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 ?
7001	2^338518+114633	101905	Stefano Morozzi	05/2022
7002	2^338518-12621	101905	Stefano Morozzi	12/2022
7003	2^338518-187325	101905	Stefano Morozzi	12/2022
7011	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
7004	2^338517-125955	101904	Stefano Morozzi	12/2021
7005	2^338517+126437	101904	Stefano Morozzi	12/2021
7006	2^338517-53499	101904	Stefano Morozzi	01/2022
7007	2^338515+30369	101904	Stefano Morozzi	01/2022
7008	2^338517-184623	101904	Stefano Morozzi	04/2022
7009	2^338515+89333	101904	Stefano Morozzi	05/2022
7010	2^338515+198813	101904	Stefano Morozzi	02/2023
7014	24502^14419+14419^24502	101903	Hans Havermann	01/2019
7012	2^338512-827	101903	Stefano Morozzi	12/2021
7013	2^338514-6611	101903	Stefano Morozzi	03/2022
7015	2^338509+5139	101902	Stefano Morozzi	01/2022
7016	2^338509+40205	101902	Stefano Morozzi	06/2022
7017	2^338511+19959	101902	Stefano Morozzi	09/2022
7018	2^338510-37877	101902	Stefano Morozzi	12/2022
7019	2^338507-188655	101901	Stefano Morozzi	12/2022
7020	2^338507-114457	101901	Stefano Morozzi	01/2023
7021	2^338504-152615	101900	Stefano Morozzi	01/2022
7022	2^338502-4587	101900	Stefano Morozzi	02/2022
7023	2^338502-166275	101900	Stefano Morozzi	01/2023
7024	2^338500-26865	101899	Stefano Morozzi	12/2021
7025	2^338501-177471	101899	Stefano Morozzi	12/2021
7026	2^338499-3915	101899	Stefano Morozzi	01/2022
7027	2^338501+32051	101899	Stefano Morozzi	02/2022
7028	2^338499+183533	101899	Stefano Morozzi	03/2022
7029	2^338500+35625	101899	Stefano Morozzi	03/2022
7030	2^338499+87579	101899	Stefano Morozzi	04/2022
7031	2^338498-117683	101899	Stefano Morozzi	02/2023
7034	2^338497-17041	101898	Enzo Doria	05/2013
7032	2^338497+150405	101898	Stefano Morozzi	11/2021
7033	2^338495+100533	101898	Stefano Morozzi	12/2021
7035	2^338494+36057	101897	Stefano Morozzi	03/2022
7036	2^338492+39015	101897	Stefano Morozzi	05/2022
7037	2^338494+168007	101897	Stefano Morozzi	09/2022
7038	2^338490+61149	101896	Stefano Morozzi	03/2022
7039	2^338489+161369	101896	Stefano Morozzi	04/2022
7040	2^338491+22961	101896	Stefano Morozzi	11/2022
7041	2^338487-3555	101895	Stefano Morozzi	01/2022
7042	2^338487-183129	101895	Stefano Morozzi	04/2022
7043	2^338484+128767	101894	Stefano Morozzi	01/2022
7044	2^338484-31895	101894	Stefano Morozzi	03/2022
7045	2^338483-67899	101894	Stefano Morozzi	02/2023
7046	2^338483-192129	101894	Stefano Morozzi	02/2023
7047	2^338478+10893	101893	Stefano Morozzi	03/2022
7048	2^338479+87243	101893	Stefano Morozzi	04/2022
7049	2^338479+167619	101893	Stefano Morozzi	09/2022
7050	2^338480+197503	101893	Stefano Morozzi	11/2022
7051	2^338481-11421	101893	Stefano Morozzi	12/2022
7052	2^338479-89649	101893	Stefano Morozzi	01/2023
7053	(29*34^66532-12833)/33	101893	Eric Chen	03/2023
7056	2^338475+54615	101892	Lelio R Paula	10/2016
7054	2^338475-59775	101892	Stefano Morozzi	04/2022
7055	2^338476-134237	101892	Stefano Morozzi	04/2022
7057	2^338474+100767	101891	Stefano Morozzi	11/2021
7058	2^338474+81165	101891	Stefano Morozzi	01/2022
7059	2^338474+41137	101891	Stefano Morozzi	06/2022
7060	2^338472-110445	101891	Stefano Morozzi	06/2022
7061	2^338473-89535	101891	Stefano Morozzi	01/2023
7062	2^338470+27777	101890	Stefano Morozzi	01/2022
