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 ?
9001	(11^98221-5^98221)/6	102286	Robert Price	01/2013
9002	3^214365+1820	102279	Lelio R Paula	10/2016
9003	31978^1579+1579^31978	102278	Hans Havermann	03/2019
9004	(89*10^102262-467)/9	102263	Robert Price	04/2022
9005	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
9006	2^339694-16995	102259	Lelio R Paula	09/2016
9007	(56*10^102255+691)/9	102256	Robert Price	05/2019
9008	122^49008+121	102249	Norbert Schneider	10/2018
9009	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
9010	7^120985-38	102245	Lelio R Paula	10/2016
9011	10^102244+122961	102245	Patrick De Geest	12/2016
9012	10^102244-27	102244	Lelio R Paula	09/2016
9013	7^120982-62	102242	Lelio R Paula	10/2016
9014	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
9015	4*6^131382-5	102236	Lelio R Paula	11/2014
9016	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
9017	2^339586-1091	102226	Yves Minet	11/2012
9018	11^98161-3072000	102225	Enzo Doria	12/2012
9019	9*7^120961-4	102225	Lelio R Paula	11/2014
9020	5*3^214250+2	102224	Serge Batalov	10/2010
9021	12^94713-59	102213	Lelio R Paula	10/2016
9022	12^94705+89	102204	Lelio R Paula	10/2016
9023	L(2*339475)%(2^339475)	102193	Henri Lifchitz	06/2025
9024	2^339407-177	102172	Lelio R Paula	08/2011
9025	4*10^102163-57	102164	Robert Price	10/2018
9026	2^339355+65	102157	Lelio R Paula	07/2011
9027	(28*10^102142-31)/3	102143	Robert Price	12/2019
9028	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
9029	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
9030	U(610865)	102130	Serge Batalov	07/2024
9031	s(178551)	102122	Robert Price	05/2020
9032	(797*10^102112-23)/9	102114	Robert Price	01/2022
9033	(5*10^102107+7)/3	102108	Tyler Busby	02/2023
9034	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
9037	2^339168+21	102100	Lelio R Paula	07/2011
9036	2^339167-108807	102100	Enzo Doria	03/2014
9035	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
9038	2^339156+163	102097	Lelio R Paula	08/2011
9039	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
9040	(25*10^102076-67)/3	102077	Robert Price	06/2019
9041	2^339081-4543	102074	Yves Minet	03/2019
9042	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
9043	2*10^102062+77	102063	Robert Price	08/2020
9044	24327^15668+15668^24327	102053	Hans Havermann	02/2019
9045	10^102052+66793	102053	Patrick De Geest	09/2022
9047	10^102052-7000001	102052	Robert Price	06/2021
9046	10^102052-618623	102052	Patrick De Geest	09/2022
9048	2^339000-175635	102050	Stefano Morozzi	12/2021
9049	2^339000-151667	102050	Stefano Morozzi	12/2021
9050	2^338999+79289	102049	Stefano Morozzi	01/2022
9051	2^338998-63897	102049	Stefano Morozzi	12/2022
9052	2^338997+99659	102049	Stefano Morozzi	02/2023
9053	2^338994+188757	102048	Stefano Morozzi	05/2022
9054	2^338995+70785	102048	Stefano Morozzi	11/2022
9055	2^338994-12183	102048	Stefano Morozzi	12/2022
9056	2^338992+181591	102047	Stefano Morozzi	01/2022
9057	2^338992+136171	102047	Stefano Morozzi	03/2022
9058	2^338991-109435	102047	Stefano Morozzi	04/2022
9059	2^338991+193611	102047	Stefano Morozzi	09/2022
9060	2^338988-134619	102046	Stefano Morozzi	04/2022
9061	2^338987-62557	102046	Stefano Morozzi	12/2022
9062	2^338986-60141	102045	Stefano Morozzi	06/2022
