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	10^150029-41	150029	Serge Batalov	12/2014
4002	33185^33185+618^618	150028	Serge Batalov	04/2024
4003	9*34^97952+529	150013	Eric Chen	08/2023
4004	10^150000+1158603	150001	Patrick De Geest	09/2018
4005	10^150000-245703	150000	Patrick De Geest	09/2018
4006	(38*10^149999+691)/9	150000	Robert Price	10/2018
4007	2043563126843649194^8192+2043563126843649185^8192	150000	Youcef Lemsafer	01/2023
4008	(2043563126843649232^8192+2043563126843649201^8192)/147457	149994	Youcef Lemsafer	01/2023
4009	2^498238-53	149985	Lelio R Paula	12/2017
4010	45728^1905+1905^45728	149984	Hans Havermann	10/2020
4011	(211^65024+1)/(211^512+1)	149945	Martin Hopf	12/2023
4012	5*10^149907+23	149908	Robert Price	03/2019
4013	32^99585-829	149891	Eric Chen	11/2023
4014	39347^6442+6442^39347	149874	Hans Havermann	09/2020
4015	2^497850+81049	149868	Enzo Doria	07/2016
4016	V(1075416)	149830	Serge Batalov	07/2024
4017	37228^10575+10575^37228	149816	Hans Havermann	10/2020
4018	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
4019	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
4020	(2*10^149803-143)/3	149803	Robert Price	03/2018
4021	33845^26604+26604^33845	149763	Hans Havermann	09/2020
4022	2^497434-2784191	149743	Enzo Doria	10/2015
4023	(865*10^149737-1)/9	149739	Robert Price	04/2020
4024	10^149695-7000001	149695	Robert Price	06/2021
4025	38237^8214+8214^38237	149681	Hans Havermann	09/2020
4026	Phi(745791,2)/1491583	149664	Anonymous	03/2025
4027	(497167*2^497167-1)/70975	149664	Anonymous	04/2025
4028	(23*10^149655+19)/3	149656	Robert Price	07/2019
4029	2^497068-113579	149633	Enzo Doria	08/2014
4030	2^497037+73727	149624	Enzo Doria	04/2016
4031	11*10^149618+3	149620	Robert Price	07/2021
4032	34942^19067+19067^34942	149562	Hans Havermann	09/2020
4033	33696^27449+27449^33696	149561	Hans Havermann	09/2020
4034	2^496773+77747	149544	Enzo Doria	05/2016
4035	29937^33400-33400^29937	149506	Frank Doornink	06/2024
4036	(7*10^149483-493)/9	149483	Robert Price	04/2021
4037	(206*10^149459+7)/3	149461	Robert Price	07/2020
4038	34589^20940+20940^34589	149459	Hans Havermann	09/2020
4039	2^496477-113485	149455	Enzo Doria	08/2014
4040	(496423*2^496423-1)/223573	149439	Anonymous	04/2025
4041	3*2^496411-5	149436	Jon Grantham	07/2023
4042	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
4043	2^496270-49451	149393	Enzo Doria	10/2015
4044	2^496238-1865081	149383	Enzo Doria	01/2016
4045	33831^26030+26030^33831	149380	Hans Havermann	09/2020
4046	34131^23780+23780^34131	149365	Hans Havermann	09/2020
4047	(5*10^149335-53)/3	149336	Robert Price	09/2020
4048	26043^33818-33818^26043	149330	Frank Doornink	03/2024
4049	2^495968-1853699	149302	Enzo Doria	09/2015
4050	2^495935-4117	149292	Yves Minet	02/2018
4051	5*2^495930+3	149291	Jon Grantham	07/2023
4052	35816^14709+14709^35816	149267	Hans Havermann	09/2020
4053	(10^149264+7)/191/2683/80557	149254	Alfred Reich	07/2021
4054	10^149240-40000001	149240	Robert Price	07/2022
4055	10^149240-10809	149240	Alfred Reich	08/2024
4056	2^495712-396765	149225	Enzo Doria	07/2013
4057	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
4058	2^495420+1880701	149137	Enzo Doria	10/2016
4059	25646^33823-33823^25646	149127	Frank Doornink	02/2024
4060	2^495337-1847293	149112	Enzo Doria	07/2015
4061	(2^495193-7)/5	149068	Lelio R Paula	10/2015
4062	2^495163+111546435	149059	Paul Bourdelais	10/2021
