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 ?
6751	(536*10^102533-23)/9	102535	Robert Price	02/2020
6752	2^340547-108897	102515	Enzo Doria	03/2014
6753	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
6754	25592^10119+10119^25592	102500	Hans Havermann	02/2019
6755	(5*10^102492-23)/9	102492	Serge Batalov	11/2022
6756	7^121268+82	102484	Lelio R Paula	10/2016
6757	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
6758	2^340434-5955	102481	Lelio R Paula	11/2016
6759	(7*10^102480-19)/3	102481	Robert Price	10/2020
6760	(2^340381+47)/7	102465	Lelio R Paula	12/2013
6761	111^50095+110	102461	Norbert Schneider	04/2017
6762	2^340291-20301	102438	Enzo Doria	06/2013
6763	12^94915+89	102431	Lelio R Paula	10/2016
6764	(106*10^102422+17)/3	102424	Robert Price	04/2021
6765	24466^15349+15349^24466	102417	Hans Havermann	03/2019
6766	2^340212+111546435	102415	Paul Bourdelais	10/2021
6767	2^340208-20373	102413	Enzo Doria	06/2013
6768	6^131598-17273	102404	Enzo Doria	02/2013
6769	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
6770	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
6771	2^340115-21181	102385	Enzo Doria	06/2013
6772	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
6773	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
6774	89^52511-88^52511	102365	Robert Price	06/2015
6775	3^214539-112756	102362	Enzo Doria	07/2014
6776	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
6777	2^340000-19877	102351	Enzo Doria	06/2013
6778	2^339990-114845	102348	Enzo Doria	05/2015
6779	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
6780	20^78661-99	102341	Lelio R Paula	09/2016
6782	2^339951-19585	102336	Enzo Doria	05/2013
6781	(17*10^102335-167)/3	102336	Robert Price	05/2022
6783	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
6784	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
6785	5*10^102323-91	102324	Robert Price	03/2021
6787	2^339889+29327	102317	Yves Minet	06/2010
6786	(167*10^102315-17)/3	102317	Robert Price	03/2020
6788	26348^7641+7641^26348	102314	Hans Havermann	03/2019
6789	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
6790	2^339834-109493	102301	Enzo Doria	04/2014
6791	(16*10^102299-19)/3	102300	Robert Price	02/2019
6792	(11^98221-5^98221)/6	102286	Robert Price	01/2013
6793	3^214365+1820	102279	Lelio R Paula	10/2016
6794	31978^1579+1579^31978	102278	Hans Havermann	03/2019
6795	(89*10^102262-467)/9	102263	Robert Price	04/2022
6796	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
6797	2^339694-16995	102259	Lelio R Paula	09/2016
6798	(56*10^102255+691)/9	102256	Robert Price	05/2019
6799	122^49008+121	102249	Norbert Schneider	10/2018
6800	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
6801	7^120985-38	102245	Lelio R Paula	10/2016
6802	10^102244+122961	102245	Patrick De Geest	12/2016
6803	10^102244-27	102244	Lelio R Paula	09/2016
6804	7^120982-62	102242	Lelio R Paula	10/2016
6805	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
6806	4*6^131382-5	102236	Lelio R Paula	11/2014
6807	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
6808	2^339586-1091	102226	Yves Minet	11/2012
6809	11^98161-3072000	102225	Enzo Doria	12/2012
6810	9*7^120961-4	102225	Lelio R Paula	11/2014
6811	5*3^214250+2	102224	Serge Batalov	10/2010
6812	12^94713-59	102213	Lelio R Paula	10/2016
