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 ?
7501	2^338406-184175	101871	Stefano Morozzi	04/2022
7502	2^338405+94451	101871	Stefano Morozzi	09/2022
7503	2^338406-161217	101871	Stefano Morozzi	12/2022
7504	2^338406+199929	101871	Stefano Morozzi	02/2023
7505	2^338404+55717	101870	Stefano Morozzi	01/2022
7506	2^338403+36261	101870	Stefano Morozzi	04/2022
7507	2^338402-34431	101870	Stefano Morozzi	04/2022
7508	2^338404-159215	101870	Stefano Morozzi	04/2022
7509	2^338403+18363	101870	Stefano Morozzi	09/2022
7510	2^338403+170235	101870	Stefano Morozzi	11/2022
7511	2^338399+23045	101869	Stefano Morozzi	11/2022
7512	2^338399-65535	101869	Stefano Morozzi	01/2023
7513	2^338395-127449	101868	Stefano Morozzi	12/2021
7514	2^338398-127637	101868	Stefano Morozzi	01/2022
7515	2^338398-166533	101868	Stefano Morozzi	01/2023
7516	2^338394+100317	101867	Stefano Morozzi	11/2021
7517	2^338393-152749	101867	Stefano Morozzi	01/2022
7518	2^338393+163025	101867	Stefano Morozzi	04/2022
7519	2^338393+89229	101867	Stefano Morozzi	05/2022
7520	2^338393+99647	101867	Stefano Morozzi	02/2023
7521	2^338394-192471	101867	Stefano Morozzi	02/2023
7522	2^338390+76627	101866	Stefano Morozzi	12/2021
7523	2^338389-85081	101866	Stefano Morozzi	06/2022
7524	2^338390+148113	101866	Stefano Morozzi	11/2022
7525	2^338389-14253	101866	Stefano Morozzi	01/2023
7526	2^338390-114297	101866	Stefano Morozzi	01/2023
7527	2^338391-64225	101866	Stefano Morozzi	01/2023
7528	2^338389-16971	101866	Stefano Morozzi	02/2023
7529	2^338387-75685	101865	Stefano Morozzi	12/2021
7530	2^338388-53459	101865	Stefano Morozzi	01/2022
7531	2^338388-36575	101865	Stefano Morozzi	12/2022
7532	2^338385-190311	101865	Stefano Morozzi	01/2023
7533	2^338384+131563	101864	Stefano Morozzi	01/2022
7534	2^338382+109069	101864	Stefano Morozzi	03/2022
7535	2^338384+168987	101864	Stefano Morozzi	09/2022
7536	2^338383-42367	101864	Stefano Morozzi	02/2023
7537	2^338380+77125	101863	Stefano Morozzi	12/2021
7538	2^338381-35539	101863	Stefano Morozzi	06/2022
7539	2^338378-125841	101862	Stefano Morozzi	12/2021
7540	2^338375+27815	101862	Stefano Morozzi	01/2022
7541	2^338375-28509	101862	Stefano Morozzi	01/2022
7542	2^338375+29985	101862	Stefano Morozzi	01/2022
7543	2^338377+157881	101862	Stefano Morozzi	02/2022
7544	2^338375+59589	101862	Stefano Morozzi	03/2022
7545	2^338378+36399	101862	Stefano Morozzi	04/2022
7546	2^338378-159773	101862	Stefano Morozzi	04/2022
7547	2^338378+14883	101862	Stefano Morozzi	05/2022
7548	2^338376+140173	101862	Stefano Morozzi	06/2022
7549	2^338375+18761	101862	Stefano Morozzi	09/2022
7550	2^338373-75103	101861	Stefano Morozzi	12/2021
7551	2^338372+128877	101861	Stefano Morozzi	01/2022
7552	2^338374-28731	101861	Stefano Morozzi	01/2022
7553	2^338374-128427	101861	Stefano Morozzi	01/2022
7554	2^338372+37875	101861	Stefano Morozzi	04/2022
7555	2^338373+161541	101861	Stefano Morozzi	04/2022
7556	2^338374+37759	101861	Stefano Morozzi	04/2022
7557	2^338372+93235	101861	Stefano Morozzi	09/2022
7558	2^338373-63273	101861	Stefano Morozzi	12/2022
7559	2^338369+29427	101860	Stefano Morozzi	01/2022
7560	2^338370+179133	101860	Stefano Morozzi	01/2022
7561	2^338369+131501	101860	Stefano Morozzi	01/2022
7562	2^338369+181649	101860	Stefano Morozzi	02/2022
