PRP Records

Probable Primes Top 10000

(300674 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(2^8247949-1)/10623358313/23839855293703/1796076682962964611744892482834Anonymous06/2024
18(17^1990523-1)/162449236Paul Bourdelais08/2020
19(35963^524288+1)/22388581Ryan Propper08/2022
20500186^54465+54465^5001862368940Ryan Propper08/2024
21(11^2264611+1)/122358349Paul Bourdelais07/2021
22(5^3300593-1)/42307015Anonymous02/2022
23(3^4694803+2^4694803)/52239990Ryan Propper12/2023
24(2^7313983-1)/3054920802761932201714Oliver Kruse03/2018
25(3^4571447+2^4571447)/52181134Ryan Propper12/2023
26(15^1848811+1)/162174370Paul Bourdelais07/2024
27F(10367321)2166642Ryan Propper08/2024
28(15^1841911+1)/162166255Paul Bourdelais07/2024
294532794^3+3^45327942162693Ryan Propper10/2023
30F(10317107)2156148Ryan Propper07/2024
31(2^7080247-1)/156822217506727/11283326312536321/96329405483303395932131318Gord Palameta10/2017
32360834^356345+356345^3608342003304Ryan Propper02/2024
33360339^356572+356572^3603392000656Ryan Propper05/2024
34(11^1868983-1)/101946345Paul Bourdelais06/2021
35(36^1145393+1)/371782577Paul Bourdelais11/2023
361343238^19+19^13432381717671Ryan Propper05/2023
37(3^3598867-1)/21717096Ryan Propper12/2021
38(13^1503503-1)/121674817Paul Bourdelais04/2020
39Mills(3,30,6,80,12,450,894,3636,70756,97220,66768,300840,1623568,8436308)1665461Ryan Propper + Sergey Batalov05/2024
40F(7789819)1627976Ryan Propper07/2024
41(10^1600787+1)/111600786Paul Bourdelais05/2020
42(18^1270141-1)/171594372Paul Bourdelais12/2021
43(14^1385203+1)/151587619Paul Bourdelais02/2022
44(2^5243339-2^2621670+1)/51578402Ryan Propper + Sergey Batalov06/2020
45(2^5240707-1)/753928109031577600Tony Prest / Never Odd Or Even07/2016
462^5146295+416931549190Engracio Esmenda / Five or Bust11/2009
47(2^4834891-1)/1701881633/706596885755771455425Gord Palameta01/2017
48300102^59935+59935^3001021433792Ryan Propper05/2023
49(187503^262144+1)/21382288Ryan Propper08/2022
502^4583176+21311379674Ben Maloney / Five or Bust09/2009
51F(6530879)1364873Ryan Propper08/2022
52(2^4533073+2^2266537+1)/51364591Serge Batalov03/2014
53(13^1199467+1)/141336138Paul Bourdelais12/2015
54(5^1888279-1)/41319850Paul Bourdelais04/2018
55(5^1856147+1)/61297391Paul Bourdelais02/2019
56(3^2704981-1)/21290604Ryan Propper12/2021
57(20^984349-1)/191280667Paul Bourdelais09/2021
58(3^2674381+1)/41276004Paul Bourdelais03/2024
591139148^13+13^11391481268947Ryan Propper07/2023
60(2^4194304+1026473)/31262611Tony Prest / Never Odd Or Even07/2017
61(2^4187251-1)/722343423715191260475Tony Prest / Never Odd Or Even05/2016
62(14^1091401+1)/151250885Paul Bourdelais03/2014
63(16^1025393+1)/171234695Paul Bourdelais08/2014
6411^1181716+11817161230631Kellen Shenton07/2023
65(2^4031399+1)/31213572Tony Reix / Diepeveen-Underwood -Reix02/2010
66(3^2533963+1)/41209008Paul Bourdelais03/2020
67L(5466311)1142392Ryan Propper08/2022
68(34^735439+1)/351126308Paul Bourdelais10/2023
69(67*10^1116676+23)/91116677Ryan Propper + Sergey Batalov01/2023
702^3701725-1391114331Stefano Morozzi09/2024
712^3701370-7771114224Stefano Morozzi09/2024
722^3690839-18684071111054Enzo Doria03/2021
732^3678448+3845411107324Enzo Doria03/2022
742^3668660+18888011104377Enzo Doria03/2020
75(106*23^800873-7)/111090573Curtis Bright05/2015
76(7^1264699-1)/61068794Paul Bourdelais01/2014
77(6^1365019-1)/51062191Paul Bourdelais12/2019
