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 ?
7751	2^338391-64225	101866	Stefano Morozzi	01/2023
7752	2^338389-16971	101866	Stefano Morozzi	02/2023
7753	2^338387-75685	101865	Stefano Morozzi	12/2021
7754	2^338388-53459	101865	Stefano Morozzi	01/2022
7755	2^338388-36575	101865	Stefano Morozzi	12/2022
7756	2^338385-190311	101865	Stefano Morozzi	01/2023
7757	2^338384+131563	101864	Stefano Morozzi	01/2022
7758	2^338382+109069	101864	Stefano Morozzi	03/2022
7759	2^338384+168987	101864	Stefano Morozzi	09/2022
7760	2^338383-42367	101864	Stefano Morozzi	02/2023
7761	2^338380+77125	101863	Stefano Morozzi	12/2021
7762	2^338381-35539	101863	Stefano Morozzi	06/2022
7763	2^338378-125841	101862	Stefano Morozzi	12/2021
7764	2^338375+27815	101862	Stefano Morozzi	01/2022
7765	2^338375-28509	101862	Stefano Morozzi	01/2022
7766	2^338375+29985	101862	Stefano Morozzi	01/2022
7767	2^338377+157881	101862	Stefano Morozzi	02/2022
7768	2^338375+59589	101862	Stefano Morozzi	03/2022
7769	2^338378+36399	101862	Stefano Morozzi	04/2022
7770	2^338378-159773	101862	Stefano Morozzi	04/2022
7771	2^338378+14883	101862	Stefano Morozzi	05/2022
7772	2^338376+140173	101862	Stefano Morozzi	06/2022
7773	2^338375+18761	101862	Stefano Morozzi	09/2022
7774	2^338373-75103	101861	Stefano Morozzi	12/2021
7775	2^338372+128877	101861	Stefano Morozzi	01/2022
7776	2^338374-28731	101861	Stefano Morozzi	01/2022
7777	2^338374-128427	101861	Stefano Morozzi	01/2022
7778	2^338372+37875	101861	Stefano Morozzi	04/2022
7779	2^338373+161541	101861	Stefano Morozzi	04/2022
7780	2^338374+37759	101861	Stefano Morozzi	04/2022
7781	2^338372+93235	101861	Stefano Morozzi	09/2022
7782	2^338373-63273	101861	Stefano Morozzi	12/2022
7783	2^338369+29427	101860	Stefano Morozzi	01/2022
7784	2^338370+179133	101860	Stefano Morozzi	01/2022
7785	2^338369+131501	101860	Stefano Morozzi	01/2022
7786	2^338369+181649	101860	Stefano Morozzi	02/2022
7787	2^338370-4787	101860	Stefano Morozzi	02/2022
7788	2^338371-133491	101860	Stefano Morozzi	04/2022
7789	2^338371+42023	101860	Stefano Morozzi	09/2022
7790	2^338371+145323	101860	Stefano Morozzi	11/2022
7791	2^338371-138145	101860	Stefano Morozzi	12/2022
7798	2^338368-20369	101859	Enzo Doria	06/2013
7799	2^338366+74179	101859	Enzo Doria	04/2016
7792	2^338366+53853	101859	Stefano Morozzi	01/2022
7793	2^338365-31665	101859	Stefano Morozzi	03/2022
7794	2^338368-156345	101859	Stefano Morozzi	03/2022
7795	2^338366-159867	101859	Stefano Morozzi	04/2022
7796	2^338368-63509	101859	Stefano Morozzi	12/2022
7797	2^338365-190975	101859	Stefano Morozzi	01/2023
7800	2^338362-180845	101858	Stefano Morozzi	02/2022
7801	2^338364-155769	101858	Stefano Morozzi	02/2022
7802	2^338362+142843	101858	Stefano Morozzi	09/2022
7803	2^338362+170019	101858	Stefano Morozzi	11/2022
7804	2^338361-100875	101857	Stefano Morozzi	12/2021
7805	2^338361+154169	101857	Stefano Morozzi	01/2022
7806	2^338359-189645	101857	Stefano Morozzi	01/2023
7807	2^338356+101271	101856	Stefano Morozzi	12/2021
7808	2^338356+53383	101856	Stefano Morozzi	01/2022
7809	2^338355+59393	101856	Stefano Morozzi	03/2022
7810	2^338356+60775	101856	Stefano Morozzi	03/2022
7811	2^338356-106257	101856	Stefano Morozzi	03/2022
7812	2^338357-58921	101856	Stefano Morozzi	04/2022