4063	33282^30097+30097^33282	149055	Hans Havermann	09/2020
4064	37384^9705+9705^37384	149050	Hans Havermann	09/2020
4065	34808^19143+19143^34808	149049	Hans Havermann	09/2020
4066	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
4067	30657^33212-33212^30657	149007	Frank Doornink	06/2024
4068	47^89113-46^89113	149006	Robert Price	10/2012
4069	V(891190)	148997	Serge Batalov	07/2024
4070	2^494916+87855	148985	Lelio R Paula	01/2016
4071	6*10^148982+73	148983	Robert Price	04/2019
4072	3^312155-4	148936	Anonymous	02/2023
4073	10^148934+1530019	148935	Patrick De Geest	02/2021
4074	10^148934-1000000001	148934	Robert Price	11/2020
4075	10^148934-512057	148934	Patrick De Geest	02/2021
4076	39000^6571+6571^39000	148888	Hans Havermann	10/2020
4077	2^494586-2791991	148886	Enzo Doria	02/2016
4078	8*10^148860-3	148861	Ray Chandler	04/2011
4079	38262^7769+7769^38262	148854	Hans Havermann	10/2020
4080	10^148816-500001	148816	Robert Price	03/2022
4081	(53*10^148811-287)/9	148812	Robert Price	02/2022
4082	2^494333-286183	148810	Enzo Doria	06/2015
4083	2^494144-264119	148753	Enzo Doria	05/2014
4084	6*10^148734+47	148735	Robert Price	06/2022
4085	28724^33353-33353^28724	148696	Frank Doornink	06/2024
4086	36502^11823+11823^36502	148663	Hans Havermann	11/2020
4087	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
4088	64239^206+206^64239	148641	Hans Havermann	10/2020
4089	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
4090	(23*10^148627-137)/3	148628	Robert Price	08/2021
4091	(151*10^148601-1)/3	148603	Robert Price	03/2020
4092	2^493636+82081	148600	Enzo Doria	09/2016
4093	((((((((((((((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
4094	27134^33509-33509^27134	148563	Frank Doornink	01/2024
4095	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
4096	(2*10^148460-23)/3	148460	Robert Price	04/2018
4097	(28*10^148445+101)/3	148446	Robert Price	09/2020
4098	2^493065+225	148428	Henri Lifchitz	11/2024
4099	36203^12556+12556^36203	148391	Hans Havermann	10/2020
4100	33912^23749+23749^33912	148387	Hans Havermann	10/2020
4101	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
4102	34294^21117+21117^34294	148309	Hans Havermann	10/2020
4103	(71*10^148306-539)/9	148307	Robert Price	07/2019
4104	30814^33039-33039^30814	148304	Frank Doornink	06/2024
4105	38042^7875+7875^38042	148222	Hans Havermann	10/2020
4106	5^211959-12874	148153	Enzo Doria	05/2014
4107	34142^21831+21831^34142	148145	Hans Havermann	10/2020
4108	10^148112+34059	148113	Patrick De Geest	05/2021
4109	10^148112-70000001	148112	Robert Price	03/2021
4110	10^148112-106593	148112	Patrick De Geest	05/2021
4111	36303^12016+12016^36303	148108	Hans Havermann	10/2020
4112	(77*10^148089-149)/9	148090	Robert Price	03/2022
4113	(16*10^148071+41)/3	148072	Robert Price	03/2019
4114	187^65175-2	148068	Lelio R Paula	11/2017
4115	2^491851+1871453	148062	Enzo Doria	05/2016
4116	(68*10^148060-257)/9	148061	Robert Price	07/2019
4117	(151*10^148020-1)/3	148022	Robert Price	03/2020
4118	39153^6032+6032^39153	148017	Hans Havermann	10/2020
4119	36798^10507+10507^36798	147983	Hans Havermann	12/2020
4120	(26*10^147973-23)/3	147974	Robert Price	12/2019
4121	2^491521-1865323	147963	Enzo Doria	02/2016
4122	(2^491476+7)/71	147948	Lelio R Paula	10/2015
4123	2*10^147928+47	147929	Robert Price	12/2021
4124	2^491391-7807	147924	Lelio R Paula	01/2013
4125	2^491384+236221	147922	Enzo Doria	05/2025
