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 ?
7008	2^338891-18885	102017	Enzo Doria	05/2013
7001	2^338893+128727	102017	Stefano Morozzi	01/2022
7002	2^338890-52965	102017	Stefano Morozzi	01/2022
7003	2^338892-55467	102017	Stefano Morozzi	02/2022
7004	2^338892-83393	102017	Stefano Morozzi	04/2022
7005	2^338893+13649	102017	Stefano Morozzi	05/2022
7006	2^338892+117957	102017	Stefano Morozzi	09/2022
7007	2^338892-14643	102017	Stefano Morozzi	01/2023
7009	2^338887+154029	102016	Stefano Morozzi	01/2022
7010	2^338889-104293	102016	Stefano Morozzi	02/2022
7011	2^338887+147741	102016	Stefano Morozzi	11/2022
7012	2^338889+195975	102016	Stefano Morozzi	11/2022
7013	2^338889-117873	102016	Stefano Morozzi	02/2023
7014	2^338886+177159	102015	Stefano Morozzi	12/2021
7015	2^338885+40425	102015	Stefano Morozzi	06/2022
7016	2^338884-13053	102015	Stefano Morozzi	12/2022
7017	2^338885-112569	102015	Stefano Morozzi	12/2022
7018	2^338880+11341	102014	Stefano Morozzi	03/2022
7019	2^338880-160383	102014	Stefano Morozzi	06/2022
7020	2^338880-161627	102014	Stefano Morozzi	12/2022
7021	2^338879-1059	102013	Stefano Morozzi	12/2021
7022	2^338879-54525	102013	Stefano Morozzi	02/2022
7023	2^338877-82813	102013	Stefano Morozzi	03/2022
7024	2^338878-185883	102013	Stefano Morozzi	06/2022
7025	2^338879-60355	102013	Stefano Morozzi	06/2022
7026	2^338878+43719	102013	Stefano Morozzi	09/2022
7027	2^338879+122049	102013	Stefano Morozzi	11/2022
7028	2^338874-15063	102012	Stefano Morozzi	01/2023
7029	2^338874+148993	102012	Stefano Morozzi	02/2023
7030	2^338871+7679	102011	Stefano Morozzi	02/2022
7031	2^338872+61141	102011	Stefano Morozzi	03/2022
7032	2^338872-183923	102011	Stefano Morozzi	04/2022
7033	2^338873+19527	102011	Stefano Morozzi	09/2022
7034	2^338870+70719	102011	Stefano Morozzi	11/2022
7035	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
7036	2^338870-37571	102011	Stefano Morozzi	12/2022
7037	2^338872-138573	102011	Stefano Morozzi	12/2022
7038	2^338873-63843	102011	Stefano Morozzi	12/2022
7039	2^338868-5985	102010	Stefano Morozzi	02/2022
7040	2^338867+38079	102010	Stefano Morozzi	05/2022
7041	2^338868+140437	102010	Stefano Morozzi	06/2022
7042	2^338868-110175	102010	Stefano Morozzi	06/2022
7043	2^338868+123337	102010	Stefano Morozzi	11/2022
7044	2^338867-13327	102010	Stefano Morozzi	12/2022
7045	2^338868-11279	102010	Stefano Morozzi	12/2022
7046	2^338868-115685	102010	Stefano Morozzi	01/2023
7047	2^338864+158191	102009	Stefano Morozzi	02/2022
7048	2^338865-39699	102009	Stefano Morozzi	01/2023
7049	2^338865-40789	102009	Stefano Morozzi	01/2023
7050	2^338862+60433	102008	Stefano Morozzi	03/2022
7051	2^338861-9453	102008	Stefano Morozzi	04/2022
7052	2^338861+98067	102008	Stefano Morozzi	11/2022
7053	2^338862+146545	102008	Stefano Morozzi	11/2022
7054	2^338863-186207	102008	Stefano Morozzi	12/2022
7055	2^338860-41429	102008	Stefano Morozzi	01/2023
7056	2^338862-115833	102008	Stefano Morozzi	01/2023
7057	2^338863+74259	102008	Stefano Morozzi	02/2023
7058	2^338863-193017	102008	Stefano Morozzi	02/2023
7059	2^338858-190185	102007	Stefano Morozzi	01/2023
7060	2^338855+102141	102006	Stefano Morozzi	12/2021
7061	2^338856-27173	102006	Stefano Morozzi	12/2021
7062	2^338856-102839	102006	Stefano Morozzi	01/2022