7813	2^338356+94605	101856	Stefano Morozzi	09/2022
7814	2^338356+117813	101856	Stefano Morozzi	09/2022
7815	2^338358-38475	101856	Stefano Morozzi	12/2022
7816	2^338353-190291	101855	Stefano Morozzi	01/2023
7817	2^338350-152933	101854	Stefano Morozzi	01/2022
7818	2^338350+6337	101854	Stefano Morozzi	01/2022
7819	2^338350+168759	101854	Stefano Morozzi	09/2022
7822	27088^5755+5755^27088	101853	Hans Havermann	01/2019
7820	2^338347+125901	101853	Stefano Morozzi	11/2021
7821	2^338346-10643	101853	Stefano Morozzi	06/2022
7823	2^338343+152271	101852	Stefano Morozzi	12/2021
7824	2^338345+154107	101852	Stefano Morozzi	01/2022
7825	2^338342+155397	101852	Stefano Morozzi	01/2022
7826	2^338342-130767	101852	Stefano Morozzi	02/2022
7827	2^338345-30123	101852	Stefano Morozzi	02/2022
7828	2^338345+35747	101852	Stefano Morozzi	03/2022
7829	2^338345-133131	101852	Stefano Morozzi	04/2022
7830	2^338345-134559	101852	Stefano Morozzi	04/2022
7831	2^338342+170073	101852	Stefano Morozzi	11/2022
7832	2^338344+46567	101852	Stefano Morozzi	11/2022
7833	2^338344+97141	101852	Stefano Morozzi	11/2022
7834	2^338342-162213	101852	Stefano Morozzi	12/2022
7835	2^338339+2753	101851	Stefano Morozzi	12/2021
7836	2^338341+128415	101851	Stefano Morozzi	01/2022
7837	2^338338+2677	101850	Stefano Morozzi	12/2021
7838	2^338336+54607	101850	Stefano Morozzi	01/2022
7839	2^338338+109999	101850	Stefano Morozzi	03/2022
7840	2^338336+161575	101850	Stefano Morozzi	04/2022
7841	2^338335+51975	101849	Stefano Morozzi	12/2021
7842	2^338335-152607	101849	Stefano Morozzi	01/2022
7843	2^338334+55273	101849	Stefano Morozzi	01/2022
7844	2^338332+34315	101849	Stefano Morozzi	03/2022
7845	2^338335+158759	101849	Stefano Morozzi	03/2022
7846	2^338332+67621	101849	Stefano Morozzi	09/2022
7847	2^338332-66099	101849	Stefano Morozzi	01/2023
7848	2^338334-191043	101849	Stefano Morozzi	01/2023
7849	2^338331+83403	101848	Stefano Morozzi	02/2022
7850	2^338330-110865	101848	Stefano Morozzi	06/2022
7851	2^338330+71047	101848	Stefano Morozzi	11/2022
7852	2^338328-5295	101847	Stefano Morozzi	02/2022
7853	2^338327+143585	101847	Stefano Morozzi	09/2022
7854	2^338324-179667	101846	Stefano Morozzi	02/2022
7855	2^338322+21903	101846	Stefano Morozzi	11/2022
7856	2^338324+98047	101846	Stefano Morozzi	11/2022
7857	2^338323-87729	101846	Stefano Morozzi	12/2022
7858	2^338322-16667	101846	Stefano Morozzi	01/2023
7859	2^338325-142159	101846	Stefano Morozzi	02/2023
7860	2^338316-175857	101844	Stefano Morozzi	12/2021
7861	2^338318+54405	101844	Stefano Morozzi	01/2022
7862	2^338316+32961	101844	Stefano Morozzi	02/2022
7863	2^338317+68175	101844	Stefano Morozzi	09/2022
7864	2^338318-86171	101844	Stefano Morozzi	12/2022
7865	2^338315-178635	101843	Stefano Morozzi	01/2022
7866	2^338315+34899	101843	Stefano Morozzi	03/2022
7867	2^338314-106973	101843	Stefano Morozzi	03/2022
7868	2^338313+170411	101843	Stefano Morozzi	11/2022
7869	2^338315-88807	101843	Stefano Morozzi	12/2022
7870	2^338311-51799	101842	Stefano Morozzi	12/2021
7871	2^338309+157259	101842	Stefano Morozzi	02/2022
7872	2^338310+40903	101842	Stefano Morozzi	06/2022
7873	2^338309-168051	101842	Stefano Morozzi	02/2023
7874	2^338308-55853	101841	Stefano Morozzi	02/2022
7875	2^338307+134871	101841	Stefano Morozzi	03/2022
