Henri & Renaud Lifchitz's PRP Top records

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 ?
4001	(2^519925-5)/3	156513	Stefano Morozzi	08/2022
4002	(4*10^156501+119)/3	156502	Robert Price	12/2021
4003	(83*10^156476-101)/9	156477	Robert Price	08/2021
4004	3*10^156435-97	156436	Robert Price	07/2018
4005	10^156428+111	156429	Boyan Hu	10/2024
4006	(8*10^156371-77)/3	156372	Robert Price	07/2018
4007	53^90679-52^90679	156356	Robert Price	01/2013
4008	31267^34782-34782^31267	156349	Frank Doornink	01/2024
4009	(418*10^156309-31)/9	156311	Robert Price	05/2022
4010	2^519106-59141	156267	Enzo Doria	10/2015
4011	25929^35404-35404^25929	156266	Frank Doornink	03/2024
4012	2^519053+6077	156251	Enzo Doria	02/2016
4013	31199^34764-34764^31199	156235	Frank Doornink	01/2024
4014	2^518968-1860989	156225	Enzo Doria	11/2015
4015	(25*10^156221-7)/9	156222	Robert Price	05/2018
4016	2^518931-2782297	156214	Enzo Doria	09/2015
4017	2^518608-2939	156117	Yves Minet	09/2014
4018	10*27^109005+697	156027	Curtis Bright	05/2015
4019	(49*10^155933-319)/9	155934	Robert Price	10/2021
4020	2^517967-113485	155924	Enzo Doria	08/2014
4021	(103*10^155904+17)/3	155906	Robert Price	08/2020
4022	(8*10^155887-719)/9	155887	Robert Price	03/2021
4023	2^517789+29231	155871	Enzo Doria	02/2024
4024	4*10^155853-39	155854	Robert Price	09/2020
4025	2^517698+4429	155843	Lelio R Paula	01/2013
4026	32015^34584-34584^32015	155814	Frank Doornink	01/2024
4027	2^517543-113257	155796	Enzo Doria	07/2014
4028	(14*10^155740-143)/3	155741	Robert Price	11/2018
4029	31959^34564-34564^31959	155697	Frank Doornink	01/2024
4030	31^104309-30^104309	155563	Henri Lifchitz	08/2013
4031	2^516742-39851	155555	Enzo Doria	09/2015
4032	(22*10^155543+47)/3	155544	Robert Price	06/2021
4033	(19*10^155504+131)/3	155505	Robert Price	06/2020
4034	7*10^155496+61	155497	Robert Price	08/2019
4035	2^516440+1878421	155464	Enzo Doria	08/2016
4036	26012^35173-35173^26012	155295	Frank Doornink	03/2024
4037	2^515863-1867237	155291	Enzo Doria	03/2016
4038	2^515786-461861	155268	Enzo Doria	07/2015
4039	2^515644-113247	155225	Enzo Doria	07/2014
4040	(7*10^155203+107)/3	155204	Robert Price	02/2018
4041	10^155163+206871	155164	Patrick De Geest	05/2021
4042	10^155163-40001	155163	Robert Price	01/2021
4043	(17*10^155133-89)/9	155134	Robert Price	07/2018
4044	26024^35131-35131^26024	155117	Frank Doornink	03/2024
4045	2^515249+214457	155106	Enzo Doria	10/2023
4046	2^515227-114997	155099	Enzo Doria	06/2015
4047	26510^35061-35061^26510	155090	Frank Doornink	03/2024
4049	EPrime(155025)	155025	Eric W. Weisstein	10/2010
4048	(14*10^155024-221)/9	155025	Robert Price	04/2018
4050	(4*10^155022+173)/3	155023	Robert Price	02/2018
4051	2^514652+6561	154926	Henri Lifchitz	11/2024
4052	(266*10^154897+1)/3	154899	Robert Price	04/2020
4053	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
4054	(86*10^154853-221)/9	154854	Robert Price	09/2019
4055	2^514361+78167	154839	Enzo Doria	05/2016
4056	2^514281-115033	154815	Enzo Doria	06/2015
4057	25701^35104-35104^25701	154807	Frank Doornink	02/2024
4058	2^514194-3311	154788	Yves Minet	12/2014
4059	25930^35067-35067^25930	154779	Frank Doornink	03/2024
4060	(14*10^154773+37)/3	154774	Robert Price	12/2018
4061	(16*10^154748+131)/3	154749	Robert Price	03/2022
4062	6*10^154742-31	154743	Robert Price	07/2020