7063	2^338855+79629	102006	Stefano Morozzi	01/2022
7064	2^338856+47755	102006	Stefano Morozzi	11/2022
7065	2^338850+27987	102005	Stefano Morozzi	01/2022
7066	2^338853+111791	102005	Stefano Morozzi	04/2022
7067	2^338852+145797	102005	Stefano Morozzi	11/2022
7068	2^338852-88497	102005	Stefano Morozzi	12/2022
7069	2^338850+124843	102005	Stefano Morozzi	02/2023
7070	2^338853-167695	102005	Stefano Morozzi	02/2023
7071	2^338847+176013	102004	Stefano Morozzi	12/2021
7072	2^338847-2365	102004	Stefano Morozzi	12/2021
7073	2^338848+158941	102004	Stefano Morozzi	03/2022
7074	2^338848+16671	102004	Stefano Morozzi	06/2022
7075	2^338847-35061	102004	Stefano Morozzi	06/2022
7076	2^338848+145063	102004	Stefano Morozzi	11/2022
7077	2^338847-61885	102004	Stefano Morozzi	12/2022
7078	2^338845+135831	102003	Stefano Morozzi	03/2022
7079	2^338846+85695	102003	Stefano Morozzi	03/2022
7080	2^338845+186525	102003	Stefano Morozzi	04/2022
7081	2^338846-163473	102003	Stefano Morozzi	12/2022
7082	2^338844-16077	102003	Stefano Morozzi	01/2023
7083	2^338844-165143	102003	Stefano Morozzi	01/2023
7084	2^338843-127261	102002	Stefano Morozzi	12/2021
7085	2^338843+107205	102002	Stefano Morozzi	02/2022
7086	2^338842-33185	102002	Stefano Morozzi	04/2022
7087	2^338842+14227	102002	Stefano Morozzi	05/2022
7088	2^338842+147973	102002	Stefano Morozzi	11/2022
7096	8*10^102000+51	102001	Robert Price	08/2019
7089	2^338838+150837	102001	Stefano Morozzi	11/2021
7090	2^338838+141397	102001	Stefano Morozzi	06/2022
7091	2^338839+194363	102001	Stefano Morozzi	09/2022
7092	2^338838+95637	102001	Stefano Morozzi	11/2022
7093	2^338839+171545	102001	Stefano Morozzi	11/2022
7094	2^338837-40071	102001	Stefano Morozzi	01/2023
7095	2^338838-90251	102001	Stefano Morozzi	01/2023
7097	2^338835-150625	102000	Stefano Morozzi	12/2021
7098	2^338834-32877	102000	Stefano Morozzi	04/2022
7102	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
7099	2^338833-100905	101999	Stefano Morozzi	12/2021
7100	2^338831+54419	101999	Stefano Morozzi	01/2022
7101	2^338831-63687	101999	Stefano Morozzi	12/2022
7110	2^338829-113239	101998	Enzo Doria	07/2014
7111	2^338828-113297	101998	Enzo Doria	07/2014
7103	2^338830+25017	101998	Stefano Morozzi	11/2021
7104	2^338831+321	101998	Stefano Morozzi	11/2021
7105	2^338827-26197	101998	Stefano Morozzi	12/2021
7106	2^338829+52727	101998	Stefano Morozzi	01/2022
7107	2^338827-55461	101998	Stefano Morozzi	02/2022
7108	2^338828-65859	101998	Stefano Morozzi	01/2023
7109	2^338829+99365	101998	Stefano Morozzi	02/2023
7112	2^338825-27453	101997	Stefano Morozzi	12/2021
7113	2^338824+89355	101997	Stefano Morozzi	05/2022
7114	2^338825-10995	101997	Stefano Morozzi	06/2022
7115	2^338824+149865	101997	Stefano Morozzi	02/2023
7116	2^338822+111175	101996	Stefano Morozzi	03/2022
7117	2^338822+187819	101996	Stefano Morozzi	04/2022
7118	2^338823+139545	101996	Stefano Morozzi	05/2022
7119	2^338823-184905	101996	Stefano Morozzi	06/2022
7120	2^338821-38919	101996	Stefano Morozzi	12/2022
7121	2^338820+41317	101995	Stefano Morozzi	06/2022
7122	2^338817+46019	101995	Stefano Morozzi	11/2022
7123	2^338820+148083	101995	Stefano Morozzi	11/2022
7124	2^338817-163251	101995	Stefano Morozzi	12/2022
7125	2^338819-63705	101995	Stefano Morozzi	12/2022
7126	2^338817-92509	101995	Stefano Morozzi	02/2023
