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	2^508160-1864829	152972	Enzo Doria	01/2016
4002	10^152960+412563	152961	Patrick De Geest	05/2021
4003	10^152960-50000000001	152960	Robert Price	12/2020
4004	10^152960-423749	152960	Patrick De Geest	05/2021
4005	(71*10^152933-143)/9	152934	Robert Price	10/2021
4006	32109^33932-33932^32109	152919	Frank Doornink	02/2024
4007	2^507857-1848199	152881	Enzo Doria	07/2015
4008	2^507638-115361	152815	Enzo Doria	07/2015
4009	2^507551-114025	152789	Enzo Doria	11/2014
4010	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
4011	(22*10^152670-13)/9	152671	Robert Price	06/2018
4012	2^507085+28517	152648	Enzo Doria	01/2024
4013	2^506917+28847	152598	Enzo Doria	02/2024
4014	2^506451-22339	152457	Enzo Doria	07/2013
4015	26463^34460-34460^26463	152405	Frank Doornink	03/2024
4016	31898^33837-33837^31898	152394	Frank Doornink	01/2024
4017	2^505995-113185	152320	Enzo Doria	07/2014
4018	(8*10^152260-17)/9	152260	Serge Batalov	11/2022
4019	(4*10^152253+149)/9	152253	Robert Price	04/2018
4020	33530^33643-33643^33530	152250	Norbert Schneider	04/2024
4021	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
4022	2^505431-505431	152150	Henri Lifchitz	04/2005
4023	(203*10^152143+1)/3	152145	Robert Price	03/2020
4024	31730^33787-33787^31730	152092	Frank Doornink	01/2024
4025	2^505089+217787	152047	Enzo Doria	01/2024
4026	33565^33594-33594^33565	152043	Norbert Schneider	04/2024
4027	2^505053+73097	152037	Enzo Doria	04/2016
4028	22*10^151998+3	152000	Robert Price	01/2020
4029	(238*10^151979-1)/3	151981	Robert Price	04/2020
4030	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
4031	3^318465+4	151947	Aurel Gibier	09/2024
4032	350377#+797581	151937	Nicolas PALAU	08/2017
4033	(79*10^151906-529)/9	151907	Robert Price	01/2022
4034	2^504618-343991	151906	Enzo Doria	07/2015
4035	2^504259+211193	151798	Enzo Doria	08/2023
4036	2^504212-461939	151783	Enzo Doria	07/2015
4037	7*10^151772-41	151773	Robert Price	08/2021
4038	2^504054-2231	151736	Yves Minet	10/2011
4039	25237^34458-34458^25237	151686	Frank Doornink	11/2023
4040	(28*10^151682+191)/3	151683	Robert Price	02/2020
4041	2^503817+23961	151665	Enzo Doria	10/2023
4042	2^503475-933075	151562	Paul Bourdelais	06/2021
4043	2^503371+26289	151530	Enzo Doria	12/2023
4044	2^503361-39883	151527	Enzo Doria	09/2015
4045	2^503225+382667	151486	Enzo Doria	10/2016
4046	(206*10^151483-11)/3	151485	Robert Price	02/2022
4047	(844*10^151396-7)/9	151398	Robert Price	05/2021
4048	(26*10^151391-503)/9	151392	Robert Price	07/2018
4049	2^502769+1877567	151349	Enzo Doria	08/2016
4050	2^502576-4019	151291	Yves Minet	10/2011
4051	5*10^151257+41	151258	Robert Price	03/2019
4052	2^502290-2792501	151205	Enzo Doria	02/2016
4053	2^502181+1868417	151172	Enzo Doria	04/2016
4054	2^502055+22583	151134	Enzo Doria	09/2023
4055	(3*23^110967+41)/22	151106	Anonymous	12/2023
4056	6*10^151063-77	151064	Robert Price	09/2021
4057	2^501781-1850503	151052	Enzo Doria	08/2015
4058	(2^82589933-1)%(10^151020)	151020	Anonymous	05/2025
4059	(5*10^151007+37)/3	151008	Robert Price	03/2018
4060	3^316494+5*2^316494	151007	Jon Grantham	08/2023
4061	2^501627-991	151005	Yves Minet	02/2014
4062	2^501577-115333	150990	Enzo Doria	07/2015
4063	25239^34298-34298^25239	150983	Frank Doornink	12/2023
4064	(19*10^150977-7)/3	150978	Robert Price	12/2023
4065	8*10^150975+3	150976	Robert Price	08/2015
