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	2^515863-1867237	155291	Enzo Doria	03/2016
4002	2^515786-461861	155268	Enzo Doria	07/2015
4003	2^515644-113247	155225	Enzo Doria	07/2014
4004	(7*10^155203+107)/3	155204	Robert Price	02/2018
4005	10^155163+206871	155164	Patrick De Geest	05/2021
4006	10^155163-40001	155163	Robert Price	01/2021
4007	(17*10^155133-89)/9	155134	Robert Price	07/2018
4008	26024^35131-35131^26024	155117	Frank Doornink	03/2024
4009	2^515249+214457	155106	Enzo Doria	10/2023
4010	2^515227-114997	155099	Enzo Doria	06/2015
4011	26510^35061-35061^26510	155090	Frank Doornink	03/2024
4013	EPrime(155025)	155025	Eric W. Weisstein	10/2010
4012	(14*10^155024-221)/9	155025	Robert Price	04/2018
4014	(4*10^155022+173)/3	155023	Robert Price	02/2018
4015	2^514652+6561	154926	Henri Lifchitz	11/2024
4016	(266*10^154897+1)/3	154899	Robert Price	04/2020
4017	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
4018	(86*10^154853-221)/9	154854	Robert Price	09/2019
4019	2^514361+78167	154839	Enzo Doria	05/2016
4020	2^514281-115033	154815	Enzo Doria	06/2015
4021	25701^35104-35104^25701	154807	Frank Doornink	02/2024
4022	2^514194-3311	154788	Yves Minet	12/2014
4023	25930^35067-35067^25930	154779	Frank Doornink	03/2024
4024	(14*10^154773+37)/3	154774	Robert Price	12/2018
4025	(16*10^154748+131)/3	154749	Robert Price	03/2022
4026	6*10^154742-31	154743	Robert Price	07/2020
4027	(14*10^154645+139)/9	154646	Robert Price	11/2021
4028	2^513690+216949	154637	Enzo Doria	12/2023
4029	5*10^154618-79	154619	Robert Price	03/2021
4030	(167*10^154595+1)/3	154597	Robert Price	04/2021
4031	2^513437+1879337	154560	Enzo Doria	09/2016
4032	2^513306-113201	154521	Enzo Doria	07/2014
4033	26415^34942-34942^26415	154509	Frank Doornink	03/2024
4034	(5^739314)%L(739314)	154508	Henri Lifchitz	07/2025
4035	18^120818+19^120818-2	154497	Harsh Aggarwal	05/2024
4036	(10^154494-13)/3	154494	Robert Price	12/2017
4037	23462^35343+35343^23462	154462	Norbert Schneider	04/2023
4038	2^513042-113787	154442	Enzo Doria	09/2014
4039	(151*10^154434-7)/9	154436	Robert Price	01/2020
4040	(118*10^154428+11)/3	154430	Robert Price	03/2022
4041	2^512987+29153	154425	Enzo Doria	02/2024
4042	(14*10^154413+139)/9	154414	Robert Price	11/2021
4043	(77*10^154389-149)/9	154390	Robert Price	03/2022
4044	32184^34247-34247^32184	154374	Frank Doornink	02/2024
4045	(27393*35^99972-499)/34	154367	Eric Chen	05/2025
4046	10^154359+49	154360	Robert Price	02/2023
4047	2^512628-114053	154317	Enzo Doria	11/2014
4048	2^512529-49783	154287	Enzo Doria	10/2015
4049	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
4050	2^512315-115297	154223	Enzo Doria	06/2015
4051	(47*10^154221+241)/9	154222	Robert Price	06/2022
4052	(7*10^154211+173)/9	154211	Robert Price	01/2022
4053	2^512243+22703	154201	Enzo Doria	09/2023
4054	2^512168+79561	154178	Enzo Doria	06/2016
4055	(77*10^154175+67)/9	154176	Robert Price	12/2021
4056	(59*19^120562-5)/18	154170	Anonymous	12/2023
4057	(5*10^154158-311)/9	154158	Robert Price	12/2021
4058	27169^34758-34758^27169	154120	Frank Doornink	01/2024
4059	(89*10^154103-737)/9	154104	Robert Price	01/2022
4060	2^511857+23327	154085	Enzo Doria	10/2023
4061	4*10^154078-57	154079	Robert Price	10/2018
4062	26242^34863-34863^26242	154060	Frank Doornink	03/2024
4063	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
