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	2^338630+12867	101938	Stefano Morozzi	04/2022
6752	2^338629+42147	101938	Stefano Morozzi	09/2022
6753	2^338628+121083	101938	Stefano Morozzi	11/2022
6754	2^338630+147235	101938	Stefano Morozzi	11/2022
6755	2^338628-37679	101938	Stefano Morozzi	12/2022
6756	2^338629-41383	101938	Stefano Morozzi	01/2023
6757	2^338626-105875	101937	Stefano Morozzi	02/2022
6758	2^338625-111729	101937	Stefano Morozzi	12/2022
6759	2^338621+33069	101936	Stefano Morozzi	02/2022
6760	2^338623-106405	101936	Stefano Morozzi	03/2022
6761	2^338621+61751	101936	Stefano Morozzi	04/2022
6762	2^338623-86577	101936	Stefano Morozzi	12/2022
6763	2^338620-150735	101935	Stefano Morozzi	12/2021
6764	2^338619-27765	101935	Stefano Morozzi	01/2022
6765	2^338619-77959	101935	Stefano Morozzi	01/2022
6766	2^338619-186367	101935	Stefano Morozzi	12/2022
6767	2^338618-64905	101935	Stefano Morozzi	01/2023
6768	2^338615+151655	101934	Stefano Morozzi	12/2021
6769	2^338616+5047	101934	Stefano Morozzi	01/2022
6770	2^338616+39705	101934	Stefano Morozzi	05/2022
6771	2^338611+76659	101933	Stefano Morozzi	12/2021
6772	2^338613-109791	101933	Stefano Morozzi	04/2022
6773	2^338612+119583	101933	Stefano Morozzi	09/2022
6774	2^338611-140397	101933	Stefano Morozzi	01/2023
6775	2^338614-39653	101933	Stefano Morozzi	01/2023
6776	2^338609+130139	101932	Stefano Morozzi	01/2022
6777	2^338609+131327	101932	Stefano Morozzi	01/2022
6778	2^338608-155453	101932	Stefano Morozzi	02/2022
6779	2^338609+161721	101932	Stefano Morozzi	04/2022
6780	2^338609-10405	101932	Stefano Morozzi	06/2022
6781	2^338608+94017	101932	Stefano Morozzi	09/2022
6782	2^338610+170515	101932	Stefano Morozzi	11/2022
6783	2^338607+30611	101931	Stefano Morozzi	01/2022
6784	2^338607+106695	101931	Stefano Morozzi	02/2022
6785	2^338606-32291	101931	Stefano Morozzi	03/2022
6786	2^338606+15195	101931	Stefano Morozzi	05/2022
6787	2^338605+197789	101931	Stefano Morozzi	11/2022
6788	2^338607-90621	101931	Stefano Morozzi	01/2023
6789	2^338603-1195	101930	Stefano Morozzi	12/2021
6790	2^338601+108867	101930	Stefano Morozzi	03/2022
6791	2^338603+34311	101930	Stefano Morozzi	03/2022
6792	2^338598+57127	101929	Stefano Morozzi	02/2022
6793	2^338598+162645	101929	Stefano Morozzi	04/2022
6794	2^338599+43445	101929	Stefano Morozzi	09/2022
6795	2^338599+19485	101929	Stefano Morozzi	09/2022
6796	2^338598+46195	101929	Stefano Morozzi	11/2022
6797	2^338600-36393	101929	Stefano Morozzi	12/2022
6798	2^338596-1739	101928	Stefano Morozzi	12/2021
6799	2^338595-78687	101928	Stefano Morozzi	01/2022
6800	2^338595+181683	101928	Stefano Morozzi	02/2022
6801	2^338597-106045	101928	Stefano Morozzi	02/2022
6802	2^338595+119565	101928	Stefano Morozzi	09/2022
6803	2^338595+19623	101928	Stefano Morozzi	09/2022
6804	2^338595+21711	101928	Stefano Morozzi	11/2022
6805	2^338596-111129	101928	Stefano Morozzi	12/2022
6806	2^338591+53769	101927	Stefano Morozzi	01/2022
6807	2^338593+156989	101927	Stefano Morozzi	02/2022
6808	2^338592+36157	101927	Stefano Morozzi	03/2022
6809	2^338593+42099	101927	Stefano Morozzi	09/2022
6810	2^338591+46685	101927	Stefano Morozzi	11/2022
6811	2^338593+120437	101927	Stefano Morozzi	11/2022
6812	2^338591-165517	101927	Stefano Morozzi	01/2023
6813	2^338592-166107	101927	Stefano Morozzi	01/2023