4066	2^501512-113669	150971	Enzo Doria	09/2014
4067	34180^26101+26101^34180	150962	Norman Luhn	04/2024
4068	U(1083477)/2166953	150949	Serge Batalov	07/2024
4069	(83*10^150908+493)/9	150909	Robert Price	12/2021
4070	36267^14482+14482^36267	150901	Norman Luhn	04/2024
4071	2*10^150818+83	150819	Robert Price	12/2021
4072	48753^1240+1240^48753	150814	Norman Luhn	04/2024
4073	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
4074	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
4075	2^500899-500899	150786	Henri Lifchitz	04/2005
4076	2^500832+1876801	150766	Enzo Doria	07/2016
4077	(23*10^150763-59)/9	150764	Robert Price	05/2018
4078	46002^1891+1891^46002	150735	Norman Luhn	04/2024
4079	32001^33458-33458^32001	150734	Frank Doornink	01/2024
4080	2^500699+1884953	150726	Enzo Doria	02/2017
4081	(13*10^150675-37)/3	150676	Robert Price	01/2019
4082	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
4083	35365^18204+18204^35365	150661	Norman Luhn	05/2024
4085	2^500337-71101	150617	Enzo Doria	04/2016
4084	(74*10^150616+133)/9	150617	Robert Price	06/2019
4086	(2*10^150612-17)/3	150612	Serge Batalov	11/2022
4087	4*10^150577+91	150578	Robert Price	08/2018
4088	5649^40132+40132^5649	150575	Norbert Schneider	04/2024
4089	2^500160+80071	150564	Enzo Doria	06/2016
4090	(2^500120+5)/9	150551	Lelio R Paula	12/2017
4092	(43*10^150515-421)/9	150516	Robert Price	01/2019
4091	4695^40994+40994^4695	150516	Norbert Schneider	11/2023
4093	2^499999+15981	150515	Norman Luhn	08/2023
4094	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
4095	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
4096	26614^34005-34005^26614	150476	Frank Doornink	03/2024
4097	2^499861-29503	150474	Enzo Doria	08/2015
4098	2^499653-113533	150411	Enzo Doria	08/2014
4099	(14*10^150391-191)/3	150392	Robert Price	10/2020
4100	29033^33696+33696^29033	150382	Norbert Schneider	10/2023
4101	2^499534-221	150375	Yves Minet	06/2012
4102	30110^33567+33567^30110	150337	Norbert Schneider	10/2023
4103	26212^34023-34023^26212	150331	Frank Doornink	03/2024
4104	(28*10^150294+41)/3	150295	Robert Price	07/2021
4105	2^499225+49727	150282	Enzo Doria	09/2016
4106	(695*10^150274+7)/9	150276	Robert Price	12/2021
4107	2^499054-29261	150231	Enzo Doria	07/2015
4108	18580^35187+35187^18580	150215	Norbert Schneider	10/2023
4109	(844*10^150196-7)/9	150198	Robert Price	05/2021
4110	2^498907-933075	150186	Paul Bourdelais	06/2021
4111	(2^498898-7)/9	150183	Lelio R Paula	10/2015
4112	3*10^150182+17	150183	Robert Price	07/2018
4113	5*10^150175+63	150176	Robert Price	09/2020
4114	29273^33618-33618^29273	150154	Frank Doornink	06/2024
4115	32363^33292+33292^32363	150149	Norbert Schneider	07/2022
4116	32^99753-99753^32	150144	Henri Lifchitz	08/2024
4117	(77*10^150128+67)/9	150129	Robert Price	12/2021
4118	(710^(275062+1)-9*10^75062-7)/9	150125	Robert Price	12/2023
4119	2^498623+1866983	150101	Enzo Doria	03/2016
4120	33194^33194-213^213	150073	Serge Batalov	04/2024
4121	27868^33759-33759^27868	150063	Frank Doornink	06/2024
4122	(25*10^150050-403)/9	150051	Robert Price	12/2020
4123	numbpart(18140942830)	150033	Serge Batalov	04/2017
4124	10^150029+4381	150030	Patrick De Geest	05/2016
4125	10^150029-41	150029	Serge Batalov	12/2014
4126	33185^33185+618^618	150028	Serge Batalov	04/2024
4127	9*34^97952+529	150013	Eric Chen	08/2023
4128	10^150000+1158603	150001	Patrick De Geest	09/2018