9063	2^338986+98209	102045	Stefano Morozzi	11/2022
9064	2^338981+106391	102044	Stefano Morozzi	01/2022
9065	2^338982+34069	102044	Stefano Morozzi	03/2022
9066	2^338982-58781	102044	Stefano Morozzi	04/2022
9067	2^338980+70833	102044	Stefano Morozzi	11/2022
9068	2^338982-92111	102044	Stefano Morozzi	02/2023
9069	2^338977+83007	102043	Stefano Morozzi	02/2022
9070	2^338979-83601	102043	Stefano Morozzi	04/2022
9071	2^338975+28355	102042	Stefano Morozzi	01/2022
9072	2^338973+134619	102042	Stefano Morozzi	03/2022
9073	2^338974+183777	102042	Stefano Morozzi	03/2022
9074	2^338975+69293	102042	Stefano Morozzi	09/2022
9082	25080^11711+11711^25080	102041	Hans Havermann	02/2019
9075	2^338972+152343	102041	Stefano Morozzi	12/2021
9076	2^338972-180623	102041	Stefano Morozzi	02/2022
9077	2^338972+84441	102041	Stefano Morozzi	03/2022
9078	2^338971+64875	102041	Stefano Morozzi	05/2022
9079	2^338971+44985	102041	Stefano Morozzi	11/2022
9080	2^338971+145065	102041	Stefano Morozzi	11/2022
9081	2^338972-16635	102041	Stefano Morozzi	01/2023
9083	2^338968+53461	102040	Stefano Morozzi	01/2022
9084	2^338969+160175	102040	Stefano Morozzi	03/2022
9085	2^338967+13409	102040	Stefano Morozzi	04/2022
9086	2^338969+67635	102040	Stefano Morozzi	09/2022
9087	2^338969-15913	102040	Stefano Morozzi	01/2023
9088	2^338963-127455	102039	Stefano Morozzi	12/2021
9089	2^338963+132195	102039	Stefano Morozzi	02/2022
9090	2^338966+137919	102039	Stefano Morozzi	04/2022
9091	2^338963-87529	102039	Stefano Morozzi	12/2022
9092	2^338963-116859	102039	Stefano Morozzi	02/2023
9099	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
9093	2^338960+53935	102038	Stefano Morozzi	01/2022
9094	2^338962+83157	102038	Stefano Morozzi	02/2022
9095	2^338961+12341	102038	Stefano Morozzi	04/2022
9096	2^338960+63933	102038	Stefano Morozzi	05/2022
9097	2^338960+170791	102038	Stefano Morozzi	11/2022
9098	2^338962+21679	102038	Stefano Morozzi	11/2022
9100	2^338959-30919	102037	Stefano Morozzi	02/2022
9101	2^338959+164769	102037	Stefano Morozzi	05/2022
9102	2^338958-43161	102037	Stefano Morozzi	02/2023
9103	2^338954-177003	102036	Stefano Morozzi	12/2021
9104	2^338954+154207	102036	Stefano Morozzi	01/2022
9105	2^338956+182493	102036	Stefano Morozzi	02/2022
9106	2^338954+162715	102036	Stefano Morozzi	04/2022
9107	2^338955-158241	102036	Stefano Morozzi	04/2022
9108	2^338956-33395	102036	Stefano Morozzi	04/2022
9109	2^338954+190915	102036	Stefano Morozzi	06/2022
9110	2^338955+41643	102036	Stefano Morozzi	09/2022
9111	2^338954+194427	102036	Stefano Morozzi	09/2022
9112	2^338956+117967	102036	Stefano Morozzi	09/2022
9113	2^338956+195495	102036	Stefano Morozzi	11/2022
9114	2^338954-186371	102036	Stefano Morozzi	12/2022
9115	2^338950+175077	102035	Stefano Morozzi	12/2021
9116	2^338951-51687	102035	Stefano Morozzi	12/2021
9117	2^338951+66123	102035	Stefano Morozzi	06/2022
9118	2^338950+19317	102035	Stefano Morozzi	09/2022
9119	2^338951-161479	102035	Stefano Morozzi	12/2022
9120	2^338950-66335	102035	Stefano Morozzi	01/2023
9121	2^338951-41611	102035	Stefano Morozzi	02/2023
9122	2^338952-142887	102035	Stefano Morozzi	02/2023
9123	2^338949+85449	102034	Stefano Morozzi	03/2022
9124	2^338949-184585	102034	Stefano Morozzi	04/2022
9125	2^338949-88555	102034	Stefano Morozzi	12/2022