6814	2^338592-189249	101927	Stefano Morozzi	01/2023
6815	2^338594-40493	101927	Stefano Morozzi	01/2023
6816	2^338590+182007	101926	Stefano Morozzi	02/2022
6817	2^338590+60747	101926	Stefano Morozzi	03/2022
6818	2^338588+62397	101926	Stefano Morozzi	04/2022
6819	2^338589-9685	101926	Stefano Morozzi	04/2022
6826	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
6820	2^338586+1153	101925	Stefano Morozzi	12/2021
6821	2^338587-51709	101925	Stefano Morozzi	12/2021
6822	2^338586+105303	101925	Stefano Morozzi	01/2022
6823	2^338585-131773	101925	Stefano Morozzi	03/2022
6824	2^338587+168039	101925	Stefano Morozzi	09/2022
6825	2^338585-140719	101925	Stefano Morozzi	01/2023
6827	2^338584+100771	101924	Stefano Morozzi	11/2021
6828	2^338581-150415	101924	Stefano Morozzi	12/2021
6829	2^338581-2349	101924	Stefano Morozzi	12/2021
6830	2^338582+42933	101924	Stefano Morozzi	09/2022
6831	2^338584+93267	101924	Stefano Morozzi	09/2022
6832	2^338582-86697	101924	Stefano Morozzi	12/2022
6833	2^338582-138035	101924	Stefano Morozzi	12/2022
6834	2^338584-115569	101924	Stefano Morozzi	01/2023
6835	2^338578+67593	101923	Stefano Morozzi	09/2022
6836	2^338580+142201	101923	Stefano Morozzi	09/2022
6837	2^338579-14635	101923	Stefano Morozzi	01/2023
6838	2^338579-164985	101923	Stefano Morozzi	01/2023
6839	2^338575-28815	101922	Stefano Morozzi	01/2022
6840	2^338575-33645	101922	Stefano Morozzi	04/2022
6841	2^338573-156693	101921	Stefano Morozzi	03/2022
6842	2^338572+193305	101921	Stefano Morozzi	09/2022
6847	2^338568+37	101920	Lelio R Paula	07/2011
6843	2^338570-53933	101920	Stefano Morozzi	02/2022
6844	2^338569+87201	101920	Stefano Morozzi	04/2022
6845	2^338570-36897	101920	Stefano Morozzi	12/2022
6846	2^338570-61157	101920	Stefano Morozzi	12/2022
6848	2^338567-9619	101919	Stefano Morozzi	04/2022
6849	2^338565-141589	101919	Stefano Morozzi	01/2023
6850	2^338564-56763	101918	Stefano Morozzi	03/2022
6851	2^338561+112007	101918	Stefano Morozzi	04/2022
6852	2^338561-9315	101918	Stefano Morozzi	04/2022
6853	2^338564+41965	101918	Stefano Morozzi	09/2022
6854	2^338561+121139	101918	Stefano Morozzi	11/2022
6855	2^338562+21799	101918	Stefano Morozzi	11/2022
6863	2^338559-1858777	101917	Enzo Doria	04/2016
6856	2^338558+4825	101917	Stefano Morozzi	01/2022
6857	2^338559-127935	101917	Stefano Morozzi	01/2022
6858	2^338560+154891	101917	Stefano Morozzi	01/2022
6859	2^338559+131885	101917	Stefano Morozzi	02/2022
6860	2^338558+93735	101917	Stefano Morozzi	09/2022
6861	2^338559-90957	101917	Stefano Morozzi	01/2023
6862	2^338559-190761	101917	Stefano Morozzi	01/2023
6864	2^338555+189981	101916	Stefano Morozzi	05/2022
6865	2^338553-125383	101915	Stefano Morozzi	12/2021
6866	2^338554-82821	101915	Stefano Morozzi	03/2022
6867	2^338548+76923	101914	Stefano Morozzi	12/2021
6868	2^338549+158517	101914	Stefano Morozzi	03/2022
6869	2^338549+85397	101914	Stefano Morozzi	03/2022
6870	2^338548+138121	101914	Stefano Morozzi	05/2022
6871	2^338550-110301	101914	Stefano Morozzi	06/2022
6872	2^338547+129321	101913	Stefano Morozzi	01/2022
6873	2^338547-153481	101913	Stefano Morozzi	01/2022
6874	2^338545-11059	101913	Stefano Morozzi	12/2022
6875	2^338544+107853	101912	Stefano Morozzi	02/2022
6876	2^338542+172813	101912	Stefano Morozzi	11/2022