4064	7*10^154038-57	154039	Robert Price	06/2020
4065	2^511658-114371	154025	Enzo Doria	02/2015
4066	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
4067	2^511580-1846679	154001	Enzo Doria	07/2015
4068	(259*10^153998-1)/3	154000	Robert Price	12/2020
4069	2^511541-113713	153990	Enzo Doria	09/2014
4070	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
4071	10^153935+970801	153936	Patrick De Geest	05/2021
4072	10^153935-1000001	153935	Robert Price	08/2020
4073	(16*10^153868-73)/3	153869	Robert Price	07/2020
4074	9*10^153851-67	153852	Robert Price	11/2020
4075	2^511077-112723	153850	Enzo Doria	06/2014
4076	69^83653-68^83653	153826	Robert Price	12/2013
4077	2^510963-113707	153816	Enzo Doria	09/2014
4078	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
4079	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
4080	2*10^153746-3	153747	Robert Price	07/2015
4081	2^510626+1179379	153714	Enzo Doria	05/2016
4082	(7*10^153664+113)/3	153665	Robert Price	02/2018
4083	2^510448+24991	153661	Enzo Doria	11/2023
4084	2^510420+81121	153652	Enzo Doria	07/2016
4085	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
4086	2^509894-459161	153494	Enzo Doria	05/2015
4087	(74*10^153489+673)/9	153490	Robert Price	02/2022
4088	(49*10^153484-211)/9	153485	Robert Price	06/2022
4089	2^509841+71657	153478	Enzo Doria	04/2016
4090	9*10^153446+41	153447	Robert Price	08/2020
4091	2^509533-1846723	153385	Enzo Doria	07/2015
4092	2^509468-39989	153366	Enzo Doria	09/2015
4093	70^83117-69^83117	153360	Robert Price	01/2014
4094	(209246*34^99997-81)/11	153148	Eric Chen	08/2023
4095	(7*10^153116-1)/3	153117	Robert Price	08/2022
4096	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
4097	31912^33975-33975^31912	153022	Frank Doornink	01/2024
4098	(19*10^153010+131)/3	153011	Robert Price	06/2020
4099	2^508174-1855151	152976	Enzo Doria	09/2015
4100	181^67757-2	152974	Lelio R Paula	12/2017
4101	2^508160-1864829	152972	Enzo Doria	01/2016
4102	10^152960+412563	152961	Patrick De Geest	05/2021
4103	10^152960-50000000001	152960	Robert Price	12/2020
4104	10^152960-423749	152960	Patrick De Geest	05/2021
4105	(71*10^152933-143)/9	152934	Robert Price	10/2021
4106	32109^33932-33932^32109	152919	Frank Doornink	02/2024
4107	2^507857-1848199	152881	Enzo Doria	07/2015
4108	2^507638-115361	152815	Enzo Doria	07/2015
4109	2^507551-114025	152789	Enzo Doria	11/2014
4110	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
4111	(22*10^152670-13)/9	152671	Robert Price	06/2018
4112	2^507085+28517	152648	Enzo Doria	01/2024
4113	2^506917+28847	152598	Enzo Doria	02/2024
4114	2^506451-22339	152457	Enzo Doria	07/2013
4115	26463^34460-34460^26463	152405	Frank Doornink	03/2024
4116	31898^33837-33837^31898	152394	Frank Doornink	01/2024
4117	2^505995-113185	152320	Enzo Doria	07/2014
4118	(8*10^152260-17)/9	152260	Serge Batalov	11/2022
4119	(4*10^152253+149)/9	152253	Robert Price	04/2018
4120	33530^33643-33643^33530	152250	Norbert Schneider	04/2024
4121	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
4122	2^505431-505431	152150	Henri Lifchitz	04/2005
4123	(203*10^152143+1)/3	152145	Robert Price	03/2020
4124	31730^33787-33787^31730	152092	Frank Doornink	01/2024
4125	2^505089+217787	152047	Enzo Doria	01/2024
4126	33565^33594-33594^33565	152043	Norbert Schneider	04/2024