782^3511529-151057076Stefano Morozzi06/2023
79(3^2215303-1)/21056968Paul Bourdelais02/2019
802^3480081-91047609Stefano Morozzi05/2023
8110^1043372+71043373Alfred Reich12/2021
82(2^3464473-1)/6048745082991771042896Anand Nair10/2014
83202628^128217+128217^2026281035013Ryan Propper12/2023
84202688^125163+125163^2026881033198Ryan Propper12/2023
85201868^129567+129567^2018681032050Ryan Propper11/2023
86202168^126585+126585^2021681031539Ryan Propper11/2023
87202336^124213+124213^2023361030734Ryan Propper11/2023
88201754^125605+125605^2017541028746Ryan Propper10/2023
89(6^1313371+1)/71022001Paul Bourdelais01/2019
90200307^126128+126128^2003071021729Ryan Propper10/2023
91193143^193143+214^2141020931Ryan Propper + Sergey Batalov05/2024
92200026^126791+126791^2000261020751Ryan Propper09/2023
93200068^125561+125561^2000681020118Ryan Propper09/2023
94192223^192223+166^1661015669Ryan Propper + Sergey Batalov05/2024
95(2^3352132+9)/51009092Tony Prest / Never Odd Or Even06/2018
96(2^3351958+191)/3/3/5/17/67/207061/11066359/1608561247/674729942211009003Tony Prest / Never Odd Or Even08/2019
97(2^3351556+159)/5/7/7/2927/14552647/117615601/7068740758371008886Tony Prest / Never Odd Or Even08/2019
98(2^3351346+113)/3/548533/39539021/946508381271008831Tony Prest / Never Odd Or Even11/2022
99(2^3350899+115)/3/3/11/4091008717Tony Prest / Never Odd Or Even04/2020
100(2^3350068+183)/953/157612311008461Tony Prest / Never Odd Or Even03/2020
101(2^3349565+57)/23/263/778931008311Tony Prest / Never Odd Or Even03/2020
102(2^3349080+137)/3/79/80604190991008162Tony Prest / Never Odd Or Even07/2020
103(2^3349027+183)/23/1277/11638321/50448485271008137Tony Prest / Never Odd Or Even09/2022
104(2^3348456+23)/3/411007984Tony Prest / Never Odd Or Even01/2019
105(2^3348338+213)/71007950Tony Prest / Never Odd Or Even10/2018
106(2^3348184+123)/12491/3229442631007892Tony Prest / Never Odd Or Even01/2021
107(2^3348131+207)/5/11/41/43/12661193081/868684167491007862Tony Prest / Never Odd Or Even05/2021
108(2^3348111+245)/9721/215412555797/198704945240871007854Tony Prest / Never Odd Or Even05/2021
109(2^3347690+143)/3/7/167/5858771007746Tony Prest / Never Odd Or Even06/2020
110(2^3347613+103)/3/5/1948091007726Tony Prest / Never Odd Or Even02/2020
111(2^3347274+143)/3/3/3/234786457/34840035575691007608Tony Prest / Never Odd Or Even07/2022
112(2^3346590+185)/3/31/83/2201765933/3262109845431007400Tony Prest / Never Odd Or Even04/2021
113(2^3346468+257)/3/7/13/71/108471007379Tony Prest / Never Odd Or Even05/2020
114L(4819961)1007313Ryan Propper07/2022
115(2^3346066+139)/168803/71205272050631007249Tony Prest / Never Odd Or Even05/2023
116(2^3345946+187)/7/31229571007223Tony Prest / Never Odd Or Even03/2019
1172^3345603+631007127Tony Prest / Never Odd Or Even05/2018
118(2^3345474+255)/19/29/25571007082Tony Prest / Never Odd Or Even12/2019
119(2^3345364+43)/53/79/109/2389/10889/168383091007035Tony Prest / Never Odd Or Even07/2022
120(2^3345080+247)/31/39671006965Tony Prest / Never Odd Or Even03/2019
121(2^3343888+209)/3/3/5/31/1791006606Tony Prest / Never Odd Or Even11/2019
122(2^3343774+115)/122391006573Tony Prest / Never Odd Or Even10/2018
123(2^3343633+105)/1371006532Tony Prest / Never Odd Or Even10/2018
124(2^3343714+149)/3/11/17/6047/23869/3993469/1713889507211006530Tony Prest / Never Odd Or Even01/2021
