(2^3342732+41)/3/7/285138001393791006248Tony Prest / Never Odd Or Even03/2023
121(2^3342588+95)/3/619/13174671553/227610668471006196Tony Prest / Never Odd Or Even08/2018
122194968^136197+136197^1949681000999Hans Havermann12/2023
123191319^170462+170462^1913191000910Hans Havermann07/2023
124197180^119151+119151^1971801000905Hans Havermann08/2023
125202818^85523+85523^2028181000316Gabor Levai08/2023
126(2^3322799+505)/31000262Stefano Morozzi08/2022
127265341^5882+5882^2653411000210Gabor Levai04/2024
128218767^37314+37314^2187671000175Gabor Levai03/2023
1292^3322077+6591000045Stefano Morozzi04/2022
130211185^54364+54364^2111851000027Gabor Levai05/2022
13610^999999+5934991000000Peter Kaiser02/2013
13110^999999+308267*10^292000+11000000Sergey Batalov09/2021
132138159533888769035882147()973433052122012098003208^4096+11000000Anonymous11/2021
133138159533888769035882147()973433052122012098115876^4096+11000000Anonymous11/2021
134190880568043619196745858()064791100275825910782112^2048+11000000Anonymous05/2023
135190880568043619196745858()064791100275825910980374^2048+11000000Anonymous05/2023
13710^999999-172473999999Patrick De Geest12/2016
13810^999999-1087604*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
13910^999999-1022306*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
140(7^1178033+1)/8995553Paul Bourdelais01/2019
14110^995256+7995257Alfred Reich11/2021
142F(4740217)990647Ryan Propper07/2022
143(3^2052329+2^2052329)/5979210Ryan Propper12/2023
1442^3223639+74333970413Enzo Doria10/2021
1452^3118435+73793938743Enzo Doria01/2021
1462^3037438+1885789914360Enzo Doria05/2019
1472^3032354+74209912830Enzo Doria01/2020
1482^3018556+31908676Robert Price09/2019
149(3^1896463+1)/4904843Paul Bourdelais01/2020
150Tau(181^72558)900969Nik Lygeros / Olivier Rozier / LR team07/2018
1512^2976221+2041857895932Makoto Morimoto09/2014
1521839730^3+3^1839730877775Ryan Propper06/2023
153(35^568453-1)/34877729Paul Bourdelais10/2021
154L(4161629)869730Ryan Propper07/2022
155(2^2860553+1)/(3*1528891204123*11630352659013691)861084Gord Palameta03/2019
1562^2843446+1885789855963Enzo Doria05/2019
1573^1753088+2836436Paul Bourdelais03/2022
158(12^769543-1)/11830476Paul Bourdelais12/2014
1592^2740174+1884385824875Enzo Doria01/2019
160Tau(229^63498)824146Nik Lygeros / Olivier Rozier / LR team07/2020
161(168326^157609-1)/(168326^397-1)821614Ryan Propper11/2023
162(9^860029+1)/10820676Paul Bourdelais09/2020
1632^2723045+60227819719Enzo Doria01/2020
1642^2711746+74179816317Enzo Doria11/2019
165(2^2687383+1)/(3*440088720954577)808968Gord Palameta03/2019
166684614^15+15^684614805169Ryan Propper05/2023
167(31^535571-1)/30798729Alexander Zhirkov08/2019
168(9^835391-7^835391)/2797166Jon Grantham07/2023
169(64*10^779465-1)/81779465Serge Batalov09/2014
170(8^854149-3^854149)/5771373Jon Grantham08/2023
171(64*10^762811-1)/9762812Serge Batalov09/2014
1722^2515946+60529757376Enzo Doria10/2018
173(15^639833-1)/14752501Paul Bourdelais04/2019
1742^2442546+74209735280Enzo Doria03/2020
175(110212^143641-1)/(110212^379-1)722361Ryan Propper11/2023
176(79^379703+1)/80720533Paul Bourdelais10/2023
177(10^718580+269)/9718580Serge Batalov12/2014
178(7^846913-2^846913)/5715724Jon Grantham08/2023
179(99^357779+1)/100713995Paul Bourdelais02/2022
180558232^19+19^558232713842Ryan Propper05/2023
181(26^501409+1)/27709479Paul Bourdelais10/2023
182(81^370421+1)/82706942Paul Bourdelais12/2021
