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 ?
8751	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
8752	4*6^131382-5	102236	Lelio R Paula	11/2014
8753	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
8754	2^339586-1091	102226	Yves Minet	11/2012
8755	11^98161-3072000	102225	Enzo Doria	12/2012
8756	9*7^120961-4	102225	Lelio R Paula	11/2014
8757	5*3^214250+2	102224	Serge Batalov	10/2010
8758	12^94713-59	102213	Lelio R Paula	10/2016
8759	12^94705+89	102204	Lelio R Paula	10/2016
8760	2^339407-177	102172	Lelio R Paula	08/2011
8761	4*10^102163-57	102164	Robert Price	10/2018
8762	2^339355+65	102157	Lelio R Paula	07/2011
8763	(28*10^102142-31)/3	102143	Robert Price	12/2019
8764	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
8765	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
8766	U(610865)	102130	Serge Batalov	07/2024
8767	s(178551)	102122	Robert Price	05/2020
8768	(797*10^102112-23)/9	102114	Robert Price	01/2022
8769	(5*10^102107+7)/3	102108	Tyler Busby	02/2023
8770	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
8772	2^339168+21	102100	Lelio R Paula	07/2011
8773	2^339167-108807	102100	Enzo Doria	03/2014
8771	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
8774	2^339156+163	102097	Lelio R Paula	08/2011
8775	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
8776	(25*10^102076-67)/3	102077	Robert Price	06/2019
8777	2^339081-4543	102074	Yves Minet	03/2019
8778	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
8779	2*10^102062+77	102063	Robert Price	08/2020
8781	24327^15668+15668^24327	102053	Hans Havermann	02/2019
8780	10^102052+66793	102053	Patrick De Geest	09/2022
8783	10^102052-7000001	102052	Robert Price	06/2021
8782	10^102052-618623	102052	Patrick De Geest	09/2022
8784	2^339000-175635	102050	Stefano Morozzi	12/2021
8785	2^339000-151667	102050	Stefano Morozzi	12/2021
8786	2^338999+79289	102049	Stefano Morozzi	01/2022
8787	2^338998-63897	102049	Stefano Morozzi	12/2022
8788	2^338997+99659	102049	Stefano Morozzi	02/2023
8789	2^338994+188757	102048	Stefano Morozzi	05/2022
8790	2^338995+70785	102048	Stefano Morozzi	11/2022
8791	2^338994-12183	102048	Stefano Morozzi	12/2022
8792	2^338992+181591	102047	Stefano Morozzi	01/2022
8793	2^338992+136171	102047	Stefano Morozzi	03/2022
8794	2^338991-109435	102047	Stefano Morozzi	04/2022
8795	2^338991+193611	102047	Stefano Morozzi	09/2022
8796	2^338988-134619	102046	Stefano Morozzi	04/2022
8797	2^338987-62557	102046	Stefano Morozzi	12/2022
8798	2^338986-60141	102045	Stefano Morozzi	06/2022
8799	2^338986+98209	102045	Stefano Morozzi	11/2022
8800	2^338981+106391	102044	Stefano Morozzi	01/2022
8801	2^338982+34069	102044	Stefano Morozzi	03/2022
8802	2^338982-58781	102044	Stefano Morozzi	04/2022
8803	2^338980+70833	102044	Stefano Morozzi	11/2022
8804	2^338982-92111	102044	Stefano Morozzi	02/2023
8805	2^338977+83007	102043	Stefano Morozzi	02/2022
8806	2^338979-83601	102043	Stefano Morozzi	04/2022
8807	2^338975+28355	102042	Stefano Morozzi	01/2022
8808	2^338973+134619	102042	Stefano Morozzi	03/2022
8809	2^338974+183777	102042	Stefano Morozzi	03/2022
8810	2^338975+69293	102042	Stefano Morozzi	09/2022
8818	25080^11711+11711^25080	102041	Hans Havermann	02/2019
8811	2^338972+152343	102041	Stefano Morozzi	12/2021