9126	2^338948+49393	102034	Stefano Morozzi	02/2023
9127	2^338949-17601	102034	Stefano Morozzi	02/2023
9128	2^338943+127103	102033	Stefano Morozzi	12/2021
9129	2^338944-84003	102033	Stefano Morozzi	04/2022
9130	2^338945+138605	102033	Stefano Morozzi	05/2022
9131	2^338943+95133	102033	Stefano Morozzi	11/2022
9132	2^338943+147435	102033	Stefano Morozzi	11/2022
9133	2^338943-116067	102033	Stefano Morozzi	01/2023
9134	2^338940+78607	102032	Stefano Morozzi	01/2022
9135	2^338942-86687	102032	Stefano Morozzi	12/2022
9136	2^338939+151569	102031	Stefano Morozzi	12/2021
9137	2^338938+183975	102031	Stefano Morozzi	03/2022
9138	2^338937-33429	102031	Stefano Morozzi	04/2022
9139	2^338939-183259	102031	Stefano Morozzi	04/2022
9140	2^338937-139951	102031	Stefano Morozzi	01/2023
9141	2^338938-40151	102031	Stefano Morozzi	01/2023
9142	2^338938+74449	102031	Stefano Morozzi	02/2023
9143	2^338935+179999	102030	Stefano Morozzi	01/2022
9144	2^338936+84147	102030	Stefano Morozzi	03/2022
9145	2^338935+171261	102030	Stefano Morozzi	11/2022
9146	2^338936-41355	102030	Stefano Morozzi	01/2023
9147	2^338931+2349	102029	Stefano Morozzi	12/2021
9148	2^338933+79935	102029	Stefano Morozzi	01/2022
9149	2^338930+33819	102029	Stefano Morozzi	03/2022
9150	2^338931-31555	102029	Stefano Morozzi	03/2022
9151	2^338933+64169	102029	Stefano Morozzi	05/2022
9152	2^338932-184965	102029	Stefano Morozzi	06/2022
9153	2^338932+66943	102029	Stefano Morozzi	09/2022
9154	2^338932+92995	102029	Stefano Morozzi	09/2022
9155	2^338931+97001	102029	Stefano Morozzi	11/2022
9156	2^338932-165453	102029	Stefano Morozzi	01/2023
9157	2^338933-40899	102029	Stefano Morozzi	01/2023
9158	2^338928+2367	102028	Stefano Morozzi	12/2021
9159	2^338927+52779	102028	Stefano Morozzi	01/2022
9160	2^338927-79539	102028	Stefano Morozzi	02/2022
9161	2^338929+60819	102028	Stefano Morozzi	03/2022
9162	2^338928-156959	102028	Stefano Morozzi	03/2022
9163	2^338927-63919	102028	Stefano Morozzi	12/2022
9164	2^338925+106631	102027	Stefano Morozzi	01/2022
9165	2^338926+80235	102027	Stefano Morozzi	01/2022
9166	2^338926+41607	102027	Stefano Morozzi	09/2022
9167	2^338925+195435	102027	Stefano Morozzi	11/2022
9168	2^338924-92885	102027	Stefano Morozzi	02/2023
9169	2^338922-27291	102026	Stefano Morozzi	12/2021
9170	2^338919-103849	102025	Stefano Morozzi	01/2022
9171	2^338919+130221	102025	Stefano Morozzi	01/2022
9172	2^338918-91967	102025	Stefano Morozzi	02/2023
9173	2^338917+561057	102025	Boyan Hu	03/2024
9174	2^338914-79121	102024	Stefano Morozzi	02/2022
9175	2^338916+134047	102024	Stefano Morozzi	03/2022
9176	2^338914-11315	102024	Stefano Morozzi	12/2022
9177	2^338910+81027	102023	Stefano Morozzi	01/2022
9178	2^338912+179821	102023	Stefano Morozzi	01/2022
9179	2^338909+100769	102022	Stefano Morozzi	11/2021
9180	2^338908-100839	102022	Stefano Morozzi	12/2021
9181	2^338909-25951	102022	Stefano Morozzi	12/2021
9182	2^338909+66845	102022	Stefano Morozzi	09/2022
9183	2^338907+73509	102022	Stefano Morozzi	11/2022
9184	2^338906-25823	102021	Stefano Morozzi	12/2021
9185	2^338904+75951	102021	Stefano Morozzi	12/2021
9186	2^338906+6685	102021	Stefano Morozzi	01/2022
9187	2^338905+160365	102021	Stefano Morozzi	03/2022
9188	2^338906+92617	102021	Stefano Morozzi	09/2022
9189	2^338904+47065	102021	Stefano Morozzi	11/2022