7127	2^338815+151175	101994	Stefano Morozzi	12/2021
7128	2^338814-30011	101994	Stefano Morozzi	02/2022
7129	2^338814+12309	101994	Stefano Morozzi	04/2022
7130	2^338816-60647	101994	Stefano Morozzi	06/2022
7131	2^338816+171043	101994	Stefano Morozzi	11/2022
7132	2^338814-11513	101994	Stefano Morozzi	12/2022
7133	2^338811-126999	101993	Stefano Morozzi	12/2021
7134	2^338811+131621	101993	Stefano Morozzi	02/2022
7135	2^338812-107637	101993	Stefano Morozzi	03/2022
7136	2^338813+192725	101993	Stefano Morozzi	09/2022
7137	2^338812+94731	101993	Stefano Morozzi	11/2022
7138	2^338813+49205	101993	Stefano Morozzi	02/2023
7139	2^338809-152755	101992	Stefano Morozzi	01/2022
7140	2^338808+156531	101992	Stefano Morozzi	01/2022
7141	2^338808+7885	101992	Stefano Morozzi	02/2022
7142	2^338808-105797	101992	Stefano Morozzi	02/2022
7143	2^338807-35899	101992	Stefano Morozzi	06/2022
7144	2^338808-89175	101992	Stefano Morozzi	01/2023
7145	2^338808-91475	101992	Stefano Morozzi	01/2023
7146	2^338805+29879	101991	Stefano Morozzi	01/2022
7147	2^338805+157925	101991	Stefano Morozzi	02/2022
7148	2^338804-6809	101991	Stefano Morozzi	03/2022
7149	2^338806-157095	101991	Stefano Morozzi	03/2022
7150	2^338804-133173	101991	Stefano Morozzi	04/2022
7151	2^338805-115189	101991	Stefano Morozzi	01/2023
7152	2^338802+150403	101990	Stefano Morozzi	11/2021
7153	2^338801+154587	101990	Stefano Morozzi	01/2022
7154	2^338802-180603	101990	Stefano Morozzi	02/2022
7155	2^338803-31921	101990	Stefano Morozzi	03/2022
7156	2^338803-81735	101990	Stefano Morozzi	03/2022
7157	2^338803+195141	101990	Stefano Morozzi	11/2022
7158	2^338800+160141	101989	Stefano Morozzi	03/2022
7159	2^338797-82489	101989	Stefano Morozzi	03/2022
7164	2^338796+93	101988	Donovan Johnson	06/2008
7160	2^338795+455	101988	Stefano Morozzi	11/2021
7161	2^338795-102075	101988	Stefano Morozzi	12/2021
7162	2^338794-3483	101988	Stefano Morozzi	01/2022
7163	2^338796+179641	101988	Stefano Morozzi	01/2022
7165	2^338793-5155	101987	Stefano Morozzi	02/2022
7166	2^338793+111107	101987	Stefano Morozzi	03/2022
7167	2^338791+112083	101987	Stefano Morozzi	04/2022
7168	2^338792-85097	101987	Stefano Morozzi	06/2022
7169	(61*10^101986+47)/9	101987	Robert Price	07/2022
7170	2^338787+53309	101986	Stefano Morozzi	01/2022
7171	2^338787-153817	101986	Stefano Morozzi	01/2022
7172	2^338789+56229	101986	Stefano Morozzi	01/2022
7173	2^338790+6429	101986	Stefano Morozzi	01/2022
7174	2^338788+131701	101986	Stefano Morozzi	02/2022
7175	2^338785+104639	101985	Stefano Morozzi	01/2022
7176	2^338784+37591	101985	Stefano Morozzi	04/2022
7177	2^338786-9831	101985	Stefano Morozzi	04/2022
7178	2^338783+109065	101984	Stefano Morozzi	03/2022
7179	2^338779+86711	101983	Stefano Morozzi	04/2022
7180	2^338778+113589	101983	Stefano Morozzi	05/2022
7181	2^338775-30369	101982	Stefano Morozzi	02/2022
7182	2^338774+159135	101982	Stefano Morozzi	03/2022
7183	2^338776+113001	101982	Stefano Morozzi	04/2022
7184	2^338774+117039	101982	Stefano Morozzi	09/2022
7185	2^338775+167109	101982	Stefano Morozzi	09/2022
7186	2^338774+147595	101982	Stefano Morozzi	11/2022
7187	2^338772+42733	101981	Stefano Morozzi	09/2022
7188	2^338771-138805	101981	Stefano Morozzi	12/2022
7189	2^338768-181007	101980	Stefano Morozzi	02/2022