4127	2^505053+73097	152037	Enzo Doria	04/2016
4128	22*10^151998+3	152000	Robert Price	01/2020
4129	(238*10^151979-1)/3	151981	Robert Price	04/2020
4130	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
4131	3^318465+4	151947	Aurel Gibier	09/2024
4132	350377#+797581	151937	Nicolas PALAU	08/2017
4133	(79*10^151906-529)/9	151907	Robert Price	01/2022
4134	2^504618-343991	151906	Enzo Doria	07/2015
4135	2^504259+211193	151798	Enzo Doria	08/2023
4136	2^504212-461939	151783	Enzo Doria	07/2015
4137	7*10^151772-41	151773	Robert Price	08/2021
4138	2^504054-2231	151736	Yves Minet	10/2011
4139	25237^34458-34458^25237	151686	Frank Doornink	11/2023
4140	(28*10^151682+191)/3	151683	Robert Price	02/2020
4141	2^503817+23961	151665	Enzo Doria	10/2023
4142	2^503475-933075	151562	Paul Bourdelais	06/2021
4143	2^503371+26289	151530	Enzo Doria	12/2023
4144	2^503361-39883	151527	Enzo Doria	09/2015
4145	2^503225+382667	151486	Enzo Doria	10/2016
4146	(206*10^151483-11)/3	151485	Robert Price	02/2022
4147	(844*10^151396-7)/9	151398	Robert Price	05/2021
4148	(26*10^151391-503)/9	151392	Robert Price	07/2018
4149	2^502769+1877567	151349	Enzo Doria	08/2016
4150	2^502576-4019	151291	Yves Minet	10/2011
4151	5*10^151257+41	151258	Robert Price	03/2019
4152	2^502290-2792501	151205	Enzo Doria	02/2016
4153	2^502181+1868417	151172	Enzo Doria	04/2016
4154	2^502055+22583	151134	Enzo Doria	09/2023
4155	(3*23^110967+41)/22	151106	Anonymous	12/2023
4156	6*10^151063-77	151064	Robert Price	09/2021
4157	2^501781-1850503	151052	Enzo Doria	08/2015
4158	(2^82589933-1)%(10^151020)	151020	Anonymous	05/2025
4159	(5*10^151007+37)/3	151008	Robert Price	03/2018
4160	3^316494+5*2^316494	151007	Jon Grantham	08/2023
4161	2^501627-991	151005	Yves Minet	02/2014
4162	2^501577-115333	150990	Enzo Doria	07/2015
4163	25239^34298-34298^25239	150983	Frank Doornink	12/2023
4164	(19*10^150977-7)/3	150978	Robert Price	12/2023
4165	8*10^150975+3	150976	Robert Price	08/2015
4166	2^501512-113669	150971	Enzo Doria	09/2014
4167	34180^26101+26101^34180	150962	Norman Luhn	04/2024
4168	U(1083477)/2166953	150949	Serge Batalov	07/2024
4169	(83*10^150908+493)/9	150909	Robert Price	12/2021
4170	36267^14482+14482^36267	150901	Norman Luhn	04/2024
4171	2*10^150818+83	150819	Robert Price	12/2021
4172	48753^1240+1240^48753	150814	Norman Luhn	04/2024
4173	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
4174	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
4175	2^500899-500899	150786	Henri Lifchitz	04/2005
4176	2^500832+1876801	150766	Enzo Doria	07/2016
4177	(23*10^150763-59)/9	150764	Robert Price	05/2018
4178	46002^1891+1891^46002	150735	Norman Luhn	04/2024
4179	32001^33458-33458^32001	150734	Frank Doornink	01/2024
4180	2^500699+1884953	150726	Enzo Doria	02/2017
4181	(13*10^150675-37)/3	150676	Robert Price	01/2019
4182	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
4183	35365^18204+18204^35365	150661	Norman Luhn	05/2024
4185	2^500337-71101	150617	Enzo Doria	04/2016
4184	(74*10^150616+133)/9	150617	Robert Price	06/2019
4186	(2*10^150612-17)/3	150612	Serge Batalov	11/2022
4187	4*10^150577+91	150578	Robert Price	08/2018
4188	5649^40132+40132^5649	150575	Norbert Schneider	04/2024
4189	2^500160+80071	150564	Enzo Doria	06/2016
4190	(2^500120+5)/9	150551	Lelio R Paula	12/2017
4192	(43*10^150515-421)/9	150516	Robert Price	01/2019