9190	2^338905+70427	102021	Stefano Morozzi	11/2022
9191	2^338905-163975	102021	Stefano Morozzi	12/2022
9192	2^338903+4155	102020	Stefano Morozzi	01/2022
9193	2^338901+55571	102020	Stefano Morozzi	01/2022
9194	2^338901-55479	102020	Stefano Morozzi	02/2022
9195	2^338903+33555	102020	Stefano Morozzi	03/2022
9196	2^338901+39777	102020	Stefano Morozzi	05/2022
9197	2^338903+165981	102020	Stefano Morozzi	06/2022
9198	2^338901-34863	102020	Stefano Morozzi	06/2022
9199	2^338899-150051	102019	Stefano Morozzi	12/2021
9200	2^338899+125951	102019	Stefano Morozzi	12/2021
9201	2^338898+179623	102019	Stefano Morozzi	01/2022
9202	2^338899-154467	102019	Stefano Morozzi	02/2022
9203	2^338898-60753	102019	Stefano Morozzi	06/2022
9204	2^338898+68635	102019	Stefano Morozzi	09/2022
9205	2^338897-85963	102019	Stefano Morozzi	12/2022
9206	2^338898+174129	102019	Stefano Morozzi	02/2023
9207	2^338894-133295	102018	Stefano Morozzi	04/2022
9208	2^338894+165573	102018	Stefano Morozzi	06/2022
9209	2^338894-60957	102018	Stefano Morozzi	06/2022
9210	2^338894-89463	102018	Stefano Morozzi	01/2023
9220	2^338891-18885	102017	Enzo Doria	05/2013
9211	2^338891+26499	102017	Stefano Morozzi	12/2021
9212	2^338891-2625	102017	Stefano Morozzi	12/2021
9213	2^338893+128727	102017	Stefano Morozzi	01/2022
9214	2^338890-52965	102017	Stefano Morozzi	01/2022
9215	2^338892-55467	102017	Stefano Morozzi	02/2022
9216	2^338892-83393	102017	Stefano Morozzi	04/2022
9217	2^338893+13649	102017	Stefano Morozzi	05/2022
9218	2^338892+117957	102017	Stefano Morozzi	09/2022
9219	2^338892-14643	102017	Stefano Morozzi	01/2023
9221	2^338887+154029	102016	Stefano Morozzi	01/2022
9222	2^338889-104293	102016	Stefano Morozzi	02/2022
9223	2^338887+147741	102016	Stefano Morozzi	11/2022
9224	2^338889+195975	102016	Stefano Morozzi	11/2022
9225	2^338889-117873	102016	Stefano Morozzi	02/2023
9226	2^338886+177159	102015	Stefano Morozzi	12/2021
9227	2^338885+40425	102015	Stefano Morozzi	06/2022
9228	2^338884-13053	102015	Stefano Morozzi	12/2022
9229	2^338885-112569	102015	Stefano Morozzi	12/2022
9230	2^338880+11341	102014	Stefano Morozzi	03/2022
9231	2^338880-160383	102014	Stefano Morozzi	06/2022
9232	2^338880-161627	102014	Stefano Morozzi	12/2022
9233	2^338879-1059	102013	Stefano Morozzi	12/2021
9234	2^338879-54525	102013	Stefano Morozzi	02/2022
9235	2^338877-82813	102013	Stefano Morozzi	03/2022
9236	2^338878-185883	102013	Stefano Morozzi	06/2022
9237	2^338879-60355	102013	Stefano Morozzi	06/2022
9238	2^338878+43719	102013	Stefano Morozzi	09/2022
9239	2^338879+122049	102013	Stefano Morozzi	11/2022
9240	2^338874-15063	102012	Stefano Morozzi	01/2023
9241	2^338874+148993	102012	Stefano Morozzi	02/2023
9242	2^338871+7679	102011	Stefano Morozzi	02/2022
9243	2^338872+61141	102011	Stefano Morozzi	03/2022
9244	2^338872-183923	102011	Stefano Morozzi	04/2022
9245	2^338873+19527	102011	Stefano Morozzi	09/2022
9246	2^338870+70719	102011	Stefano Morozzi	11/2022
9247	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
9248	2^338870-37571	102011	Stefano Morozzi	12/2022
9249	2^338872-138573	102011	Stefano Morozzi	12/2022
9250	2^338873-63843	102011	Stefano Morozzi	12/2022

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Probable Primes Top 10000

(301737 PRPs in the top)