7563	2^338370-4787	101860	Stefano Morozzi	02/2022
7564	2^338371-133491	101860	Stefano Morozzi	04/2022
7565	2^338371+42023	101860	Stefano Morozzi	09/2022
7566	2^338371+145323	101860	Stefano Morozzi	11/2022
7567	2^338371-138145	101860	Stefano Morozzi	12/2022
7574	2^338368-20369	101859	Enzo Doria	06/2013
7575	2^338366+74179	101859	Enzo Doria	04/2016
7568	2^338366+53853	101859	Stefano Morozzi	01/2022
7569	2^338365-31665	101859	Stefano Morozzi	03/2022
7570	2^338368-156345	101859	Stefano Morozzi	03/2022
7571	2^338366-159867	101859	Stefano Morozzi	04/2022
7572	2^338368-63509	101859	Stefano Morozzi	12/2022
7573	2^338365-190975	101859	Stefano Morozzi	01/2023
7576	2^338362-180845	101858	Stefano Morozzi	02/2022
7577	2^338364-155769	101858	Stefano Morozzi	02/2022
7578	2^338362+142843	101858	Stefano Morozzi	09/2022
7579	2^338362+170019	101858	Stefano Morozzi	11/2022
7580	2^338361-100875	101857	Stefano Morozzi	12/2021
7581	2^338361+154169	101857	Stefano Morozzi	01/2022
7582	2^338359-189645	101857	Stefano Morozzi	01/2023
7583	2^338356+101271	101856	Stefano Morozzi	12/2021
7584	2^338356+53383	101856	Stefano Morozzi	01/2022
7585	2^338355+59393	101856	Stefano Morozzi	03/2022
7586	2^338356+60775	101856	Stefano Morozzi	03/2022
7587	2^338356-106257	101856	Stefano Morozzi	03/2022
7588	2^338357-58921	101856	Stefano Morozzi	04/2022
7589	2^338356+94605	101856	Stefano Morozzi	09/2022
7590	2^338356+117813	101856	Stefano Morozzi	09/2022
7591	2^338358-38475	101856	Stefano Morozzi	12/2022
7592	2^338353-190291	101855	Stefano Morozzi	01/2023
7593	2^338350-152933	101854	Stefano Morozzi	01/2022
7594	2^338350+6337	101854	Stefano Morozzi	01/2022
7595	2^338350+168759	101854	Stefano Morozzi	09/2022
7598	27088^5755+5755^27088	101853	Hans Havermann	01/2019
7596	2^338347+125901	101853	Stefano Morozzi	11/2021
7597	2^338346-10643	101853	Stefano Morozzi	06/2022
7599	2^338343+152271	101852	Stefano Morozzi	12/2021
7600	2^338345+154107	101852	Stefano Morozzi	01/2022
7601	2^338342+155397	101852	Stefano Morozzi	01/2022
7602	2^338342-130767	101852	Stefano Morozzi	02/2022
7603	2^338345-30123	101852	Stefano Morozzi	02/2022
7604	2^338345+35747	101852	Stefano Morozzi	03/2022
7605	2^338345-133131	101852	Stefano Morozzi	04/2022
7606	2^338345-134559	101852	Stefano Morozzi	04/2022
7607	2^338342+170073	101852	Stefano Morozzi	11/2022
7608	2^338344+46567	101852	Stefano Morozzi	11/2022
7609	2^338344+97141	101852	Stefano Morozzi	11/2022
7610	2^338342-162213	101852	Stefano Morozzi	12/2022
7611	2^338339+2753	101851	Stefano Morozzi	12/2021
7612	2^338341+128415	101851	Stefano Morozzi	01/2022
7613	2^338338+2677	101850	Stefano Morozzi	12/2021
7614	2^338336+54607	101850	Stefano Morozzi	01/2022
7615	2^338338+109999	101850	Stefano Morozzi	03/2022
7616	2^338336+161575	101850	Stefano Morozzi	04/2022
7617	2^338335+51975	101849	Stefano Morozzi	12/2021
7618	2^338335-152607	101849	Stefano Morozzi	01/2022
7619	2^338334+55273	101849	Stefano Morozzi	01/2022
7620	2^338332+34315	101849	Stefano Morozzi	03/2022
7621	2^338335+158759	101849	Stefano Morozzi	03/2022
7622	2^338332+67621	101849	Stefano Morozzi	09/2022
7623	2^338332-66099	101849	Stefano Morozzi	01/2023
7624	2^338334-191043	101849	Stefano Morozzi	01/2023
7625	2^338331+83403	101848	Stefano Morozzi	02/2022
7626	2^338330-110865	101848	Stefano Morozzi	06/2022