4126	39736^5279+5279^39736	147920	Hans Havermann	11/2020
4127	2^491370-113297	147918	Enzo Doria	07/2014
4128	(3^707753)%F(707753)	147912	Henri Lifchitz	06/2025
4129	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
4130	44368^2155+2155^44368	147899	Hans Havermann	12/2020
4131	(17*10^147890+79)/3	147891	Robert Price	04/2019
4132	94*10^147871-3	147873	Robert Price	05/2020
4133	10^147843+620967	147844	Patrick De Geest	05/2021
4134	10^147843-50000000001	147843	Robert Price	12/2020
4135	10^147843-182891	147843	Patrick De Geest	05/2021
4136	35805^13346+13346^35805	147709	Hans Havermann	11/2020
4137	2^490672+255255	147707	Paul Bourdelais	10/2021
4138	2^490660-17	147704	Lelio R Paula	12/2017
4139	(229*10^147699-1)/3	147701	Robert Price	07/2020
4140	40656^4289+4289^40656	147678	Hans Havermann	11/2020
4141	(85*10^147676-31)/9	147677	Rytis Slatkevicius	12/2024
4142	2^490550+1179439	147671	Enzo Doria	06/2016
4143	27249^33292-33292^27249	147662	Frank Doornink	06/2024
4144	(23*10^147649-59)/9	147650	Robert Price	05/2018
4145	2^490303+2793653	147596	Enzo Doria	03/2016
4146	2^490266+255255	147585	Paul Bourdelais	10/2021
4147	199^64181-2	147543	Lelio R Paula	11/2017
4148	32849^30958+30958^32849	147518	Hans Havermann	11/2020
4149	2^489871-286987	147466	Enzo Doria	07/2015
4150	2^489864-351899	147464	Enzo Doria	07/2015
4151	175^65724-2	147422	Lelio R Paula	11/2017
4152	2^489712+1874851	147419	Enzo Doria	06/2016
4153	34473^18830+18830^34473	147367	Hans Havermann	11/2020
4154	63^81896-2	147359	Lelio R Paula	10/2017
4155	34580^18237+18237^34580	147344	Hans Havermann	11/2020
4156	(11*10^147313-107)/3	147314	Robert Price	09/2018
4157	(397*10^147310+17)/9	147312	Robert Price	03/2022
4158	2^489305-59815	147296	Enzo Doria	10/2015
4159	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
4160	2*10^147264-61	147265	Robert Price	10/2021
4161	2*10^147260+29	147261	Robert Price	02/2021
4162	33556^24457+24457^33556	147258	Hans Havermann	11/2020
4163	12^136450-11	147255	Riley Fisher	12/2024
4164	2^489125+80357	147242	Enzo Doria	06/2016
4165	10^147240-40000001	147240	Robert Price	07/2022
4166	10^147240-371331	147240	Alfred Reich	09/2024
4167	10^147240-464727	147240	Alfred Reich	09/2024
4168	32835^30452+30452^32835	147220	Hans Havermann	12/2020
4169	(19*10^147213-97)/3	147214	Robert Price	10/2021
4170	27123^33190-33190^27123	147143	Frank Doornink	01/2024
4171	(148*10^147139-1)/3	147141	Robert Price	03/2020
4172	34338^19255+19255^34338	147123	Hans Havermann	11/2020
4173	2^488648-112799	147098	Enzo Doria	07/2014
4174	2^488627-350317	147092	Enzo Doria	06/2015
4175	33432^25075+25075^33432	147076	Hans Havermann	12/2020
4176	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
4177	2^488280-2165	146987	Yves Minet	07/2014
4178	2^488278+45	146987	Lelio R Paula	12/2017
4179	(3^834646)/(2^834646)	146974	Henri Lifchitz	06/2025
4180	32568^32568+32561^32561	146973	Henri Lifchitz	08/2024
4181	2^487927-39	146881	Lelio R Paula	12/2017
4182	(7*10^146860-13)/3	146861	Robert Price	07/2018
4183	(26*10^146856-77)/3	146857	Robert Price	11/2019
4184	32948^28611+28611^32948	146834	Hans Havermann	11/2020
4185	42596^2799+2799^42596	146829	Hans Havermann	12/2020
4186	2^487726-1863341	146821	Enzo Doria	12/2015
4187	43838^2229+2229^43838	146775	Hans Havermann	11/2020
4188	35005^15594+15594^35005	146775	Hans Havermann	11/2020
4189	(167*10^146764+7)/3	146766	Robert Price	04/2021
4190	53^85114+85114	146761	Kellen Shenton	05/2022