7063	2^338468+31351	101890	Stefano Morozzi	01/2022
7064	2^338469-106339	101890	Stefano Morozzi	03/2022
7065	2^338471+187469	101890	Stefano Morozzi	04/2022
7066	2^338468+96613	101890	Stefano Morozzi	11/2022
7067	2^338469+46167	101890	Stefano Morozzi	11/2022
7068	2^338470+71527	101890	Stefano Morozzi	11/2022
7069	2^338469-112783	101890	Stefano Morozzi	12/2022
7070	2^338470-115665	101890	Stefano Morozzi	01/2023
7071	2^338467-25665	101889	Stefano Morozzi	12/2021
7072	2^338465+152139	101889	Stefano Morozzi	12/2021
7073	2^338466-28643	101889	Stefano Morozzi	01/2022
7074	2^338465+181517	101889	Stefano Morozzi	01/2022
7075	2^338466+115917	101889	Stefano Morozzi	06/2022
7076	2^338465-88291	101889	Stefano Morozzi	12/2022
7077	2^338464-104009	101888	Stefano Morozzi	02/2022
7078	2^338463+185169	101888	Stefano Morozzi	03/2022
7079	2^338464+60595	101888	Stefano Morozzi	03/2022
7080	2^338464-66377	101888	Stefano Morozzi	01/2023
7081	2^338458+60273	101887	Stefano Morozzi	03/2022
7082	2^338461+135867	101887	Stefano Morozzi	03/2022
7083	2^338455-4621	101886	Stefano Morozzi	02/2022
7084	2^338457+187827	101886	Stefano Morozzi	04/2022
7085	2^338455+173349	101886	Stefano Morozzi	11/2022
7086	2^338454+133737	101885	Stefano Morozzi	03/2022
7087	2^338454-158501	101885	Stefano Morozzi	04/2022
7088	2^338454-184217	101885	Stefano Morozzi	04/2022
7089	2^338453+164451	101885	Stefano Morozzi	05/2022
7090	2^338452-136137	101885	Stefano Morozzi	12/2022
7091	2^338450+106275	101884	Stefano Morozzi	01/2022
7092	2^338450+168439	101884	Stefano Morozzi	09/2022
7093	(133*10^101881+17)/3	101883	Robert Price	11/2021
7094	2^338445-80461	101883	Stefano Morozzi	02/2022
7095	2^338446-131211	101883	Stefano Morozzi	02/2022
7096	2^338448+187167	101883	Stefano Morozzi	04/2022
7097	2^338446-160115	101883	Stefano Morozzi	06/2022
7098	2^338447-164157	101883	Stefano Morozzi	01/2023
7099	2^338447-191001	101883	Stefano Morozzi	01/2023
7100	2^338444+127623	101882	Stefano Morozzi	12/2021
7101	2^338443-113827	101882	Stefano Morozzi	12/2022
7102	2^338441-5893	101881	Stefano Morozzi	02/2022
7103	2^338439-162565	101881	Stefano Morozzi	12/2022
7104	2^338436+153657	101880	Stefano Morozzi	01/2022
7105	2^338437-153159	101880	Stefano Morozzi	01/2022
7106	2^338436-83783	101880	Stefano Morozzi	04/2022
7107	2^338435+89109	101880	Stefano Morozzi	05/2022
7108	2^338435+13871	101880	Stefano Morozzi	05/2022
7109	2^338436+149691	101880	Stefano Morozzi	02/2023
7110	2^338434+81537	101879	Stefano Morozzi	01/2022
7111	2^338432+33495	101879	Stefano Morozzi	03/2022
7112	2^338432-7043	101879	Stefano Morozzi	03/2022
7113	2^338433-32629	101879	Stefano Morozzi	03/2022
7114	2^338430-9903	101878	Stefano Morozzi	04/2022
7122	2^338426-19797	101877	Enzo Doria	06/2013
7115	2^338427-77797	101877	Stefano Morozzi	01/2022
7116	2^338427-178687	101877	Stefano Morozzi	01/2022
7117	2^338428-54873	101877	Stefano Morozzi	02/2022
7118	2^338425+41357	101877	Stefano Morozzi	06/2022
7119	2^338428+90855	101877	Stefano Morozzi	06/2022
7120	2^338428-39807	101877	Stefano Morozzi	01/2023
7121	2^338425-192381	101877	Stefano Morozzi	02/2023
7123	2^338422-188787	101876	Stefano Morozzi	12/2022
7124	2^338423-187755	101876	Stefano Morozzi	12/2022
7125	2^338422-115865	101876	Stefano Morozzi	01/2023