6813	12^94705+89	102204	Lelio R Paula	10/2016
6814	2^339407-177	102172	Lelio R Paula	08/2011
6815	4*10^102163-57	102164	Robert Price	10/2018
6816	2^339355+65	102157	Lelio R Paula	07/2011
6817	(28*10^102142-31)/3	102143	Robert Price	12/2019
6818	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
6819	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
6820	s(178551)	102122	Robert Price	05/2020
6821	(797*10^102112-23)/9	102114	Robert Price	01/2022
6822	(5*10^102107+7)/3	102108	Tyler Busby	02/2023
6823	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
6825	2^339168+21	102100	Lelio R Paula	07/2011
6826	2^339167-108807	102100	Enzo Doria	03/2014
6824	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
6827	2^339156+163	102097	Lelio R Paula	08/2011
6828	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
6829	(25*10^102076-67)/3	102077	Robert Price	06/2019
6830	2^339081-4543	102074	Yves Minet	03/2019
6831	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
6832	2*10^102062+77	102063	Robert Price	08/2020
6834	24327^15668+15668^24327	102053	Hans Havermann	02/2019
6833	10^102052+66793	102053	Patrick De Geest	09/2022
6835	10^102052-7000001	102052	Robert Price	06/2021
6836	10^102052-618623	102052	Patrick De Geest	09/2022
6837	2^339000-175635	102050	Stefano Morozzi	12/2021
6838	2^339000-151667	102050	Stefano Morozzi	12/2021
6839	2^338999+79289	102049	Stefano Morozzi	01/2022
6840	2^338998-63897	102049	Stefano Morozzi	12/2022
6841	2^338997+99659	102049	Stefano Morozzi	02/2023
6842	2^338994+188757	102048	Stefano Morozzi	05/2022
6843	2^338995+70785	102048	Stefano Morozzi	11/2022
6844	2^338994-12183	102048	Stefano Morozzi	12/2022
6845	2^338992+181591	102047	Stefano Morozzi	01/2022
6846	2^338992+136171	102047	Stefano Morozzi	03/2022
6847	2^338991-109435	102047	Stefano Morozzi	04/2022
6848	2^338991+193611	102047	Stefano Morozzi	09/2022
6849	2^338988-134619	102046	Stefano Morozzi	04/2022
6850	2^338987-62557	102046	Stefano Morozzi	12/2022
6851	2^338986-60141	102045	Stefano Morozzi	06/2022
6852	2^338986+98209	102045	Stefano Morozzi	11/2022
6853	2^338981+106391	102044	Stefano Morozzi	01/2022
6854	2^338982+34069	102044	Stefano Morozzi	03/2022
6855	2^338982-58781	102044	Stefano Morozzi	04/2022
6856	2^338980+70833	102044	Stefano Morozzi	11/2022
6857	2^338982-92111	102044	Stefano Morozzi	02/2023
6858	2^338977+83007	102043	Stefano Morozzi	02/2022
6859	2^338979-83601	102043	Stefano Morozzi	04/2022
6860	2^338975+28355	102042	Stefano Morozzi	01/2022
6861	2^338973+134619	102042	Stefano Morozzi	03/2022
6862	2^338974+183777	102042	Stefano Morozzi	03/2022
6863	2^338975+69293	102042	Stefano Morozzi	09/2022
6871	25080^11711+11711^25080	102041	Hans Havermann	02/2019
6864	2^338972+152343	102041	Stefano Morozzi	12/2021
6865	2^338972-180623	102041	Stefano Morozzi	02/2022
6866	2^338972+84441	102041	Stefano Morozzi	03/2022
6867	2^338971+64875	102041	Stefano Morozzi	05/2022
6868	2^338971+44985	102041	Stefano Morozzi	11/2022
6869	2^338971+145065	102041	Stefano Morozzi	11/2022
6870	2^338972-16635	102041	Stefano Morozzi	01/2023
6872	2^338968+53461	102040	Stefano Morozzi	01/2022
6873	2^338969+160175	102040	Stefano Morozzi	03/2022
6874	2^338967+13409	102040	Stefano Morozzi	04/2022
6875	2^338969+67635	102040	Stefano Morozzi	09/2022