4191	(59*10^146738+157)/9	146739	Robert Price	12/2021
4192	((10^73362-1)10000/9+6701)10^73362+(10^73362-1)/9	146728	Hans Havermann	09/2019
4193	32963^28234+28234^32963	146711	Hans Havermann	12/2020
4194	(22*10^146661-19)/3	146662	Robert Price	04/2019
4195	33958^20825+20825^33958	146651	Hans Havermann	12/2020
4196	26289^33178-33178^26289	146640	Frank Doornink	03/2024
4197	2^487121-39523	146639	Enzo Doria	09/2015
4198	61063^252+252^61063	146637	Hans Havermann	12/2020
4199	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
4200	34099^19900+19900^34099	146587	Hans Havermann	11/2020
4201	2^486893-79	146570	Yves Minet	09/2017
4202	36818^9567+9567^36818	146565	Hans Havermann	12/2020
4203	2^486840+1879141	146554	Enzo Doria	08/2016
4204	2^486774-87	146534	Lelio R Paula	12/2017
4205	38655^6176+6176^38655	146530	Hans Havermann	11/2020
4206	8*10^146522-81	146523	Robert Price	02/2021
4207	32820^29059+29059^32820	146485	Hans Havermann	12/2020
4208	37261^8530+8530^37261	146472	Hans Havermann	12/2020
4209	66953^154+154^66953	146462	Hans Havermann	12/2020
4210	96^73877-95^73877	146445	Robert Price	10/2015
4211	8*10^146421+81	146422	Robert Price	08/2019
4212	33153^26090+26090^33153	146420	Hans Havermann	11/2020
4213	2^486275+23961	146384	Enzo Doria	10/2023
4214	(12^135607-1)/18437127731	146335	Paul Vanderveen	06/2025
4215	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
4216	179^64935+2	146290	Lelio R Paula	10/2017
4217	32595^30758+30758^32595	146285	Hans Havermann	11/2020
4218	34972^15157+15157^34972	146205	Hans Havermann	12/2020
4219	(16*10^146200+131)/3	146201	Robert Price	03/2022
4220	(19*10^146181-49)/3	146182	Robert Price	05/2019
4221	2^485531-114621	146160	Enzo Doria	05/2015
4222	2^485473-933075	146142	Paul Bourdelais	06/2021
4223	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
4224	(22*10^146130-193)/9	146131	Robert Price	07/2022
4225	2^485389+81887	146117	Enzo Doria	08/2016
4226	32554^30773+30773^32554	146108	Hans Havermann	11/2020
4227	28075^32844-32844^28075	146101	Frank Doornink	06/2024
4228	(10^146063+71)/9	146063	Serge Batalov	07/2015
4229	2*10^146051-63	146052	Robert Price	01/2022
4230	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
4231	(22*10^146029+257)/9	146030	Robert Price	06/2018
4232	7*10^145982-53	145983	Robert Price	06/2020
4233	2^484743+1872923	145923	Enzo Doria	05/2016
4234	33140^25287+25287^33140	145913	Hans Havermann	01/2021
4235	37875^7112+7112^37875	145895	Hans Havermann	01/2021
4236	30542^32529-32529^30542	145890	Frank Doornink	06/2024
4237	32862^27473+27473^32862	145872	Hans Havermann	01/2021
4238	V(1046652)/2093303	145817	Serge Batalov	07/2024
4239	32836^27587+27587^32836	145815	Hans Havermann	01/2021
4240	2^484341+1879157	145802	Enzo Doria	08/2016
4241	2*10^145784-91	145785	Robert Price	04/2020
4242	2^484271-51	145781	Lelio R Paula	11/2017
4243	(188*10^145750-11)/3	145752	Robert Price	02/2022
4244	70^78989-69^78989	145743	Robert Price	01/2014
4245	51^85334+2	145714	Robert Price	07/2015
4246	10^2^72843+72843^2^10	145687	Henri Lifchitz	03/2025
4247	2^483886-1857101	145665	Enzo Doria	10/2015
4248	29312^32607-32607^29312	145657	Frank Doornink	06/2024
4249	33350^23307+23307^33350	145656	Hans Havermann	01/2021
4250	(19*10^145585+131)/3	145586	Robert Price	06/2020

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Probable Primes Top 10000

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