6877	2^338544-12687	101912	Stefano Morozzi	12/2022
6878	2^338543-140677	101912	Stefano Morozzi	01/2023
6879	2^338541+152721	101911	Stefano Morozzi	01/2022
6880	2^338539+60825	101911	Stefano Morozzi	03/2022
6881	2^338539+160881	101911	Stefano Morozzi	03/2022
6882	2^338541-182523	101911	Stefano Morozzi	03/2022
6883	2^338540+87645	101911	Stefano Morozzi	04/2022
6884	2^338541+148305	101911	Stefano Morozzi	11/2022
6885	2^338541-163075	101911	Stefano Morozzi	12/2022
6886	2^338536-100785	101910	Stefano Morozzi	12/2021
6887	2^338535-51837	101910	Stefano Morozzi	12/2021
6888	2^338535-158745	101910	Stefano Morozzi	04/2022
6889	2^338536-189977	101910	Stefano Morozzi	01/2023
6890	2^338537-65623	101910	Stefano Morozzi	01/2023
6891	2^338532+39445	101909	Stefano Morozzi	05/2022
6892	2^338532+141415	101909	Stefano Morozzi	06/2022
6893	2^338532-136037	101909	Stefano Morozzi	06/2022
6894	2^338531+81081	101908	Stefano Morozzi	01/2022
6895	2^338530+59835	101908	Stefano Morozzi	03/2022
6896	2^338529+186551	101908	Stefano Morozzi	04/2022
6897	2^338531+61313	101908	Stefano Morozzi	04/2022
6898	2^338531-9277	101908	Stefano Morozzi	04/2022
6899	2^338527+191205	101907	Stefano Morozzi	06/2022
6900	2^338524+54421	101906	Stefano Morozzi	01/2022
6901	2^338522-155811	101906	Stefano Morozzi	02/2022
6902	2^338523-16291	101906	Stefano Morozzi	01/2023
6903	2^338521+183131	101905	Stefano Morozzi	02/2022
6904	2^338520+34945	101905	Stefano Morozzi	03/2022
6905	2^338518-182885	101905	Stefano Morozzi	04/2022
6906	2^338518+114633	101905	Stefano Morozzi	05/2022
6907	2^338518-12621	101905	Stefano Morozzi	12/2022
6908	2^338518-187325	101905	Stefano Morozzi	12/2022
6915	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
6909	2^338517-125955	101904	Stefano Morozzi	12/2021
6910	2^338517+126437	101904	Stefano Morozzi	12/2021
6911	2^338517-53499	101904	Stefano Morozzi	01/2022
6912	2^338515+30369	101904	Stefano Morozzi	01/2022
6913	2^338517-184623	101904	Stefano Morozzi	04/2022
6914	2^338515+89333	101904	Stefano Morozzi	05/2022
6918	24502^14419+14419^24502	101903	Hans Havermann	01/2019
6916	2^338512-827	101903	Stefano Morozzi	12/2021
6917	2^338514-6611	101903	Stefano Morozzi	03/2022
6919	2^338509+5139	101902	Stefano Morozzi	01/2022
6920	2^338509+40205	101902	Stefano Morozzi	06/2022
6921	2^338511+19959	101902	Stefano Morozzi	09/2022
6922	2^338510-37877	101902	Stefano Morozzi	12/2022
6923	2^338507-188655	101901	Stefano Morozzi	12/2022
6924	2^338507-114457	101901	Stefano Morozzi	01/2023
6925	2^338504-152615	101900	Stefano Morozzi	01/2022
6926	2^338502-4587	101900	Stefano Morozzi	02/2022
6927	2^338502-166275	101900	Stefano Morozzi	01/2023
6928	2^338500-26865	101899	Stefano Morozzi	12/2021
6929	2^338501-177471	101899	Stefano Morozzi	12/2021
6930	2^338499-3915	101899	Stefano Morozzi	01/2022
6931	2^338501+32051	101899	Stefano Morozzi	02/2022
6932	2^338499+183533	101899	Stefano Morozzi	03/2022
6933	2^338500+35625	101899	Stefano Morozzi	03/2022
6934	2^338499+87579	101899	Stefano Morozzi	04/2022
6937	2^338497-17041	101898	Enzo Doria	05/2013
6935	2^338497+150405	101898	Stefano Morozzi	11/2021
6936	2^338495+100533	101898	Stefano Morozzi	12/2021
6938	2^338494+36057	101897	Stefano Morozzi	03/2022
6939	2^338492+39015	101897	Stefano Morozzi	05/2022