4063	(14*10^154645+139)/9	154646	Robert Price	11/2021
4064	2^513690+216949	154637	Enzo Doria	12/2023
4065	5*10^154618-79	154619	Robert Price	03/2021
4066	(167*10^154595+1)/3	154597	Robert Price	04/2021
4067	2^513437+1879337	154560	Enzo Doria	09/2016
4068	2^513306-113201	154521	Enzo Doria	07/2014
4069	26415^34942-34942^26415	154509	Frank Doornink	03/2024
4070	(5^739314)%L(739314)	154508	Henri Lifchitz	07/2025
4071	18^120818+19^120818-2	154497	Harsh Aggarwal	05/2024
4072	(10^154494-13)/3	154494	Robert Price	12/2017
4073	23462^35343+35343^23462	154462	Norbert Schneider	04/2023
4074	2^513042-113787	154442	Enzo Doria	09/2014
4075	(151*10^154434-7)/9	154436	Robert Price	01/2020
4076	(118*10^154428+11)/3	154430	Robert Price	03/2022
4077	2^512987+29153	154425	Enzo Doria	02/2024
4078	(14*10^154413+139)/9	154414	Robert Price	11/2021
4079	(77*10^154389-149)/9	154390	Robert Price	03/2022
4080	32184^34247-34247^32184	154374	Frank Doornink	02/2024
4081	(27393*35^99972-499)/34	154367	Eric Chen	05/2025
4082	10^154359+49	154360	Robert Price	02/2023
4083	2^512628-114053	154317	Enzo Doria	11/2014
4084	2^512529-49783	154287	Enzo Doria	10/2015
4085	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
4086	2^512315-115297	154223	Enzo Doria	06/2015
4087	(47*10^154221+241)/9	154222	Robert Price	06/2022
4088	(7*10^154211+173)/9	154211	Robert Price	01/2022
4089	2^512243+22703	154201	Enzo Doria	09/2023
4090	2^512168+79561	154178	Enzo Doria	06/2016
4091	(77*10^154175+67)/9	154176	Robert Price	12/2021
4092	(59*19^120562-5)/18	154170	Anonymous	12/2023
4093	(5*10^154158-311)/9	154158	Robert Price	12/2021
4094	27169^34758-34758^27169	154120	Frank Doornink	01/2024
4095	(89*10^154103-737)/9	154104	Robert Price	01/2022
4096	2^511857+23327	154085	Enzo Doria	10/2023
4097	4*10^154078-57	154079	Robert Price	10/2018
4098	26242^34863-34863^26242	154060	Frank Doornink	03/2024
4099	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
4100	7*10^154038-57	154039	Robert Price	06/2020
4101	2^511658-114371	154025	Enzo Doria	02/2015
4102	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
4103	2^511580-1846679	154001	Enzo Doria	07/2015
4104	(259*10^153998-1)/3	154000	Robert Price	12/2020
4105	2^511541-113713	153990	Enzo Doria	09/2014
4106	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
4107	10^153935+970801	153936	Patrick De Geest	05/2021
4108	10^153935-1000001	153935	Robert Price	08/2020
4109	(16*10^153868-73)/3	153869	Robert Price	07/2020
4110	9*10^153851-67	153852	Robert Price	11/2020
4111	2^511077-112723	153850	Enzo Doria	06/2014
4112	69^83653-68^83653	153826	Robert Price	12/2013
4113	2^510963-113707	153816	Enzo Doria	09/2014
4114	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
4115	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
4116	2*10^153746-3	153747	Robert Price	07/2015
4117	2^510626+1179379	153714	Enzo Doria	05/2016
4118	(7*10^153664+113)/3	153665	Robert Price	02/2018
4119	2^510448+24991	153661	Enzo Doria	11/2023
4120	2^510420+81121	153652	Enzo Doria	07/2016
4121	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
4122	2^509894-459161	153494	Enzo Doria	05/2015
4123	(74*10^153489+673)/9	153490	Robert Price	02/2022
4124	(49*10^153484-211)/9	153485	Robert Price	06/2022
4125	2^509841+71657	153478	Enzo Doria	04/2016