8812	2^338972-180623	102041	Stefano Morozzi	02/2022
8813	2^338972+84441	102041	Stefano Morozzi	03/2022
8814	2^338971+64875	102041	Stefano Morozzi	05/2022
8815	2^338971+44985	102041	Stefano Morozzi	11/2022
8816	2^338971+145065	102041	Stefano Morozzi	11/2022
8817	2^338972-16635	102041	Stefano Morozzi	01/2023
8819	2^338968+53461	102040	Stefano Morozzi	01/2022
8820	2^338969+160175	102040	Stefano Morozzi	03/2022
8821	2^338967+13409	102040	Stefano Morozzi	04/2022
8822	2^338969+67635	102040	Stefano Morozzi	09/2022
8823	2^338969-15913	102040	Stefano Morozzi	01/2023
8824	2^338963-127455	102039	Stefano Morozzi	12/2021
8825	2^338963+132195	102039	Stefano Morozzi	02/2022
8826	2^338966+137919	102039	Stefano Morozzi	04/2022
8827	2^338963-87529	102039	Stefano Morozzi	12/2022
8828	2^338963-116859	102039	Stefano Morozzi	02/2023
8835	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
8829	2^338960+53935	102038	Stefano Morozzi	01/2022
8830	2^338962+83157	102038	Stefano Morozzi	02/2022
8831	2^338961+12341	102038	Stefano Morozzi	04/2022
8832	2^338960+63933	102038	Stefano Morozzi	05/2022
8833	2^338960+170791	102038	Stefano Morozzi	11/2022
8834	2^338962+21679	102038	Stefano Morozzi	11/2022
8836	2^338959-30919	102037	Stefano Morozzi	02/2022
8837	2^338959+164769	102037	Stefano Morozzi	05/2022
8838	2^338958-43161	102037	Stefano Morozzi	02/2023
8839	2^338954-177003	102036	Stefano Morozzi	12/2021
8840	2^338954+154207	102036	Stefano Morozzi	01/2022
8841	2^338956+182493	102036	Stefano Morozzi	02/2022
8842	2^338954+162715	102036	Stefano Morozzi	04/2022
8843	2^338955-158241	102036	Stefano Morozzi	04/2022
8844	2^338956-33395	102036	Stefano Morozzi	04/2022
8845	2^338954+190915	102036	Stefano Morozzi	06/2022
8846	2^338955+41643	102036	Stefano Morozzi	09/2022
8847	2^338954+194427	102036	Stefano Morozzi	09/2022
8848	2^338956+117967	102036	Stefano Morozzi	09/2022
8849	2^338956+195495	102036	Stefano Morozzi	11/2022
8850	2^338954-186371	102036	Stefano Morozzi	12/2022
8851	2^338950+175077	102035	Stefano Morozzi	12/2021
8852	2^338951-51687	102035	Stefano Morozzi	12/2021
8853	2^338951+66123	102035	Stefano Morozzi	06/2022
8854	2^338950+19317	102035	Stefano Morozzi	09/2022
8855	2^338951-161479	102035	Stefano Morozzi	12/2022
8856	2^338950-66335	102035	Stefano Morozzi	01/2023
8857	2^338951-41611	102035	Stefano Morozzi	02/2023
8858	2^338952-142887	102035	Stefano Morozzi	02/2023
8859	2^338949+85449	102034	Stefano Morozzi	03/2022
8860	2^338949-184585	102034	Stefano Morozzi	04/2022
8861	2^338949-88555	102034	Stefano Morozzi	12/2022
8862	2^338948+49393	102034	Stefano Morozzi	02/2023
8863	2^338949-17601	102034	Stefano Morozzi	02/2023
8864	2^338943+127103	102033	Stefano Morozzi	12/2021
8865	2^338944-84003	102033	Stefano Morozzi	04/2022
8866	2^338945+138605	102033	Stefano Morozzi	05/2022
8867	2^338943+95133	102033	Stefano Morozzi	11/2022
8868	2^338943+147435	102033	Stefano Morozzi	11/2022
8869	2^338943-116067	102033	Stefano Morozzi	01/2023
8870	2^338940+78607	102032	Stefano Morozzi	01/2022
8871	2^338942-86687	102032	Stefano Morozzi	12/2022
8872	2^338939+151569	102031	Stefano Morozzi	12/2021
8873	2^338938+183975	102031	Stefano Morozzi	03/2022
8874	2^338937-33429	102031	Stefano Morozzi	04/2022
8875	2^338939-183259	102031	Stefano Morozzi	04/2022