125(2^3343629+183)/5/35107/2154259/282128297091006511Tony Prest / Never Odd Or Even05/2022
126(2^3343142+13)/587/212195573363/37759700667191006360Tony Prest / Never Odd Or Even05/2018
127(2^3342880+215)/3/7/157/239/8211006299Tony Prest / Never Odd Or Even04/2020
128(2^3342804+51)/13/13/43/2069/1491731006272Tony Prest / Never Odd Or Even01/2023
129(2^3342732+41)/3/7/285138001393791006248Tony Prest / Never Odd Or Even03/2023
130(2^3342588+95)/3/619/13174671553/227610668471006196Tony Prest / Never Odd Or Even08/2018
131194968^136197+136197^1949681000999Hans Havermann12/2023
132191319^170462+170462^1913191000910Hans Havermann07/2023
133197180^119151+119151^1971801000905Hans Havermann08/2023
134202818^85523+85523^2028181000316Gabor Levai08/2023
135(2^3322799+505)/31000262Stefano Morozzi08/2022
1362^3322627-5251000211Stefano Morozzi07/2024
137265341^5882+5882^2653411000210Gabor Levai04/2024
138218767^37314+37314^2187671000175Gabor Levai03/2023
1392^3322077+6591000045Stefano Morozzi04/2022
140211185^54364+54364^2111851000027Gabor Levai05/2022
14710^999999+5934991000000Peter Kaiser02/2013
14110^999999+308267*10^292000+11000000Sergey Batalov09/2021
142138159533888769035882147()973433052122012098003208^4096+11000000Anonymous11/2021
143138159533888769035882147()973433052122012098115876^4096+11000000Anonymous11/2021
144190880568043619196745858()064791100275825910782112^2048+11000000Anonymous05/2023
145190880568043619196745858()064791100275825910980374^2048+11000000Anonymous05/2023
146(sqrtnint(10^999999,1024)+407852)^1024+11000000Anonymous06/2024
14810^999999-172473999999Patrick De Geest12/2016
14910^999999-1087604*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
15010^999999-1022306*10^287000-1999999Ryan Propper + Sergey Batalov09/2021
151(7^1178033+1)/8995553Paul Bourdelais01/2019
15210^995256+7995257Alfred Reich11/2021
153F(4740217)990647Ryan Propper07/2022
154(3^2052329+2^2052329)/5979210Ryan Propper12/2023
1552^3223639+74333970413Enzo Doria10/2021
1562^3118435+73793938743Enzo Doria01/2021
1572^3037438+1885789914360Enzo Doria05/2019
1582^3032354+74209912830Enzo Doria01/2020
1592^3018556+31908676Robert Price09/2019
160(3^1896463+1)/4904843Paul Bourdelais01/2020
161Tau(181^72558)900969Nik Lygeros / Olivier Rozier / LR team07/2018
1622^2976221+2041857895932Makoto Morimoto09/2014
1631839730^3+3^1839730877775Ryan Propper06/2023
164(35^568453-1)/34877729Paul Bourdelais10/2021
165L(4161629)869730Ryan Propper07/2022
166(2^2860553+1)/(3*1528891204123*11630352659013691)861084Gord Palameta03/2019
1672^2843446+1885789855963Enzo Doria05/2019
1683^1753088+2836436Paul Bourdelais03/2022
169(12^769543-1)/11830476Paul Bourdelais12/2014
1702^2740174+1884385824875Enzo Doria01/2019
171Tau(229^63498)824146Nik Lygeros / Olivier Rozier / LR team07/2020
172(168326^157609-1)/(168326^397-1)821614Ryan Propper11/2023
173(9^860029+1)/10820676Paul Bourdelais09/2020
1742^2723045+60227819719Enzo Doria01/2020
1752^2711746+74179816317Enzo Doria11/2019
176(2^2687383+1)/(3*440088720954577)808968Gord Palameta03/2019
177684614^15+15^684614805169Ryan Propper05/2023
178(31^535571-1)/30798729Alexander Zhirkov08/2019
179(9^835391-7^835391)/2797166Jon Grantham07/2023
180(64*10^779465-1)/81779465Serge Batalov09/2014
181(8^854149-3^854149)/5771373Jon Grantham08/2023
182(64*10^762811-1)/9762812Serge Batalov09/2014
1832^2515946+60529757376Enzo Doria10/2018