4129	10^150000-245703	150000	Patrick De Geest	09/2018
4130	(38*10^149999+691)/9	150000	Robert Price	10/2018
4131	2043563126843649194^8192+2043563126843649185^8192	150000	Youcef Lemsafer	01/2023
4132	(2043563126843649232^8192+2043563126843649201^8192)/147457	149994	Youcef Lemsafer	01/2023
4133	2^498238-53	149985	Lelio R Paula	12/2017
4134	45728^1905+1905^45728	149984	Hans Havermann	10/2020
4135	(211^65024+1)/(211^512+1)	149945	Martin Hopf	12/2023
4136	5*10^149907+23	149908	Robert Price	03/2019
4137	32^99585-829	149891	Eric Chen	11/2023
4138	39347^6442+6442^39347	149874	Hans Havermann	09/2020
4139	2^497850+81049	149868	Enzo Doria	07/2016
4140	V(1075416)	149830	Serge Batalov	07/2024
4141	37228^10575+10575^37228	149816	Hans Havermann	10/2020
4142	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
4143	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
4144	(2*10^149803-143)/3	149803	Robert Price	03/2018
4145	33845^26604+26604^33845	149763	Hans Havermann	09/2020
4146	2^497434-2784191	149743	Enzo Doria	10/2015
4147	(865*10^149737-1)/9	149739	Robert Price	04/2020
4148	10^149695-7000001	149695	Robert Price	06/2021
4149	38237^8214+8214^38237	149681	Hans Havermann	09/2020
4150	Phi(745791,2)/1491583	149664	Anonymous	03/2025
4151	(497167*2^497167-1)/70975	149664	Anonymous	04/2025
4152	(23*10^149655+19)/3	149656	Robert Price	07/2019
4153	2^497068-113579	149633	Enzo Doria	08/2014
4154	2^497037+73727	149624	Enzo Doria	04/2016
4155	11*10^149618+3	149620	Robert Price	07/2021
4156	34942^19067+19067^34942	149562	Hans Havermann	09/2020
4157	33696^27449+27449^33696	149561	Hans Havermann	09/2020
4158	2^496773+77747	149544	Enzo Doria	05/2016
4159	29937^33400-33400^29937	149506	Frank Doornink	06/2024
4160	(7*10^149483-493)/9	149483	Robert Price	04/2021
4161	(206*10^149459+7)/3	149461	Robert Price	07/2020
4162	34589^20940+20940^34589	149459	Hans Havermann	09/2020
4163	2^496477-113485	149455	Enzo Doria	08/2014
4164	(496423*2^496423-1)/223573	149439	Anonymous	04/2025
4165	3*2^496411-5	149436	Jon Grantham	07/2023
4166	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
4167	2^496270-49451	149393	Enzo Doria	10/2015
4168	2^496238-1865081	149383	Enzo Doria	01/2016
4169	33831^26030+26030^33831	149380	Hans Havermann	09/2020
4170	34131^23780+23780^34131	149365	Hans Havermann	09/2020
4171	(5*10^149335-53)/3	149336	Robert Price	09/2020
4172	26043^33818-33818^26043	149330	Frank Doornink	03/2024
4173	2^495968-1853699	149302	Enzo Doria	09/2015
4174	2^495935-4117	149292	Yves Minet	02/2018
4175	5*2^495930+3	149291	Jon Grantham	07/2023
4176	35816^14709+14709^35816	149267	Hans Havermann	09/2020
4177	(10^149264+7)/191/2683/80557	149254	Alfred Reich	07/2021
4178	10^149240-40000001	149240	Robert Price	07/2022
4179	10^149240-10809	149240	Alfred Reich	08/2024
4180	2^495712-396765	149225	Enzo Doria	07/2013
4181	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
4182	2^495420+1880701	149137	Enzo Doria	10/2016
4183	25646^33823-33823^25646	149127	Frank Doornink	02/2024
4184	2^495337-1847293	149112	Enzo Doria	07/2015
4185	(2^495193-7)/5	149068	Lelio R Paula	10/2015
4186	2^495163+111546435	149059	Paul Bourdelais	10/2021
4187	33282^30097+30097^33282	149055	Hans Havermann	09/2020
4188	37384^9705+9705^37384	149050	Hans Havermann	09/2020
4189	34808^19143+19143^34808	149049	Hans Havermann	09/2020
4190	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