7126	2^338420-178829	101875	Stefano Morozzi	01/2022
7127	2^338421-105423	101875	Stefano Morozzi	02/2022
7128	2^338419-82761	101875	Stefano Morozzi	03/2022
7129	2^338420+193143	101875	Stefano Morozzi	09/2022
7130	2^338419+199641	101875	Stefano Morozzi	02/2023
7131	2^338420-143103	101875	Stefano Morozzi	02/2023
7132	2^338418-50903	101874	Stefano Morozzi	12/2021
7133	2^338418+158355	101874	Stefano Morozzi	02/2022
7134	2^338418+159339	101874	Stefano Morozzi	03/2022
7135	2^338416+14953	101874	Stefano Morozzi	05/2022
7136	2^338416+166051	101874	Stefano Morozzi	06/2022
7137	2^338418-138765	101874	Stefano Morozzi	12/2022
7138	2^338417+49737	101874	Stefano Morozzi	02/2023
7139	2^338413-125919	101873	Stefano Morozzi	12/2021
7140	2^338414+26083	101873	Stefano Morozzi	12/2021
7141	2^338412-152379	101873	Stefano Morozzi	12/2021
7142	2^338413+54797	101873	Stefano Morozzi	01/2022
7143	2^338412+157951	101873	Stefano Morozzi	02/2022
7144	2^338414+81627	101873	Stefano Morozzi	02/2022
7145	2^338413+133679	101873	Stefano Morozzi	03/2022
7146	2^338413+197735	101873	Stefano Morozzi	11/2022
7147	2^338413-114301	101873	Stefano Morozzi	01/2023
7148	2^338409-52183	101872	Stefano Morozzi	12/2021
7149	2^338411-3789	101872	Stefano Morozzi	01/2022
7150	2^338409+173237	101872	Stefano Morozzi	11/2022
7151	2^338406-184175	101871	Stefano Morozzi	04/2022
7152	2^338405+94451	101871	Stefano Morozzi	09/2022
7153	2^338406-161217	101871	Stefano Morozzi	12/2022
7154	2^338406+199929	101871	Stefano Morozzi	02/2023
7155	2^338404+55717	101870	Stefano Morozzi	01/2022
7156	2^338403+36261	101870	Stefano Morozzi	04/2022
7157	2^338402-34431	101870	Stefano Morozzi	04/2022
7158	2^338404-159215	101870	Stefano Morozzi	04/2022
7159	2^338403+18363	101870	Stefano Morozzi	09/2022
7160	2^338403+170235	101870	Stefano Morozzi	11/2022
7161	2^338399+23045	101869	Stefano Morozzi	11/2022
7162	2^338399-65535	101869	Stefano Morozzi	01/2023
7163	2^338395-127449	101868	Stefano Morozzi	12/2021
7164	2^338398-127637	101868	Stefano Morozzi	01/2022
7165	2^338398-166533	101868	Stefano Morozzi	01/2023
7166	2^338394+100317	101867	Stefano Morozzi	11/2021
7167	2^338393-152749	101867	Stefano Morozzi	01/2022
7168	2^338393+163025	101867	Stefano Morozzi	04/2022
7169	2^338393+89229	101867	Stefano Morozzi	05/2022
7170	2^338393+99647	101867	Stefano Morozzi	02/2023
7171	2^338394-192471	101867	Stefano Morozzi	02/2023
7172	2^338390+76627	101866	Stefano Morozzi	12/2021
7173	2^338389-85081	101866	Stefano Morozzi	06/2022
7174	2^338390+148113	101866	Stefano Morozzi	11/2022
7175	2^338389-14253	101866	Stefano Morozzi	01/2023
7176	2^338390-114297	101866	Stefano Morozzi	01/2023
7177	2^338391-64225	101866	Stefano Morozzi	01/2023
7178	2^338389-16971	101866	Stefano Morozzi	02/2023
7179	2^338387-75685	101865	Stefano Morozzi	12/2021
7180	2^338388-53459	101865	Stefano Morozzi	01/2022
7181	2^338388-36575	101865	Stefano Morozzi	12/2022
7182	2^338385-190311	101865	Stefano Morozzi	01/2023
7183	2^338384+131563	101864	Stefano Morozzi	01/2022
7184	2^338382+109069	101864	Stefano Morozzi	03/2022
7185	2^338384+168987	101864	Stefano Morozzi	09/2022
7186	2^338383-42367	101864	Stefano Morozzi	02/2023
7187	2^338380+77125	101863	Stefano Morozzi	12/2021
7188	2^338381-35539	101863	Stefano Morozzi	06/2022
7189	2^338378-125841	101862	Stefano Morozzi	12/2021