4191	4695^40994+40994^4695	150516	Norbert Schneider	11/2023
4193	2^499999+15981	150515	Norman Luhn	08/2023
4194	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
4195	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
4196	26614^34005-34005^26614	150476	Frank Doornink	03/2024
4197	2^499861-29503	150474	Enzo Doria	08/2015
4198	2^499653-113533	150411	Enzo Doria	08/2014
4199	(14*10^150391-191)/3	150392	Robert Price	10/2020
4200	29033^33696+33696^29033	150382	Norbert Schneider	10/2023
4201	2^499534-221	150375	Yves Minet	06/2012
4202	30110^33567+33567^30110	150337	Norbert Schneider	10/2023
4203	26212^34023-34023^26212	150331	Frank Doornink	03/2024
4204	(28*10^150294+41)/3	150295	Robert Price	07/2021
4205	2^499225+49727	150282	Enzo Doria	09/2016
4206	(695*10^150274+7)/9	150276	Robert Price	12/2021
4207	2^499054-29261	150231	Enzo Doria	07/2015
4208	18580^35187+35187^18580	150215	Norbert Schneider	10/2023
4209	(844*10^150196-7)/9	150198	Robert Price	05/2021
4210	2^498907-933075	150186	Paul Bourdelais	06/2021
4211	(2^498898-7)/9	150183	Lelio R Paula	10/2015
4212	3*10^150182+17	150183	Robert Price	07/2018
4213	5*10^150175+63	150176	Robert Price	09/2020
4214	29273^33618-33618^29273	150154	Frank Doornink	06/2024
4215	32363^33292+33292^32363	150149	Norbert Schneider	07/2022
4216	32^99753-99753^32	150144	Henri Lifchitz	08/2024
4217	(77*10^150128+67)/9	150129	Robert Price	12/2021
4218	(710^(275062+1)-9*10^75062-7)/9	150125	Robert Price	12/2023
4219	2^498623+1866983	150101	Enzo Doria	03/2016
4220	33194^33194-213^213	150073	Serge Batalov	04/2024
4221	27868^33759-33759^27868	150063	Frank Doornink	06/2024
4222	(25*10^150050-403)/9	150051	Robert Price	12/2020
4223	numbpart(18140942830)	150033	Serge Batalov	04/2017
4224	10^150029+4381	150030	Patrick De Geest	05/2016
4225	10^150029-41	150029	Serge Batalov	12/2014
4226	33185^33185+618^618	150028	Serge Batalov	04/2024
4227	9*34^97952+529	150013	Eric Chen	08/2023
4228	10^150000+1158603	150001	Patrick De Geest	09/2018
4229	10^150000-245703	150000	Patrick De Geest	09/2018
4230	(38*10^149999+691)/9	150000	Robert Price	10/2018
4231	2043563126843649194^8192+2043563126843649185^8192	150000	Youcef Lemsafer	01/2023
4232	(2043563126843649232^8192+2043563126843649201^8192)/147457	149994	Youcef Lemsafer	01/2023
4233	2^498238-53	149985	Lelio R Paula	12/2017
4234	45728^1905+1905^45728	149984	Hans Havermann	10/2020
4235	(211^65024+1)/(211^512+1)	149945	Martin Hopf	12/2023
4236	5*10^149907+23	149908	Robert Price	03/2019
4237	32^99585-829	149891	Eric Chen	11/2023
4238	39347^6442+6442^39347	149874	Hans Havermann	09/2020
4239	2^497850+81049	149868	Enzo Doria	07/2016
4240	V(1075416)	149830	Serge Batalov	07/2024
4241	37228^10575+10575^37228	149816	Hans Havermann	10/2020
4242	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
4243	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
4244	(2*10^149803-143)/3	149803	Robert Price	03/2018
4245	33845^26604+26604^33845	149763	Hans Havermann	09/2020
4246	2^497434-2784191	149743	Enzo Doria	10/2015
4247	(865*10^149737-1)/9	149739	Robert Price	04/2020
4248	10^149695-7000001	149695	Robert Price	06/2021
4249	38237^8214+8214^38237	149681	Hans Havermann	09/2020
4250	Phi(745791,2)/1491583	149664	Anonymous	03/2025

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