7876	2^338307+19689	101841	Stefano Morozzi	09/2022
7877	2^338308+66873	101841	Stefano Morozzi	09/2022
7878	2^338306+124399	101841	Stefano Morozzi	02/2023
7879	2^338306-91913	101841	Stefano Morozzi	02/2023
7880	2^338304+78757	101840	Stefano Morozzi	01/2022
7881	2^338304-5807	101840	Stefano Morozzi	02/2022
7882	2^338305+110879	101840	Stefano Morozzi	03/2022
7883	2^338304+91147	101840	Stefano Morozzi	06/2022
7884	2^338304-64475	101840	Stefano Morozzi	01/2023
7885	2^338299+85611	101839	Stefano Morozzi	03/2022
7886	2^338299-189985	101839	Stefano Morozzi	01/2023
7887	2^338298-25571	101838	Stefano Morozzi	12/2021
7888	2^338297+35547	101838	Stefano Morozzi	03/2022
7889	2^338298+111199	101838	Stefano Morozzi	03/2022
7890	2^338297+145455	101838	Stefano Morozzi	11/2022
7891	2^338297-166285	101838	Stefano Morozzi	01/2023
7892	2^338294-150711	101837	Stefano Morozzi	12/2021
7893	2^338294+177597	101837	Stefano Morozzi	12/2021
7894	2^338294-177807	101837	Stefano Morozzi	01/2022
7895	2^338295-52929	101837	Stefano Morozzi	01/2022
7896	2^338293+37407	101837	Stefano Morozzi	04/2022
7897	2^338292+40573	101837	Stefano Morozzi	06/2022
7898	2^338294+172425	101837	Stefano Morozzi	11/2022
7899	2^338293-191799	101837	Stefano Morozzi	02/2023
7900	2^338289+30957	101836	Stefano Morozzi	01/2022
7901	2^338291+131825	101836	Stefano Morozzi	02/2022
7902	2^338291+110111	101836	Stefano Morozzi	03/2022
7903	2^338290-156423	101836	Stefano Morozzi	03/2022
7904	2^338291-157845	101836	Stefano Morozzi	03/2022
7905	2^338290+69243	101836	Stefano Morozzi	09/2022
7906	2^338291-189327	101836	Stefano Morozzi	01/2023
7907	2^338291+74079	101836	Stefano Morozzi	02/2023
7908	2^338288+26623	101835	Stefano Morozzi	12/2021
7909	2^338286+33325	101835	Stefano Morozzi	02/2022
7910	2^338287+132633	101835	Stefano Morozzi	02/2022
7911	2^338287+157149	101835	Stefano Morozzi	02/2022
7912	2^338288-107193	101835	Stefano Morozzi	03/2022
7913	2^338286-83333	101835	Stefano Morozzi	04/2022
7914	2^338287+114425	101835	Stefano Morozzi	05/2022
7915	2^338288+194403	101835	Stefano Morozzi	09/2022
7916	2^338288-113177	101835	Stefano Morozzi	12/2022
7917	2^338288-65747	101835	Stefano Morozzi	01/2023
7918	2^338285+82131	101834	Stefano Morozzi	02/2022
7919	2^338284-104217	101834	Stefano Morozzi	02/2022
7920	2^338282-84533	101834	Stefano Morozzi	04/2022
7921	2^338283+67545	101834	Stefano Morozzi	09/2022
7922	2^338283-65439	101834	Stefano Morozzi	01/2023
7931	2^338280-19745	101833	Enzo Doria	06/2013
7923	2^338279-125947	101833	Stefano Morozzi	12/2021
7924	2^338280-50343	101833	Stefano Morozzi	12/2021
7925	2^338279+133331	101833	Stefano Morozzi	02/2022
7926	2^338281-54561	101833	Stefano Morozzi	02/2022
7927	2^338280+192063	101833	Stefano Morozzi	09/2022
7928	2^338281+18971	101833	Stefano Morozzi	09/2022
7929	2^338281-186711	101833	Stefano Morozzi	12/2022
7930	2^338281-91273	101833	Stefano Morozzi	01/2023
7932	2^338278+188215	101832	Stefano Morozzi	05/2022
7933	2^338273+181101	101831	Stefano Morozzi	01/2022
7934	2^338275+32909	101831	Stefano Morozzi	02/2022
7935	2^338272+166431	101831	Stefano Morozzi	06/2022
7936	2^338272+22011	101831	Stefano Morozzi	11/2022
7937	2^338275+148271	101831	Stefano Morozzi	11/2022
7938	2^338270-135725	101830	Stefano Morozzi	06/2022