7627	2^338330+71047	101848	Stefano Morozzi	11/2022
7628	2^338328-5295	101847	Stefano Morozzi	02/2022
7629	2^338327+143585	101847	Stefano Morozzi	09/2022
7630	2^338324-179667	101846	Stefano Morozzi	02/2022
7631	2^338322+21903	101846	Stefano Morozzi	11/2022
7632	2^338324+98047	101846	Stefano Morozzi	11/2022
7633	2^338323-87729	101846	Stefano Morozzi	12/2022
7634	2^338322-16667	101846	Stefano Morozzi	01/2023
7635	2^338325-142159	101846	Stefano Morozzi	02/2023
7636	2^338316-175857	101844	Stefano Morozzi	12/2021
7637	2^338318+54405	101844	Stefano Morozzi	01/2022
7638	2^338316+32961	101844	Stefano Morozzi	02/2022
7639	2^338317+68175	101844	Stefano Morozzi	09/2022
7640	2^338318-86171	101844	Stefano Morozzi	12/2022
7641	2^338315-178635	101843	Stefano Morozzi	01/2022
7642	2^338315+34899	101843	Stefano Morozzi	03/2022
7643	2^338314-106973	101843	Stefano Morozzi	03/2022
7644	2^338313+170411	101843	Stefano Morozzi	11/2022
7645	2^338315-88807	101843	Stefano Morozzi	12/2022
7646	2^338311-51799	101842	Stefano Morozzi	12/2021
7647	2^338309+157259	101842	Stefano Morozzi	02/2022
7648	2^338310+40903	101842	Stefano Morozzi	06/2022
7649	2^338309-168051	101842	Stefano Morozzi	02/2023
7650	2^338308-55853	101841	Stefano Morozzi	02/2022
7651	2^338307+134871	101841	Stefano Morozzi	03/2022
7652	2^338307+19689	101841	Stefano Morozzi	09/2022
7653	2^338308+66873	101841	Stefano Morozzi	09/2022
7654	2^338306+124399	101841	Stefano Morozzi	02/2023
7655	2^338306-91913	101841	Stefano Morozzi	02/2023
7656	2^338304+78757	101840	Stefano Morozzi	01/2022
7657	2^338304-5807	101840	Stefano Morozzi	02/2022
7658	2^338305+110879	101840	Stefano Morozzi	03/2022
7659	2^338304+91147	101840	Stefano Morozzi	06/2022
7660	2^338304-64475	101840	Stefano Morozzi	01/2023
7661	2^338299+85611	101839	Stefano Morozzi	03/2022
7662	2^338299-189985	101839	Stefano Morozzi	01/2023
7663	2^338298-25571	101838	Stefano Morozzi	12/2021
7664	2^338297+35547	101838	Stefano Morozzi	03/2022
7665	2^338298+111199	101838	Stefano Morozzi	03/2022
7666	2^338297+145455	101838	Stefano Morozzi	11/2022
7667	2^338297-166285	101838	Stefano Morozzi	01/2023
7668	2^338294-150711	101837	Stefano Morozzi	12/2021
7669	2^338294+177597	101837	Stefano Morozzi	12/2021
7670	2^338294-177807	101837	Stefano Morozzi	01/2022
7671	2^338295-52929	101837	Stefano Morozzi	01/2022
7672	2^338293+37407	101837	Stefano Morozzi	04/2022
7673	2^338292+40573	101837	Stefano Morozzi	06/2022
7674	2^338294+172425	101837	Stefano Morozzi	11/2022
7675	2^338293-191799	101837	Stefano Morozzi	02/2023
7676	2^338289+30957	101836	Stefano Morozzi	01/2022
7677	2^338291+131825	101836	Stefano Morozzi	02/2022
7678	2^338291+110111	101836	Stefano Morozzi	03/2022
7679	2^338290-156423	101836	Stefano Morozzi	03/2022
7680	2^338291-157845	101836	Stefano Morozzi	03/2022
7681	2^338290+69243	101836	Stefano Morozzi	09/2022
7682	2^338291-189327	101836	Stefano Morozzi	01/2023
7683	2^338291+74079	101836	Stefano Morozzi	02/2023
7684	2^338288+26623	101835	Stefano Morozzi	12/2021
7685	2^338286+33325	101835	Stefano Morozzi	02/2022
7686	2^338287+132633	101835	Stefano Morozzi	02/2022
7687	2^338287+157149	101835	Stefano Morozzi	02/2022
7688	2^338288-107193	101835	Stefano Morozzi	03/2022
7689	2^338286-83333	101835	Stefano Morozzi	04/2022