8876	2^338937-139951	102031	Stefano Morozzi	01/2023
8877	2^338938-40151	102031	Stefano Morozzi	01/2023
8878	2^338938+74449	102031	Stefano Morozzi	02/2023
8879	2^338935+179999	102030	Stefano Morozzi	01/2022
8880	2^338936+84147	102030	Stefano Morozzi	03/2022
8881	2^338935+171261	102030	Stefano Morozzi	11/2022
8882	2^338936-41355	102030	Stefano Morozzi	01/2023
8883	2^338931+2349	102029	Stefano Morozzi	12/2021
8884	2^338933+79935	102029	Stefano Morozzi	01/2022
8885	2^338930+33819	102029	Stefano Morozzi	03/2022
8886	2^338931-31555	102029	Stefano Morozzi	03/2022
8887	2^338933+64169	102029	Stefano Morozzi	05/2022
8888	2^338932-184965	102029	Stefano Morozzi	06/2022
8889	2^338932+66943	102029	Stefano Morozzi	09/2022
8890	2^338932+92995	102029	Stefano Morozzi	09/2022
8891	2^338931+97001	102029	Stefano Morozzi	11/2022
8892	2^338932-165453	102029	Stefano Morozzi	01/2023
8893	2^338933-40899	102029	Stefano Morozzi	01/2023
8894	2^338928+2367	102028	Stefano Morozzi	12/2021
8895	2^338927+52779	102028	Stefano Morozzi	01/2022
8896	2^338927-79539	102028	Stefano Morozzi	02/2022
8897	2^338929+60819	102028	Stefano Morozzi	03/2022
8898	2^338928-156959	102028	Stefano Morozzi	03/2022
8899	2^338927-63919	102028	Stefano Morozzi	12/2022
8900	2^338925+106631	102027	Stefano Morozzi	01/2022
8901	2^338926+80235	102027	Stefano Morozzi	01/2022
8902	2^338926+41607	102027	Stefano Morozzi	09/2022
8903	2^338925+195435	102027	Stefano Morozzi	11/2022
8904	2^338924-92885	102027	Stefano Morozzi	02/2023
8905	2^338922-27291	102026	Stefano Morozzi	12/2021
8906	2^338919-103849	102025	Stefano Morozzi	01/2022
8907	2^338919+130221	102025	Stefano Morozzi	01/2022
8908	2^338918-91967	102025	Stefano Morozzi	02/2023
8909	2^338917+561057	102025	Boyan Hu	03/2024
8910	2^338914-79121	102024	Stefano Morozzi	02/2022
8911	2^338916+134047	102024	Stefano Morozzi	03/2022
8912	2^338914-11315	102024	Stefano Morozzi	12/2022
8913	2^338910+81027	102023	Stefano Morozzi	01/2022
8914	2^338912+179821	102023	Stefano Morozzi	01/2022
8915	2^338909+100769	102022	Stefano Morozzi	11/2021
8916	2^338908-100839	102022	Stefano Morozzi	12/2021
8917	2^338909-25951	102022	Stefano Morozzi	12/2021
8918	2^338909+66845	102022	Stefano Morozzi	09/2022
8919	2^338907+73509	102022	Stefano Morozzi	11/2022
8920	2^338906-25823	102021	Stefano Morozzi	12/2021
8921	2^338904+75951	102021	Stefano Morozzi	12/2021
8922	2^338906+6685	102021	Stefano Morozzi	01/2022
8923	2^338905+160365	102021	Stefano Morozzi	03/2022
8924	2^338906+92617	102021	Stefano Morozzi	09/2022
8925	2^338904+47065	102021	Stefano Morozzi	11/2022
8926	2^338905+70427	102021	Stefano Morozzi	11/2022
8927	2^338905-163975	102021	Stefano Morozzi	12/2022
8928	2^338903+4155	102020	Stefano Morozzi	01/2022
8929	2^338901+55571	102020	Stefano Morozzi	01/2022
8930	2^338901-55479	102020	Stefano Morozzi	02/2022
8931	2^338903+33555	102020	Stefano Morozzi	03/2022
8932	2^338901+39777	102020	Stefano Morozzi	05/2022
8933	2^338903+165981	102020	Stefano Morozzi	06/2022
8934	2^338901-34863	102020	Stefano Morozzi	06/2022
8935	2^338899-150051	102019	Stefano Morozzi	12/2021
8936	2^338899+125951	102019	Stefano Morozzi	12/2021
8937	2^338898+179623	102019	Stefano Morozzi	01/2022
8938	2^338899-154467	102019	Stefano Morozzi	02/2022
8939	2^338898-60753	102019	Stefano Morozzi	06/2022
