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	2^338943+95133	102033	Stefano Morozzi	11/2022
7502	2^338943+147435	102033	Stefano Morozzi	11/2022
7503	2^338943-116067	102033	Stefano Morozzi	01/2023
7504	2^338940+78607	102032	Stefano Morozzi	01/2022
7505	2^338942-86687	102032	Stefano Morozzi	12/2022
7506	2^338939+151569	102031	Stefano Morozzi	12/2021
7507	2^338938+183975	102031	Stefano Morozzi	03/2022
7508	2^338937-33429	102031	Stefano Morozzi	04/2022
7509	2^338939-183259	102031	Stefano Morozzi	04/2022
7510	2^338937-139951	102031	Stefano Morozzi	01/2023
7511	2^338938-40151	102031	Stefano Morozzi	01/2023
7512	2^338938+74449	102031	Stefano Morozzi	02/2023
7513	2^338935+179999	102030	Stefano Morozzi	01/2022
7514	2^338936+84147	102030	Stefano Morozzi	03/2022
7515	2^338935+171261	102030	Stefano Morozzi	11/2022
7516	2^338936-41355	102030	Stefano Morozzi	01/2023
7517	2^338931+2349	102029	Stefano Morozzi	12/2021
7518	2^338933+79935	102029	Stefano Morozzi	01/2022
7519	2^338930+33819	102029	Stefano Morozzi	03/2022
7520	2^338931-31555	102029	Stefano Morozzi	03/2022
7521	2^338933+64169	102029	Stefano Morozzi	05/2022
7522	2^338932-184965	102029	Stefano Morozzi	06/2022
7523	2^338932+66943	102029	Stefano Morozzi	09/2022
7524	2^338932+92995	102029	Stefano Morozzi	09/2022
7525	2^338931+97001	102029	Stefano Morozzi	11/2022
7526	2^338932-165453	102029	Stefano Morozzi	01/2023
7527	2^338933-40899	102029	Stefano Morozzi	01/2023
7528	2^338928+2367	102028	Stefano Morozzi	12/2021
7529	2^338927+52779	102028	Stefano Morozzi	01/2022
7530	2^338927-79539	102028	Stefano Morozzi	02/2022
7531	2^338929+60819	102028	Stefano Morozzi	03/2022
7532	2^338928-156959	102028	Stefano Morozzi	03/2022
7533	2^338927-63919	102028	Stefano Morozzi	12/2022
7534	2^338925+106631	102027	Stefano Morozzi	01/2022
7535	2^338926+80235	102027	Stefano Morozzi	01/2022
7536	2^338926+41607	102027	Stefano Morozzi	09/2022
7537	2^338925+195435	102027	Stefano Morozzi	11/2022
7538	2^338924-92885	102027	Stefano Morozzi	02/2023
7539	2^338922-27291	102026	Stefano Morozzi	12/2021
7540	2^338919-103849	102025	Stefano Morozzi	01/2022
7541	2^338919+130221	102025	Stefano Morozzi	01/2022
7542	2^338918-91967	102025	Stefano Morozzi	02/2023
7543	2^338917+561057	102025	Boyan Hu	03/2024
7544	2^338914-79121	102024	Stefano Morozzi	02/2022
7545	2^338916+134047	102024	Stefano Morozzi	03/2022
7546	2^338914-11315	102024	Stefano Morozzi	12/2022
7547	2^338910+81027	102023	Stefano Morozzi	01/2022
7548	2^338912+179821	102023	Stefano Morozzi	01/2022
7549	2^338909+100769	102022	Stefano Morozzi	11/2021
7550	2^338908-100839	102022	Stefano Morozzi	12/2021
7551	2^338909-25951	102022	Stefano Morozzi	12/2021
7552	2^338909+66845	102022	Stefano Morozzi	09/2022
7553	2^338907+73509	102022	Stefano Morozzi	11/2022