4126	9*10^153446+41	153447	Robert Price	08/2020
4127	2^509533-1846723	153385	Enzo Doria	07/2015
4128	2^509468-39989	153366	Enzo Doria	09/2015
4129	70^83117-69^83117	153360	Robert Price	01/2014
4130	(209246*34^99997-81)/11	153148	Eric Chen	08/2023
4131	(7*10^153116-1)/3	153117	Robert Price	08/2022
4132	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
4133	31912^33975-33975^31912	153022	Frank Doornink	01/2024
4134	(19*10^153010+131)/3	153011	Robert Price	06/2020
4135	2^508174-1855151	152976	Enzo Doria	09/2015
4136	181^67757-2	152974	Lelio R Paula	12/2017
4137	2^508160-1864829	152972	Enzo Doria	01/2016
4138	10^152960+412563	152961	Patrick De Geest	05/2021
4139	10^152960-50000000001	152960	Robert Price	12/2020
4140	10^152960-423749	152960	Patrick De Geest	05/2021
4141	(71*10^152933-143)/9	152934	Robert Price	10/2021
4142	32109^33932-33932^32109	152919	Frank Doornink	02/2024
4143	2^507857-1848199	152881	Enzo Doria	07/2015
4144	2^507638-115361	152815	Enzo Doria	07/2015
4145	2^507551-114025	152789	Enzo Doria	11/2014
4146	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
4147	(22*10^152670-13)/9	152671	Robert Price	06/2018
4148	2^507085+28517	152648	Enzo Doria	01/2024
4149	2^506917+28847	152598	Enzo Doria	02/2024
4150	2^506451-22339	152457	Enzo Doria	07/2013
4151	26463^34460-34460^26463	152405	Frank Doornink	03/2024
4152	31898^33837-33837^31898	152394	Frank Doornink	01/2024
4153	2^505995-113185	152320	Enzo Doria	07/2014
4154	(8*10^152260-17)/9	152260	Serge Batalov	11/2022
4155	(4*10^152253+149)/9	152253	Robert Price	04/2018
4156	33530^33643-33643^33530	152250	Norbert Schneider	04/2024
4157	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
4158	2^505431-505431	152150	Henri Lifchitz	04/2005
4159	(203*10^152143+1)/3	152145	Robert Price	03/2020
4160	31730^33787-33787^31730	152092	Frank Doornink	01/2024
4161	2^505089+217787	152047	Enzo Doria	01/2024
4162	33565^33594-33594^33565	152043	Norbert Schneider	04/2024
4163	2^505053+73097	152037	Enzo Doria	04/2016
4164	22*10^151998+3	152000	Robert Price	01/2020
4165	(238*10^151979-1)/3	151981	Robert Price	04/2020
4166	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
4167	3^318465+4	151947	Aurel Gibier	09/2024
4168	350377#+797581	151937	Nicolas PALAU	08/2017
4169	(79*10^151906-529)/9	151907	Robert Price	01/2022
4170	2^504618-343991	151906	Enzo Doria	07/2015
4171	2^504259+211193	151798	Enzo Doria	08/2023
4172	2^504212-461939	151783	Enzo Doria	07/2015
4173	7*10^151772-41	151773	Robert Price	08/2021
4174	2^504054-2231	151736	Yves Minet	10/2011
4175	25237^34458-34458^25237	151686	Frank Doornink	11/2023
4176	(28*10^151682+191)/3	151683	Robert Price	02/2020
4177	2^503817+23961	151665	Enzo Doria	10/2023
4178	2^503475-933075	151562	Paul Bourdelais	06/2021
4179	2^503371+26289	151530	Enzo Doria	12/2023
4180	2^503361-39883	151527	Enzo Doria	09/2015
4181	2^503225+382667	151486	Enzo Doria	10/2016
4182	(206*10^151483-11)/3	151485	Robert Price	02/2022
4183	(844*10^151396-7)/9	151398	Robert Price	05/2021
4184	(26*10^151391-503)/9	151392	Robert Price	07/2018
4185	2^502769+1877567	151349	Enzo Doria	08/2016
4186	2^502576-4019	151291	Yves Minet	10/2011
4187	5*10^151257+41	151258	Robert Price	03/2019
4188	2^502290-2792501	151205	Enzo Doria	02/2016
4189	2^502181+1868417	151172	Enzo Doria	04/2016
4190	2^502055+22583	151134	Enzo Doria	09/2023