6876	2^338969-15913	102040	Stefano Morozzi	01/2023
6877	2^338963-127455	102039	Stefano Morozzi	12/2021
6878	2^338963+132195	102039	Stefano Morozzi	02/2022
6879	2^338966+137919	102039	Stefano Morozzi	04/2022
6880	2^338963-87529	102039	Stefano Morozzi	12/2022
6881	2^338963-116859	102039	Stefano Morozzi	02/2023
6888	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
6882	2^338960+53935	102038	Stefano Morozzi	01/2022
6883	2^338962+83157	102038	Stefano Morozzi	02/2022
6884	2^338961+12341	102038	Stefano Morozzi	04/2022
6885	2^338960+63933	102038	Stefano Morozzi	05/2022
6886	2^338960+170791	102038	Stefano Morozzi	11/2022
6887	2^338962+21679	102038	Stefano Morozzi	11/2022
6889	2^338959-30919	102037	Stefano Morozzi	02/2022
6890	2^338959+164769	102037	Stefano Morozzi	05/2022
6891	2^338958-43161	102037	Stefano Morozzi	02/2023
6892	2^338954-177003	102036	Stefano Morozzi	12/2021
6893	2^338954+154207	102036	Stefano Morozzi	01/2022
6894	2^338956+182493	102036	Stefano Morozzi	02/2022
6895	2^338954+162715	102036	Stefano Morozzi	04/2022
6896	2^338955-158241	102036	Stefano Morozzi	04/2022
6897	2^338956-33395	102036	Stefano Morozzi	04/2022
6898	2^338954+190915	102036	Stefano Morozzi	06/2022
6899	2^338955+41643	102036	Stefano Morozzi	09/2022
6900	2^338954+194427	102036	Stefano Morozzi	09/2022
6901	2^338956+117967	102036	Stefano Morozzi	09/2022
6902	2^338956+195495	102036	Stefano Morozzi	11/2022
6903	2^338954-186371	102036	Stefano Morozzi	12/2022
6904	2^338950+175077	102035	Stefano Morozzi	12/2021
6905	2^338951-51687	102035	Stefano Morozzi	12/2021
6906	2^338951+66123	102035	Stefano Morozzi	06/2022
6907	2^338950+19317	102035	Stefano Morozzi	09/2022
6908	2^338951-161479	102035	Stefano Morozzi	12/2022
6909	2^338950-66335	102035	Stefano Morozzi	01/2023
6910	2^338951-41611	102035	Stefano Morozzi	02/2023
6911	2^338952-142887	102035	Stefano Morozzi	02/2023
6912	2^338949+85449	102034	Stefano Morozzi	03/2022
6913	2^338949-184585	102034	Stefano Morozzi	04/2022
6914	2^338949-88555	102034	Stefano Morozzi	12/2022
6915	2^338948+49393	102034	Stefano Morozzi	02/2023
6916	2^338949-17601	102034	Stefano Morozzi	02/2023
6917	2^338943+127103	102033	Stefano Morozzi	12/2021
6918	2^338944-84003	102033	Stefano Morozzi	04/2022
6919	2^338945+138605	102033	Stefano Morozzi	05/2022
6920	2^338943+95133	102033	Stefano Morozzi	11/2022
6921	2^338943+147435	102033	Stefano Morozzi	11/2022
6922	2^338943-116067	102033	Stefano Morozzi	01/2023
6923	2^338940+78607	102032	Stefano Morozzi	01/2022
6924	2^338942-86687	102032	Stefano Morozzi	12/2022
6925	2^338939+151569	102031	Stefano Morozzi	12/2021
6926	2^338938+183975	102031	Stefano Morozzi	03/2022
6927	2^338937-33429	102031	Stefano Morozzi	04/2022
6928	2^338939-183259	102031	Stefano Morozzi	04/2022
6929	2^338937-139951	102031	Stefano Morozzi	01/2023
6930	2^338938-40151	102031	Stefano Morozzi	01/2023
6931	2^338938+74449	102031	Stefano Morozzi	02/2023
6932	2^338935+179999	102030	Stefano Morozzi	01/2022
6933	2^338936+84147	102030	Stefano Morozzi	03/2022
6934	2^338935+171261	102030	Stefano Morozzi	11/2022
6935	2^338936-41355	102030	Stefano Morozzi	01/2023
6936	2^338931+2349	102029	Stefano Morozzi	12/2021
6937	2^338933+79935	102029	Stefano Morozzi	01/2022
6938	2^338930+33819	102029	Stefano Morozzi	03/2022