7554	2^338906-25823	102021	Stefano Morozzi	12/2021
7555	2^338904+75951	102021	Stefano Morozzi	12/2021
7556	2^338906+6685	102021	Stefano Morozzi	01/2022
7557	2^338905+160365	102021	Stefano Morozzi	03/2022
7558	2^338906+92617	102021	Stefano Morozzi	09/2022
7559	2^338904+47065	102021	Stefano Morozzi	11/2022
7560	2^338905+70427	102021	Stefano Morozzi	11/2022
7561	2^338905-163975	102021	Stefano Morozzi	12/2022
7562	2^338903+4155	102020	Stefano Morozzi	01/2022
7563	2^338901+55571	102020	Stefano Morozzi	01/2022
7564	2^338901-55479	102020	Stefano Morozzi	02/2022
7565	2^338903+33555	102020	Stefano Morozzi	03/2022
7566	2^338901+39777	102020	Stefano Morozzi	05/2022
7567	2^338903+165981	102020	Stefano Morozzi	06/2022
7568	2^338901-34863	102020	Stefano Morozzi	06/2022
7569	2^338899-150051	102019	Stefano Morozzi	12/2021
7570	2^338899+125951	102019	Stefano Morozzi	12/2021
7571	2^338898+179623	102019	Stefano Morozzi	01/2022
7572	2^338899-154467	102019	Stefano Morozzi	02/2022
7573	2^338898-60753	102019	Stefano Morozzi	06/2022
7574	2^338898+68635	102019	Stefano Morozzi	09/2022
7575	2^338897-85963	102019	Stefano Morozzi	12/2022
7576	2^338898+174129	102019	Stefano Morozzi	02/2023
7577	2^338894-133295	102018	Stefano Morozzi	04/2022
7578	2^338894+165573	102018	Stefano Morozzi	06/2022
7579	2^338894-60957	102018	Stefano Morozzi	06/2022
7580	2^338894-89463	102018	Stefano Morozzi	01/2023
7590	2^338891-18885	102017	Enzo Doria	05/2013
7581	2^338891+26499	102017	Stefano Morozzi	12/2021
7582	2^338891-2625	102017	Stefano Morozzi	12/2021
7583	2^338893+128727	102017	Stefano Morozzi	01/2022
7584	2^338890-52965	102017	Stefano Morozzi	01/2022
7585	2^338892-55467	102017	Stefano Morozzi	02/2022
7586	2^338892-83393	102017	Stefano Morozzi	04/2022
7587	2^338893+13649	102017	Stefano Morozzi	05/2022
7588	2^338892+117957	102017	Stefano Morozzi	09/2022
7589	2^338892-14643	102017	Stefano Morozzi	01/2023
7591	2^338887+154029	102016	Stefano Morozzi	01/2022
7592	2^338889-104293	102016	Stefano Morozzi	02/2022
7593	2^338887+147741	102016	Stefano Morozzi	11/2022
7594	2^338889+195975	102016	Stefano Morozzi	11/2022
7595	2^338889-117873	102016	Stefano Morozzi	02/2023
7596	2^338886+177159	102015	Stefano Morozzi	12/2021
7597	2^338885+40425	102015	Stefano Morozzi	06/2022
7598	2^338884-13053	102015	Stefano Morozzi	12/2022
7599	2^338885-112569	102015	Stefano Morozzi	12/2022
7600	2^338880+11341	102014	Stefano Morozzi	03/2022
7601	2^338880-160383	102014	Stefano Morozzi	06/2022
7602	2^338880-161627	102014	Stefano Morozzi	12/2022
7603	2^338879-1059	102013	Stefano Morozzi	12/2021
7604	2^338879-54525	102013	Stefano Morozzi	02/2022
7605	2^338877-82813	102013	Stefano Morozzi	03/2022
7606	2^338878-185883	102013	Stefano Morozzi	06/2022
7607	2^338879-60355	102013	Stefano Morozzi	06/2022