7190	2^338768+108807	101980	Stefano Morozzi	03/2022
7191	2^338767+169155	101980	Stefano Morozzi	09/2022
7192	2^338769+95369	101980	Stefano Morozzi	11/2022
7193	2^338769+195965	101980	Stefano Morozzi	11/2022
7194	2^338770-12725	101980	Stefano Morozzi	12/2022
7195	2^338768-140843	101980	Stefano Morozzi	01/2023
7196	2^338764+138013	101979	Stefano Morozzi	04/2022
7197	2^338765-160323	101979	Stefano Morozzi	06/2022
7198	2^338765+124545	101979	Stefano Morozzi	02/2023
7204	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
7199	2^338761+103671	101978	Stefano Morozzi	01/2022
7200	2^338763-7651	101978	Stefano Morozzi	03/2022
7201	2^338763+65591	101978	Stefano Morozzi	06/2022
7202	2^338762-111875	101978	Stefano Morozzi	12/2022
7203	2^338762-192237	101978	Stefano Morozzi	02/2023
7205	2^338757-5151	101977	Stefano Morozzi	02/2022
7206	2^338760-79037	101977	Stefano Morozzi	02/2022
7207	2^338757-82143	101977	Stefano Morozzi	03/2022
7208	2^338757+137007	101977	Stefano Morozzi	04/2022
7209	2^338755+158531	101976	Stefano Morozzi	03/2022
7210	2^338755+74081	101976	Stefano Morozzi	02/2023
7211	2^338752-153353	101975	Stefano Morozzi	01/2022
7212	2^338751+8001	101975	Stefano Morozzi	02/2022
7213	2^338752+32977	101975	Stefano Morozzi	02/2022
7214	2^338753-79233	101975	Stefano Morozzi	02/2022
7215	2^338752-88157	101975	Stefano Morozzi	12/2022
7216	2^338750-175625	101974	Stefano Morozzi	12/2021
7217	2^338747-2731	101974	Stefano Morozzi	12/2021
7218	2^338750-29597	101974	Stefano Morozzi	02/2022
7219	2^338748+35095	101974	Stefano Morozzi	03/2022
7220	2^338747+137475	101974	Stefano Morozzi	04/2022
7221	2^338747+162005	101974	Stefano Morozzi	04/2022
7222	2^338750+162237	101974	Stefano Morozzi	04/2022
7223	2^338747-184365	101974	Stefano Morozzi	04/2022
7224	2^338748+64341	101974	Stefano Morozzi	05/2022
7225	2^338750+24445	101974	Stefano Morozzi	02/2023
7226	2^338746+59577	101973	Stefano Morozzi	03/2022
7227	2^338746+62055	101973	Stefano Morozzi	04/2022
7228	2^338744+194065	101973	Stefano Morozzi	09/2022
7229	2^338741+25359	101972	Stefano Morozzi	12/2021
7230	2^338743+176981	101972	Stefano Morozzi	12/2021
7231	2^338741+183029	101972	Stefano Morozzi	02/2022
7232	2^338743-130309	101972	Stefano Morozzi	02/2022
7233	2^338741+86349	101972	Stefano Morozzi	04/2022
7234	2^338741+111561	101972	Stefano Morozzi	04/2022
7235	2^338743+172301	101972	Stefano Morozzi	11/2022
7236	2^338741-189969	101972	Stefano Morozzi	01/2023
7237	2^338739+76959	101971	Stefano Morozzi	12/2021
7238	2^338739-105957	101971	Stefano Morozzi	02/2022
7239	2^338739+190149	101971	Stefano Morozzi	05/2022
7240	2^338738+64947	101971	Stefano Morozzi	05/2022
7241	2^338740+119947	101971	Stefano Morozzi	11/2022
7242	2^338740-186837	101971	Stefano Morozzi	12/2022
7243	2^338737+127547	101970	Stefano Morozzi	12/2021
7244	2^338737+128591	101970	Stefano Morozzi	01/2022
7245	2^338735-153165	101970	Stefano Morozzi	01/2022
7246	2^338734+13719	101970	Stefano Morozzi	05/2022
7247	2^338734-138225	101970	Stefano Morozzi	12/2022
7248	2^338735-186129	101970	Stefano Morozzi	12/2022
7249	2^338731-150895	101969	Stefano Morozzi	12/2021
7250	2^338731+54911	101969	Stefano Morozzi	01/2022

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PRP Records

Probable Primes Top 10000

(294113 PRPs in the top)