184(15^639833-1)/14752501Paul Bourdelais04/2019
1852^2442546+74209735280Enzo Doria03/2020
186(110212^143641-1)/(110212^379-1)722361Ryan Propper11/2023
187(79^379703+1)/80720533Paul Bourdelais10/2023
188(10^718580+269)/9718580Serge Batalov12/2014
189(7^846913-2^846913)/5715724Jon Grantham08/2023
190(99^357779+1)/100713995Paul Bourdelais02/2022
191558232^19+19^558232713842Ryan Propper05/2023
192(26^501409+1)/27709479Paul Bourdelais10/2023
193(81^370421+1)/82706942Paul Bourdelais12/2021
194(2^2327417-1)/23915387348002001700606Anand Nair08/2014
195F(3340367)698096Henri Lifchitz03/2018
196(2^2305781-2^1152891+1)/5694109Serge Batalov01/2014
197135078^135078-13^13693030Henri Lifchitz11/2024
198(7^817519-3^817519)/4690884Jon Grantham08/2023
1992^2291342+73519689763Enzo Doria12/2018
200(10^685224+89)/9685224Serge Batalov12/2014
201(65^375017-1)/64679872Paul Bourdelais10/2023
202F(3244369)678033Henri Lifchitz09/2017
2032^2249255+28433677094Ben Maloney / Five or Bust01/2009
204(10^675470+269)/9675470Serge Batalov12/2014
205(2*10^672745-17)/3672745Rytis Slatkevicius09/2024
206Tau(151^56086)672156Nik Lygeros / Olivier Rozier / LR team10/2017
207(9^703393+1)/10671207Paul Bourdelais08/2015
208(121^320483+1)/122667496Paul Bourdelais08/2019
209(10^666903-7)/3666903Rytis Slatkevicius01/2023
2102^2213586+71389666356Enzo Doria04/2018
211(9614^167281-1)/(9614^409-1)664636Ryan Propper11/2023
2122^2205444+3663905Paul Bourdelais08/2020
213(41*13^592198+27)/4659677Eric Chen11/2023
2142^2191232+105659627Stefano Morozzi10/2021
2152^2187054+1886719658369Enzo Doria11/2018
216(6^840316-11)/5653893Paul Bourdelais06/2020
2172^2160082+39973650250Stefano Morozzi07/2024
2182^2160074+41857650248Stefano Morozzi06/2024
2192^2160054+24817650242Stefano Morozzi06/2024
2202^2160018+24099650231Stefano Morozzi09/2024
221(15^551927+1)/16649116Paul Bourdelais07/2013
2222^2153756+72181648346Enzo Doria04/2018
223(3^1353449-3^676725+1)/7645759Serge Batalov03/2014
224Tau(983^38932)640784Nik Lygeros / Olivier Rozier02/2016
2252^2119239+684443637955Enzo Doria11/2018
2262^2117699+89637491Stefano Morozzi10/2021
227(5*10^636570+31)/9636570Rytis Slatkevicius02/2023
2282^2114495+20753636527Enzo Doria08/2023
2292^2107382+105634386Stefano Morozzi10/2021
230(51*21^479149-1243)/4633542Curtis Bright11/2015
2312^2099459+71663632001Enzo Doria07/2018
232(10^631715+53)/9631715Rytis Slatkevicius01/2023
233Tau(881^38992)631568Nik Lygeros / Olivier Rozier01/2016
2342^2097791+60563631499Enzo Doria04/2018
2352^2086750-3628175Paul Bourdelais05/2020
2362^2083766+73519627277Enzo Doria01/2019
237(16105^146689-1)/(16105^383-1)615504Ryan Propper11/2023
238(20^472709-1)/19615008Paul Bourdelais01/2015
239PIPrime(613373)613373Adrian Bondrescu05/2016
240124452^80465+80465^124452610513Ryan Propper10/2023
24111^586020-2610277Paul Bourdelais11/2021
242(19^476929+1)/20609874Paul Bourdelais03/2015
243(7^720497-2^720497)/5608890Jon Grantham08/2023
2442^2019811+1867211608024Enzo Doria04/2018
245F(2904353)606974Henri Lifchitz07/2014
2462^2014720+71893606492Enzo Doria04/2018
247(5^866029-3^866029)/2605328Jon Grantham08/2023
248L(2894561)604928Ryan Propper06/2022
249(18^481147+1)/19603970Paul Bourdelais07/2011
250200^262144+119^262144603202Kellen Shenton08/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 01 2024 09:16 (Time in France)

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