7190	2^338375+27815	101862	Stefano Morozzi	01/2022
7191	2^338375-28509	101862	Stefano Morozzi	01/2022
7192	2^338375+29985	101862	Stefano Morozzi	01/2022
7193	2^338377+157881	101862	Stefano Morozzi	02/2022
7194	2^338375+59589	101862	Stefano Morozzi	03/2022
7195	2^338378+36399	101862	Stefano Morozzi	04/2022
7196	2^338378-159773	101862	Stefano Morozzi	04/2022
7197	2^338378+14883	101862	Stefano Morozzi	05/2022
7198	2^338376+140173	101862	Stefano Morozzi	06/2022
7199	2^338375+18761	101862	Stefano Morozzi	09/2022
7200	2^338373-75103	101861	Stefano Morozzi	12/2021
7201	2^338372+128877	101861	Stefano Morozzi	01/2022
7202	2^338374-28731	101861	Stefano Morozzi	01/2022
7203	2^338374-128427	101861	Stefano Morozzi	01/2022
7204	2^338372+37875	101861	Stefano Morozzi	04/2022
7205	2^338373+161541	101861	Stefano Morozzi	04/2022
7206	2^338374+37759	101861	Stefano Morozzi	04/2022
7207	2^338372+93235	101861	Stefano Morozzi	09/2022
7208	2^338373-63273	101861	Stefano Morozzi	12/2022
7209	2^338369+29427	101860	Stefano Morozzi	01/2022
7210	2^338370+179133	101860	Stefano Morozzi	01/2022
7211	2^338369+131501	101860	Stefano Morozzi	01/2022
7212	2^338369+181649	101860	Stefano Morozzi	02/2022
7213	2^338370-4787	101860	Stefano Morozzi	02/2022
7214	2^338371-133491	101860	Stefano Morozzi	04/2022
7215	2^338371+42023	101860	Stefano Morozzi	09/2022
7216	2^338371+145323	101860	Stefano Morozzi	11/2022
7217	2^338371-138145	101860	Stefano Morozzi	12/2022
7224	2^338368-20369	101859	Enzo Doria	06/2013
7225	2^338366+74179	101859	Enzo Doria	04/2016
7218	2^338366+53853	101859	Stefano Morozzi	01/2022
7219	2^338365-31665	101859	Stefano Morozzi	03/2022
7220	2^338368-156345	101859	Stefano Morozzi	03/2022
7221	2^338366-159867	101859	Stefano Morozzi	04/2022
7222	2^338368-63509	101859	Stefano Morozzi	12/2022
7223	2^338365-190975	101859	Stefano Morozzi	01/2023
7226	2^338362-180845	101858	Stefano Morozzi	02/2022
7227	2^338364-155769	101858	Stefano Morozzi	02/2022
7228	2^338362+142843	101858	Stefano Morozzi	09/2022
7229	2^338362+170019	101858	Stefano Morozzi	11/2022
7230	2^338361-100875	101857	Stefano Morozzi	12/2021
7231	2^338361+154169	101857	Stefano Morozzi	01/2022
7232	2^338359-189645	101857	Stefano Morozzi	01/2023
7233	2^338356+101271	101856	Stefano Morozzi	12/2021
7234	2^338356+53383	101856	Stefano Morozzi	01/2022
7235	2^338355+59393	101856	Stefano Morozzi	03/2022
7236	2^338356+60775	101856	Stefano Morozzi	03/2022
7237	2^338356-106257	101856	Stefano Morozzi	03/2022
7238	2^338357-58921	101856	Stefano Morozzi	04/2022
7239	2^338356+94605	101856	Stefano Morozzi	09/2022
7240	2^338356+117813	101856	Stefano Morozzi	09/2022
7241	2^338358-38475	101856	Stefano Morozzi	12/2022
7242	2^338353-190291	101855	Stefano Morozzi	01/2023
7243	2^338350-152933	101854	Stefano Morozzi	01/2022
7244	2^338350+6337	101854	Stefano Morozzi	01/2022
7245	2^338350+168759	101854	Stefano Morozzi	09/2022
7248	27088^5755+5755^27088	101853	Hans Havermann	01/2019
7246	2^338347+125901	101853	Stefano Morozzi	11/2021
7247	2^338346-10643	101853	Stefano Morozzi	06/2022
7249	2^338343+152271	101852	Stefano Morozzi	12/2021
7250	2^338345+154107	101852	Stefano Morozzi	01/2022

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Probable Primes Top 10000

(292102 PRPs in the top)