183(2^2327417-1)/23915387348002001700606Anand Nair08/2014
184F(3340367)698096Henri Lifchitz03/2018
185(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
186(7^817519-3^817519)/4690884Jon Grantham08/2023
1872^2291342+73519689763Enzo Doria12/2018
188(10^685224+89)/9685224Serge Batalov12/2014
189(65^375017-1)/64679872Paul Bourdelais10/2023
190F(3244369)678033Henri Lifchitz09/2017
1912^2249255+28433677094Ben Maloney / Five or Bust01/2009
192(10^675470+269)/9675470Serge Batalov12/2014
193Tau(151^56086)672156Nik Lygeros / Olivier Rozier / LR team10/2017
194(9^703393+1)/10671207Paul Bourdelais08/2015
195(121^320483+1)/122667496Paul Bourdelais08/2019
196(10^666903-7)/3666903Rytis Slatkevicius01/2023
1972^2213586+71389666356Enzo Doria04/2018
198(9614^167281-1)/(9614^409-1)664636Ryan Propper11/2023
1992^2205444+3663905Paul Bourdelais08/2020
200(41*13^592198+27)/4659677Eric Chen11/2023
2012^2191232+105659627Stefano Morozzi10/2021
2022^2187054+1886719658369Enzo Doria11/2018
203(6^840316-11)/5653893Paul Bourdelais06/2020
2042^2160074+41857650248Stefano Morozzi06/2024
2052^2160054+24817650242Stefano Morozzi06/2024
206(15^551927+1)/16649116Paul Bourdelais07/2013
2072^2153756+72181648346Enzo Doria04/2018
208(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
209Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
2102^2119239+684443637955Enzo Doria11/2018
2112^2117699+89637491Stefano Morozzi10/2021
212(5*10^636570+31)/9636570Rytis Slatkevicius02/2023
2132^2114495+20753636527Enzo Doria08/2023
2142^2107382+105634386Stefano Morozzi10/2021
215(51*21^479149-1243)/4633542Curtis Bright11/2015
2162^2099459+71663632001Enzo Doria07/2018
217(10^631715+53)/9631715Rytis Slatkevicius01/2023
218Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
2192^2097791+60563631499Enzo Doria04/2018
2202^2086750-3628175Paul Bourdelais05/2020
2212^2083766+73519627277Enzo Doria01/2019
222(16105^146689-1)/(16105^383-1)615504Ryan Propper11/2023
223(20^472709-1)/19615008Paul Bourdelais01/2015
224PIPrime(613373)613373Adrian Bondrescu05/2016
225124452^80465+80465^124452610513Ryan Propper10/2023
22611^586020-2610277Paul Bourdelais11/2021
227(19^476929+1)/20609874Paul Bourdelais03/2015
228(7^720497-2^720497)/5608890Jon Grantham08/2023
2292^2019811+1867211608024Enzo Doria04/2018
230F(2904353)606974Henri Lifchitz07/2014
2312^2014720+71893606492Enzo Doria04/2018
232(5^866029-3^866029)/2605328Jon Grantham08/2023
233L(2894561)604928Ryan Propper06/2022
234(18^481147+1)/19603970Paul Bourdelais07/2011
235200^262144+119^262144603202Kellen Shenton08/2022
236(83467^121801-1)/(83467^349-1)597728Ryan Propper11/2023
237(61448^124609-1)/(61448^353-1)595001Ryan Propper11/2023
238(15^505117-1)/14594063Paul Bourdelais01/2015
23981^310721-80^310721593007Paul Bourdelais07/2023
240(152^270217-1)/(152-1)589570Michael Stocker06/2015
241Phi(177147,94259)587458Anonymous09/2022
2422^1950002+1867369587010Enzo Doria02/2018
243116265^111218+111218^116265586694Ryan Propper10/2023
2442^1940812+3584243Paul Bourdelais06/2020
2451933695^2+2^1933695582101Ryan Propper05/2023
246(5^832151-2^832151)/3581649Jon Grantham08/2023
247(129810^113569-1)/(129810^337-1)578991Ryan Propper11/2023
2482^1923104+153578912Stefano Morozzi07/2021
249116761^87652+87652^116761577122Ryan Propper10/2023
250116395^87994+87994^116395575510Ryan Propper10/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 13 2024 11:26 (Time in France)

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