4191	(3*23^110967+41)/22	151106	Anonymous	12/2023
4192	6*10^151063-77	151064	Robert Price	09/2021
4193	2^501781-1850503	151052	Enzo Doria	08/2015
4194	(2^82589933-1)%(10^151020)	151020	Anonymous	05/2025
4195	(5*10^151007+37)/3	151008	Robert Price	03/2018
4196	3^316494+5*2^316494	151007	Jon Grantham	08/2023
4197	2^501627-991	151005	Yves Minet	02/2014
4198	2^501577-115333	150990	Enzo Doria	07/2015
4199	25239^34298-34298^25239	150983	Frank Doornink	12/2023
4200	(19*10^150977-7)/3	150978	Robert Price	12/2023
4201	8*10^150975+3	150976	Robert Price	08/2015
4202	2^501512-113669	150971	Enzo Doria	09/2014
4203	34180^26101+26101^34180	150962	Norman Luhn	04/2024
4204	U(1083477)/2166953	150949	Serge Batalov	07/2024
4205	(83*10^150908+493)/9	150909	Robert Price	12/2021
4206	36267^14482+14482^36267	150901	Norman Luhn	04/2024
4207	2*10^150818+83	150819	Robert Price	12/2021
4208	48753^1240+1240^48753	150814	Norman Luhn	04/2024
4209	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
4210	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
4211	2^500899-500899	150786	Henri Lifchitz	04/2005
4212	2^500832+1876801	150766	Enzo Doria	07/2016
4213	(23*10^150763-59)/9	150764	Robert Price	05/2018
4214	46002^1891+1891^46002	150735	Norman Luhn	04/2024
4215	32001^33458-33458^32001	150734	Frank Doornink	01/2024
4216	2^500699+1884953	150726	Enzo Doria	02/2017
4217	(13*10^150675-37)/3	150676	Robert Price	01/2019
4218	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
4219	35365^18204+18204^35365	150661	Norman Luhn	05/2024
4221	2^500337-71101	150617	Enzo Doria	04/2016
4220	(74*10^150616+133)/9	150617	Robert Price	06/2019
4222	(2*10^150612-17)/3	150612	Serge Batalov	11/2022
4223	4*10^150577+91	150578	Robert Price	08/2018
4224	5649^40132+40132^5649	150575	Norbert Schneider	04/2024
4225	2^500160+80071	150564	Enzo Doria	06/2016
4226	(2^500120+5)/9	150551	Lelio R Paula	12/2017
4228	(43*10^150515-421)/9	150516	Robert Price	01/2019
4227	4695^40994+40994^4695	150516	Norbert Schneider	11/2023
4229	2^499999+15981	150515	Norman Luhn	08/2023
4230	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
4231	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
4232	26614^34005-34005^26614	150476	Frank Doornink	03/2024
4233	2^499861-29503	150474	Enzo Doria	08/2015
4234	2^499653-113533	150411	Enzo Doria	08/2014
4235	(14*10^150391-191)/3	150392	Robert Price	10/2020
4236	29033^33696+33696^29033	150382	Norbert Schneider	10/2023
4237	2^499534-221	150375	Yves Minet	06/2012
4238	30110^33567+33567^30110	150337	Norbert Schneider	10/2023
4239	26212^34023-34023^26212	150331	Frank Doornink	03/2024
4240	(28*10^150294+41)/3	150295	Robert Price	07/2021
4241	2^499225+49727	150282	Enzo Doria	09/2016
4242	(695*10^150274+7)/9	150276	Robert Price	12/2021
4243	2^499054-29261	150231	Enzo Doria	07/2015
4244	18580^35187+35187^18580	150215	Norbert Schneider	10/2023
4245	(844*10^150196-7)/9	150198	Robert Price	05/2021
4246	2^498907-933075	150186	Paul Bourdelais	06/2021
4247	(2^498898-7)/9	150183	Lelio R Paula	10/2015
4248	3*10^150182+17	150183	Robert Price	07/2018
4249	5*10^150175+63	150176	Robert Price	09/2020
4250	29273^33618-33618^29273	150154	Frank Doornink	06/2024

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Probable Primes Top 10000

(302010 PRPs in the top)