6940	2^338494+168007	101897	Stefano Morozzi	09/2022
6941	2^338490+61149	101896	Stefano Morozzi	03/2022
6942	2^338489+161369	101896	Stefano Morozzi	04/2022
6943	2^338491+22961	101896	Stefano Morozzi	11/2022
6944	2^338487-3555	101895	Stefano Morozzi	01/2022
6945	2^338487-183129	101895	Stefano Morozzi	04/2022
6946	2^338484+128767	101894	Stefano Morozzi	01/2022
6947	2^338484-31895	101894	Stefano Morozzi	03/2022
6948	2^338478+10893	101893	Stefano Morozzi	03/2022
6949	2^338479+87243	101893	Stefano Morozzi	04/2022
6950	2^338479+167619	101893	Stefano Morozzi	09/2022
6951	2^338480+197503	101893	Stefano Morozzi	11/2022
6952	2^338481-11421	101893	Stefano Morozzi	12/2022
6953	2^338479-89649	101893	Stefano Morozzi	01/2023
6956	2^338475+54615	101892	Lelio R Paula	10/2016
6954	2^338475-59775	101892	Stefano Morozzi	04/2022
6955	2^338476-134237	101892	Stefano Morozzi	04/2022
6957	2^338474+100767	101891	Stefano Morozzi	11/2021
6958	2^338474+81165	101891	Stefano Morozzi	01/2022
6959	2^338474+41137	101891	Stefano Morozzi	06/2022
6960	2^338472-110445	101891	Stefano Morozzi	06/2022
6961	2^338473-89535	101891	Stefano Morozzi	01/2023
6962	2^338470+27777	101890	Stefano Morozzi	01/2022
6963	2^338468+31351	101890	Stefano Morozzi	01/2022
6964	2^338469-106339	101890	Stefano Morozzi	03/2022
6965	2^338471+187469	101890	Stefano Morozzi	04/2022
6966	2^338468+96613	101890	Stefano Morozzi	11/2022
6967	2^338469+46167	101890	Stefano Morozzi	11/2022
6968	2^338470+71527	101890	Stefano Morozzi	11/2022
6969	2^338469-112783	101890	Stefano Morozzi	12/2022
6970	2^338470-115665	101890	Stefano Morozzi	01/2023
6971	2^338467-25665	101889	Stefano Morozzi	12/2021
6972	2^338465+152139	101889	Stefano Morozzi	12/2021
6973	2^338466-28643	101889	Stefano Morozzi	01/2022
6974	2^338465+181517	101889	Stefano Morozzi	01/2022
6975	2^338466+115917	101889	Stefano Morozzi	06/2022
6976	2^338465-88291	101889	Stefano Morozzi	12/2022
6977	2^338464-104009	101888	Stefano Morozzi	02/2022
6978	2^338463+185169	101888	Stefano Morozzi	03/2022
6979	2^338464+60595	101888	Stefano Morozzi	03/2022
6980	2^338464-66377	101888	Stefano Morozzi	01/2023
6981	2^338458+60273	101887	Stefano Morozzi	03/2022
6982	2^338461+135867	101887	Stefano Morozzi	03/2022
6983	2^338455-4621	101886	Stefano Morozzi	02/2022
6984	2^338457+187827	101886	Stefano Morozzi	04/2022
6985	2^338455+173349	101886	Stefano Morozzi	11/2022
6986	2^338454+133737	101885	Stefano Morozzi	03/2022
6987	2^338454-158501	101885	Stefano Morozzi	04/2022
6988	2^338454-184217	101885	Stefano Morozzi	04/2022
6989	2^338453+164451	101885	Stefano Morozzi	05/2022
6990	2^338452-136137	101885	Stefano Morozzi	12/2022
6991	2^338450+106275	101884	Stefano Morozzi	01/2022
6992	2^338450+168439	101884	Stefano Morozzi	09/2022
6993	(133*10^101881+17)/3	101883	Robert Price	11/2021
6994	2^338445-80461	101883	Stefano Morozzi	02/2022
6995	2^338446-131211	101883	Stefano Morozzi	02/2022
6996	2^338448+187167	101883	Stefano Morozzi	04/2022
6997	2^338446-160115	101883	Stefano Morozzi	06/2022
6998	2^338447-164157	101883	Stefano Morozzi	01/2023
6999	2^338447-191001	101883	Stefano Morozzi	01/2023
7000	2^338444+127623	101882	Stefano Morozzi	12/2021

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Probable Primes Top 10000

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