7939	2^338269-136951	101830	Stefano Morozzi	12/2022
7940	2^338270-192701	101830	Stefano Morozzi	02/2023
7941	2^338271-42831	101830	Stefano Morozzi	02/2023
7942	2^338266+110665	101829	Stefano Morozzi	03/2022
7943	2^338267+110481	101829	Stefano Morozzi	03/2022
7944	2^338267-166035	101829	Stefano Morozzi	01/2023
7945	2^338265-154893	101828	Stefano Morozzi	02/2022
7946	2^338264+163611	101828	Stefano Morozzi	05/2022
7947	2^338263-62767	101828	Stefano Morozzi	12/2022
7948	2^338261-188119	101827	Stefano Morozzi	12/2022
7949	2^338259-40327	101827	Stefano Morozzi	01/2023
7950	2^338256+5223	101826	Stefano Morozzi	01/2022
7951	2^338257+178425	101826	Stefano Morozzi	01/2022
7952	2^338256-180569	101826	Stefano Morozzi	02/2022
7953	2^338257-5965	101826	Stefano Morozzi	02/2022
7954	2^338258-9225	101826	Stefano Morozzi	04/2022
7955	2^338255-127021	101825	Stefano Morozzi	12/2021
7956	2^338253+159005	101825	Stefano Morozzi	03/2022
7957	2^338253+64817	101825	Stefano Morozzi	05/2022
7958	2^338254-85403	101825	Stefano Morozzi	06/2022
7959	2^338254+142947	101825	Stefano Morozzi	09/2022
7960	2^338253+121095	101825	Stefano Morozzi	11/2022
7961	2^338254+196725	101825	Stefano Morozzi	11/2022
7962	2^338254-91007	101825	Stefano Morozzi	01/2023
7963	2^338251+78975	101824	Stefano Morozzi	01/2022
7964	2^338252-178709	101824	Stefano Morozzi	01/2022
7965	2^338252+129703	101824	Stefano Morozzi	01/2022
7966	2^338252+132285	101824	Stefano Morozzi	02/2022
7967	2^338251-33381	101824	Stefano Morozzi	04/2022
7968	2^338252-13805	101824	Stefano Morozzi	12/2022
7969	2^338245-134755	101822	Stefano Morozzi	04/2022
7970	2^338244-59219	101822	Stefano Morozzi	04/2022
7971	2^338244-64703	101822	Stefano Morozzi	01/2023
7979	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
7972	2^338241+1391	101821	Stefano Morozzi	12/2021
7973	2^338242+151195	101821	Stefano Morozzi	12/2021
7974	2^338240-152495	101821	Stefano Morozzi	12/2021
7975	2^338240+81745	101821	Stefano Morozzi	02/2022
7976	2^338241-155551	101821	Stefano Morozzi	02/2022
7977	2^338242-108237	101821	Stefano Morozzi	04/2022
7978	2^338242+43045	101821	Stefano Morozzi	09/2022
7980	2^338238-126735	101820	Stefano Morozzi	12/2021
7981	2^338238+183855	101820	Stefano Morozzi	03/2022
7982	2^338238+141013	101820	Stefano Morozzi	06/2022
7983	2^338237+97227	101820	Stefano Morozzi	11/2022
7984	2^338238+48429	101820	Stefano Morozzi	11/2022
7985	2^338234-80925	101819	Stefano Morozzi	02/2022
7986	2^338234-154593	101819	Stefano Morozzi	02/2022
7987	2^338235-131787	101819	Stefano Morozzi	03/2022
7988	2^338233+89781	101819	Stefano Morozzi	05/2022
7989	2^338235+169971	101819	Stefano Morozzi	11/2022
7990	2^338233-113875	101819	Stefano Morozzi	12/2022
7997	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
7991	2^338232-175539	101818	Stefano Morozzi	12/2021
7992	2^338231+57345	101818	Stefano Morozzi	02/2022
7993	2^338232+36097	101818	Stefano Morozzi	03/2022
7994	2^338230+137403	101818	Stefano Morozzi	04/2022
7995	2^338231-59569	101818	Stefano Morozzi	04/2022
7996	2^338230-86633	101818	Stefano Morozzi	12/2022
7998	2^338228+159247	101817	Stefano Morozzi	03/2022
7999	2^338227-12631	101817	Stefano Morozzi	12/2022
8000	(34*10^101815+191)/9	101816	Robert Price	08/2021

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