8940	2^338898+68635	102019	Stefano Morozzi	09/2022
8941	2^338897-85963	102019	Stefano Morozzi	12/2022
8942	2^338898+174129	102019	Stefano Morozzi	02/2023
8943	2^338894-133295	102018	Stefano Morozzi	04/2022
8944	2^338894+165573	102018	Stefano Morozzi	06/2022
8945	2^338894-60957	102018	Stefano Morozzi	06/2022
8946	2^338894-89463	102018	Stefano Morozzi	01/2023
8956	2^338891-18885	102017	Enzo Doria	05/2013
8947	2^338891+26499	102017	Stefano Morozzi	12/2021
8948	2^338891-2625	102017	Stefano Morozzi	12/2021
8949	2^338893+128727	102017	Stefano Morozzi	01/2022
8950	2^338890-52965	102017	Stefano Morozzi	01/2022
8951	2^338892-55467	102017	Stefano Morozzi	02/2022
8952	2^338892-83393	102017	Stefano Morozzi	04/2022
8953	2^338893+13649	102017	Stefano Morozzi	05/2022
8954	2^338892+117957	102017	Stefano Morozzi	09/2022
8955	2^338892-14643	102017	Stefano Morozzi	01/2023
8957	2^338887+154029	102016	Stefano Morozzi	01/2022
8958	2^338889-104293	102016	Stefano Morozzi	02/2022
8959	2^338887+147741	102016	Stefano Morozzi	11/2022
8960	2^338889+195975	102016	Stefano Morozzi	11/2022
8961	2^338889-117873	102016	Stefano Morozzi	02/2023
8962	2^338886+177159	102015	Stefano Morozzi	12/2021
8963	2^338885+40425	102015	Stefano Morozzi	06/2022
8964	2^338884-13053	102015	Stefano Morozzi	12/2022
8965	2^338885-112569	102015	Stefano Morozzi	12/2022
8966	2^338880+11341	102014	Stefano Morozzi	03/2022
8967	2^338880-160383	102014	Stefano Morozzi	06/2022
8968	2^338880-161627	102014	Stefano Morozzi	12/2022
8969	2^338879-1059	102013	Stefano Morozzi	12/2021
8970	2^338879-54525	102013	Stefano Morozzi	02/2022
8971	2^338877-82813	102013	Stefano Morozzi	03/2022
8972	2^338878-185883	102013	Stefano Morozzi	06/2022
8973	2^338879-60355	102013	Stefano Morozzi	06/2022
8974	2^338878+43719	102013	Stefano Morozzi	09/2022
8975	2^338879+122049	102013	Stefano Morozzi	11/2022
8976	2^338874-15063	102012	Stefano Morozzi	01/2023
8977	2^338874+148993	102012	Stefano Morozzi	02/2023
8978	2^338871+7679	102011	Stefano Morozzi	02/2022
8979	2^338872+61141	102011	Stefano Morozzi	03/2022
8980	2^338872-183923	102011	Stefano Morozzi	04/2022
8981	2^338873+19527	102011	Stefano Morozzi	09/2022
8982	2^338870+70719	102011	Stefano Morozzi	11/2022
8983	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
8984	2^338870-37571	102011	Stefano Morozzi	12/2022
8985	2^338872-138573	102011	Stefano Morozzi	12/2022
8986	2^338873-63843	102011	Stefano Morozzi	12/2022
8987	2^338868-5985	102010	Stefano Morozzi	02/2022
8988	2^338867+38079	102010	Stefano Morozzi	05/2022
8989	2^338868+140437	102010	Stefano Morozzi	06/2022
8990	2^338868-110175	102010	Stefano Morozzi	06/2022
8991	2^338868+123337	102010	Stefano Morozzi	11/2022
8992	2^338867-13327	102010	Stefano Morozzi	12/2022
8993	2^338868-11279	102010	Stefano Morozzi	12/2022
8994	2^338868-115685	102010	Stefano Morozzi	01/2023
8995	2^338864+158191	102009	Stefano Morozzi	02/2022
8996	2^338865-39699	102009	Stefano Morozzi	01/2023
8997	2^338865-40789	102009	Stefano Morozzi	01/2023
8998	2^338862+60433	102008	Stefano Morozzi	03/2022
8999	2^338861-9453	102008	Stefano Morozzi	04/2022
9000	2^338861+98067	102008	Stefano Morozzi	11/2022

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Probable Primes Top 10000

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