4191	30657^33212-33212^30657	149007	Frank Doornink	06/2024
4192	47^89113-46^89113	149006	Robert Price	10/2012
4193	V(891190)	148997	Serge Batalov	07/2024
4194	2^494916+87855	148985	Lelio R Paula	01/2016
4195	6*10^148982+73	148983	Robert Price	04/2019
4196	3^312155-4	148936	Anonymous	02/2023
4197	10^148934+1530019	148935	Patrick De Geest	02/2021
4198	10^148934-1000000001	148934	Robert Price	11/2020
4199	10^148934-512057	148934	Patrick De Geest	02/2021
4200	39000^6571+6571^39000	148888	Hans Havermann	10/2020
4201	2^494586-2791991	148886	Enzo Doria	02/2016
4202	8*10^148860-3	148861	Ray Chandler	04/2011
4203	38262^7769+7769^38262	148854	Hans Havermann	10/2020
4204	10^148816-500001	148816	Robert Price	03/2022
4205	(53*10^148811-287)/9	148812	Robert Price	02/2022
4206	2^494333-286183	148810	Enzo Doria	06/2015
4207	2^494144-264119	148753	Enzo Doria	05/2014
4208	6*10^148734+47	148735	Robert Price	06/2022
4209	28724^33353-33353^28724	148696	Frank Doornink	06/2024
4210	36502^11823+11823^36502	148663	Hans Havermann	11/2020
4211	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
4212	64239^206+206^64239	148641	Hans Havermann	10/2020
4213	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
4214	(23*10^148627-137)/3	148628	Robert Price	08/2021
4215	(151*10^148601-1)/3	148603	Robert Price	03/2020
4216	2^493636+82081	148600	Enzo Doria	09/2016
4217	((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	148593	Serge Batalov	07/2016
4218	27134^33509-33509^27134	148563	Frank Doornink	01/2024
4219	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
4220	(2*10^148460-23)/3	148460	Robert Price	04/2018
4221	(28*10^148445+101)/3	148446	Robert Price	09/2020
4222	2^493065+225	148428	Henri Lifchitz	11/2024
4223	36203^12556+12556^36203	148391	Hans Havermann	10/2020
4224	33912^23749+23749^33912	148387	Hans Havermann	10/2020
4225	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
4226	34294^21117+21117^34294	148309	Hans Havermann	10/2020
4227	(71*10^148306-539)/9	148307	Robert Price	07/2019
4228	30814^33039-33039^30814	148304	Frank Doornink	06/2024
4229	38042^7875+7875^38042	148222	Hans Havermann	10/2020
4230	5^211959-12874	148153	Enzo Doria	05/2014
4231	34142^21831+21831^34142	148145	Hans Havermann	10/2020
4232	10^148112+34059	148113	Patrick De Geest	05/2021
4233	10^148112-70000001	148112	Robert Price	03/2021
4234	10^148112-106593	148112	Patrick De Geest	05/2021
4235	36303^12016+12016^36303	148108	Hans Havermann	10/2020
4236	(77*10^148089-149)/9	148090	Robert Price	03/2022
4237	(16*10^148071+41)/3	148072	Robert Price	03/2019
4238	187^65175-2	148068	Lelio R Paula	11/2017
4239	2^491851+1871453	148062	Enzo Doria	05/2016
4240	(68*10^148060-257)/9	148061	Robert Price	07/2019
4241	(151*10^148020-1)/3	148022	Robert Price	03/2020
4242	39153^6032+6032^39153	148017	Hans Havermann	10/2020
4243	36798^10507+10507^36798	147983	Hans Havermann	12/2020
4244	(26*10^147973-23)/3	147974	Robert Price	12/2019
4245	2^491521-1865323	147963	Enzo Doria	02/2016
4246	(2^491476+7)/71	147948	Lelio R Paula	10/2015
4247	2*10^147928+47	147929	Robert Price	12/2021
4248	2^491391-7807	147924	Lelio R Paula	01/2013
4249	2^491384+236221	147922	Enzo Doria	05/2025
4250	39736^5279+5279^39736	147920	Hans Havermann	11/2020

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PRP Records

Probable Primes Top 10000

(301815 PRPs in the top)