7690	2^338287+114425	101835	Stefano Morozzi	05/2022
7691	2^338288+194403	101835	Stefano Morozzi	09/2022
7692	2^338288-113177	101835	Stefano Morozzi	12/2022
7693	2^338288-65747	101835	Stefano Morozzi	01/2023
7694	2^338285+82131	101834	Stefano Morozzi	02/2022
7695	2^338284-104217	101834	Stefano Morozzi	02/2022
7696	2^338282-84533	101834	Stefano Morozzi	04/2022
7697	2^338283+67545	101834	Stefano Morozzi	09/2022
7698	2^338283-65439	101834	Stefano Morozzi	01/2023
7707	2^338280-19745	101833	Enzo Doria	06/2013
7699	2^338279-125947	101833	Stefano Morozzi	12/2021
7700	2^338280-50343	101833	Stefano Morozzi	12/2021
7701	2^338279+133331	101833	Stefano Morozzi	02/2022
7702	2^338281-54561	101833	Stefano Morozzi	02/2022
7703	2^338280+192063	101833	Stefano Morozzi	09/2022
7704	2^338281+18971	101833	Stefano Morozzi	09/2022
7705	2^338281-186711	101833	Stefano Morozzi	12/2022
7706	2^338281-91273	101833	Stefano Morozzi	01/2023
7708	2^338278+188215	101832	Stefano Morozzi	05/2022
7709	2^338273+181101	101831	Stefano Morozzi	01/2022
7710	2^338275+32909	101831	Stefano Morozzi	02/2022
7711	2^338272+166431	101831	Stefano Morozzi	06/2022
7712	2^338272+22011	101831	Stefano Morozzi	11/2022
7713	2^338275+148271	101831	Stefano Morozzi	11/2022
7714	2^338270-135725	101830	Stefano Morozzi	06/2022
7715	2^338269-136951	101830	Stefano Morozzi	12/2022
7716	2^338270-192701	101830	Stefano Morozzi	02/2023
7717	2^338271-42831	101830	Stefano Morozzi	02/2023
7718	2^338266+110665	101829	Stefano Morozzi	03/2022
7719	2^338267+110481	101829	Stefano Morozzi	03/2022
7720	2^338267-166035	101829	Stefano Morozzi	01/2023
7721	2^338265-154893	101828	Stefano Morozzi	02/2022
7722	2^338264+163611	101828	Stefano Morozzi	05/2022
7723	2^338263-62767	101828	Stefano Morozzi	12/2022
7724	2^338261-188119	101827	Stefano Morozzi	12/2022
7725	2^338259-40327	101827	Stefano Morozzi	01/2023
7726	2^338256+5223	101826	Stefano Morozzi	01/2022
7727	2^338257+178425	101826	Stefano Morozzi	01/2022
7728	2^338256-180569	101826	Stefano Morozzi	02/2022
7729	2^338257-5965	101826	Stefano Morozzi	02/2022
7730	2^338258-9225	101826	Stefano Morozzi	04/2022
7731	2^338255-127021	101825	Stefano Morozzi	12/2021
7732	2^338253+159005	101825	Stefano Morozzi	03/2022
7733	2^338253+64817	101825	Stefano Morozzi	05/2022
7734	2^338254-85403	101825	Stefano Morozzi	06/2022
7735	2^338254+142947	101825	Stefano Morozzi	09/2022
7736	2^338253+121095	101825	Stefano Morozzi	11/2022
7737	2^338254+196725	101825	Stefano Morozzi	11/2022
7738	2^338254-91007	101825	Stefano Morozzi	01/2023
7739	2^338251+78975	101824	Stefano Morozzi	01/2022
7740	2^338252-178709	101824	Stefano Morozzi	01/2022
7741	2^338252+129703	101824	Stefano Morozzi	01/2022
7742	2^338252+132285	101824	Stefano Morozzi	02/2022
7743	2^338251-33381	101824	Stefano Morozzi	04/2022
7744	2^338252-13805	101824	Stefano Morozzi	12/2022
7745	2^338245-134755	101822	Stefano Morozzi	04/2022
7746	2^338244-59219	101822	Stefano Morozzi	04/2022
7747	2^338244-64703	101822	Stefano Morozzi	01/2023
7748	2^338241+1391	101821	Stefano Morozzi	12/2021
7749	2^338242+151195	101821	Stefano Morozzi	12/2021
7750	2^338240-152495	101821	Stefano Morozzi	12/2021

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Probable Primes Top 10000

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