6939	2^338931-31555	102029	Stefano Morozzi	03/2022
6940	2^338933+64169	102029	Stefano Morozzi	05/2022
6941	2^338932-184965	102029	Stefano Morozzi	06/2022
6942	2^338932+66943	102029	Stefano Morozzi	09/2022
6943	2^338932+92995	102029	Stefano Morozzi	09/2022
6944	2^338931+97001	102029	Stefano Morozzi	11/2022
6945	2^338932-165453	102029	Stefano Morozzi	01/2023
6946	2^338933-40899	102029	Stefano Morozzi	01/2023
6947	2^338928+2367	102028	Stefano Morozzi	12/2021
6948	2^338927+52779	102028	Stefano Morozzi	01/2022
6949	2^338927-79539	102028	Stefano Morozzi	02/2022
6950	2^338929+60819	102028	Stefano Morozzi	03/2022
6951	2^338928-156959	102028	Stefano Morozzi	03/2022
6952	2^338927-63919	102028	Stefano Morozzi	12/2022
6953	2^338925+106631	102027	Stefano Morozzi	01/2022
6954	2^338926+80235	102027	Stefano Morozzi	01/2022
6955	2^338926+41607	102027	Stefano Morozzi	09/2022
6956	2^338925+195435	102027	Stefano Morozzi	11/2022
6957	2^338924-92885	102027	Stefano Morozzi	02/2023
6958	2^338922-27291	102026	Stefano Morozzi	12/2021
6959	2^338919-103849	102025	Stefano Morozzi	01/2022
6960	2^338919+130221	102025	Stefano Morozzi	01/2022
6961	2^338918-91967	102025	Stefano Morozzi	02/2023
6962	2^338914-79121	102024	Stefano Morozzi	02/2022
6963	2^338916+134047	102024	Stefano Morozzi	03/2022
6964	2^338914-11315	102024	Stefano Morozzi	12/2022
6965	2^338910+81027	102023	Stefano Morozzi	01/2022
6966	2^338912+179821	102023	Stefano Morozzi	01/2022
6967	2^338909+100769	102022	Stefano Morozzi	11/2021
6968	2^338908-100839	102022	Stefano Morozzi	12/2021
6969	2^338909-25951	102022	Stefano Morozzi	12/2021
6970	2^338909+66845	102022	Stefano Morozzi	09/2022
6971	2^338907+73509	102022	Stefano Morozzi	11/2022
6972	2^338906-25823	102021	Stefano Morozzi	12/2021
6973	2^338904+75951	102021	Stefano Morozzi	12/2021
6974	2^338906+6685	102021	Stefano Morozzi	01/2022
6975	2^338905+160365	102021	Stefano Morozzi	03/2022
6976	2^338906+92617	102021	Stefano Morozzi	09/2022
6977	2^338904+47065	102021	Stefano Morozzi	11/2022
6978	2^338905+70427	102021	Stefano Morozzi	11/2022
6979	2^338905-163975	102021	Stefano Morozzi	12/2022
6980	2^338903+4155	102020	Stefano Morozzi	01/2022
6981	2^338901+55571	102020	Stefano Morozzi	01/2022
6982	2^338901-55479	102020	Stefano Morozzi	02/2022
6983	2^338903+33555	102020	Stefano Morozzi	03/2022
6984	2^338901+39777	102020	Stefano Morozzi	05/2022
6985	2^338903+165981	102020	Stefano Morozzi	06/2022
6986	2^338901-34863	102020	Stefano Morozzi	06/2022
6987	2^338899-150051	102019	Stefano Morozzi	12/2021
6988	2^338899+125951	102019	Stefano Morozzi	12/2021
6989	2^338898+179623	102019	Stefano Morozzi	01/2022
6990	2^338899-154467	102019	Stefano Morozzi	02/2022
6991	2^338898-60753	102019	Stefano Morozzi	06/2022
6992	2^338898+68635	102019	Stefano Morozzi	09/2022
6993	2^338897-85963	102019	Stefano Morozzi	12/2022
6994	2^338898+174129	102019	Stefano Morozzi	02/2023
6995	2^338894-133295	102018	Stefano Morozzi	04/2022
6996	2^338894+165573	102018	Stefano Morozzi	06/2022
6997	2^338894-60957	102018	Stefano Morozzi	06/2022
6998	2^338894-89463	102018	Stefano Morozzi	01/2023
6999	2^338891+26499	102017	Stefano Morozzi	12/2021
7000	2^338891-2625	102017	Stefano Morozzi	12/2021

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Probable Primes Top 10000

(294113 PRPs in the top)