7608	2^338878+43719	102013	Stefano Morozzi	09/2022
7609	2^338879+122049	102013	Stefano Morozzi	11/2022
7610	2^338874-15063	102012	Stefano Morozzi	01/2023
7611	2^338874+148993	102012	Stefano Morozzi	02/2023
7612	2^338871+7679	102011	Stefano Morozzi	02/2022
7613	2^338872+61141	102011	Stefano Morozzi	03/2022
7614	2^338872-183923	102011	Stefano Morozzi	04/2022
7615	2^338873+19527	102011	Stefano Morozzi	09/2022
7616	2^338870+70719	102011	Stefano Morozzi	11/2022
7617	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
7618	2^338870-37571	102011	Stefano Morozzi	12/2022
7619	2^338872-138573	102011	Stefano Morozzi	12/2022
7620	2^338873-63843	102011	Stefano Morozzi	12/2022
7621	2^338868-5985	102010	Stefano Morozzi	02/2022
7622	2^338867+38079	102010	Stefano Morozzi	05/2022
7623	2^338868+140437	102010	Stefano Morozzi	06/2022
7624	2^338868-110175	102010	Stefano Morozzi	06/2022
7625	2^338868+123337	102010	Stefano Morozzi	11/2022
7626	2^338867-13327	102010	Stefano Morozzi	12/2022
7627	2^338868-11279	102010	Stefano Morozzi	12/2022
7628	2^338868-115685	102010	Stefano Morozzi	01/2023
7629	2^338864+158191	102009	Stefano Morozzi	02/2022
7630	2^338865-39699	102009	Stefano Morozzi	01/2023
7631	2^338865-40789	102009	Stefano Morozzi	01/2023
7632	2^338862+60433	102008	Stefano Morozzi	03/2022
7633	2^338861-9453	102008	Stefano Morozzi	04/2022
7634	2^338861+98067	102008	Stefano Morozzi	11/2022
7635	2^338862+146545	102008	Stefano Morozzi	11/2022
7636	2^338863-186207	102008	Stefano Morozzi	12/2022
7637	2^338860-41429	102008	Stefano Morozzi	01/2023
7638	2^338862-115833	102008	Stefano Morozzi	01/2023
7639	2^338863+74259	102008	Stefano Morozzi	02/2023
7640	2^338863-193017	102008	Stefano Morozzi	02/2023
7641	2^338858-190185	102007	Stefano Morozzi	01/2023
7642	2^338855+102141	102006	Stefano Morozzi	12/2021
7643	2^338856-27173	102006	Stefano Morozzi	12/2021
7644	2^338856-102839	102006	Stefano Morozzi	01/2022
7645	2^338855+79629	102006	Stefano Morozzi	01/2022
7646	2^338856+47755	102006	Stefano Morozzi	11/2022
7647	2^338850+27987	102005	Stefano Morozzi	01/2022
7648	2^338853+111791	102005	Stefano Morozzi	04/2022
7649	2^338852+145797	102005	Stefano Morozzi	11/2022
7650	2^338852-88497	102005	Stefano Morozzi	12/2022
7651	2^338850+124843	102005	Stefano Morozzi	02/2023
7652	2^338853-167695	102005	Stefano Morozzi	02/2023
7653	2^338847+176013	102004	Stefano Morozzi	12/2021
7654	2^338847-2365	102004	Stefano Morozzi	12/2021
7655	2^338848+158941	102004	Stefano Morozzi	03/2022
7656	2^338848+16671	102004	Stefano Morozzi	06/2022
7657	2^338847-35061	102004	Stefano Morozzi	06/2022
7658	2^338848+145063	102004	Stefano Morozzi	11/2022
7659	2^338847-61885	102004	Stefano Morozzi	12/2022
7660	2^338845+135831	102003	Stefano Morozzi	03/2022
7661	2^338846+85695	102003	Stefano Morozzi	03/2022
7662	2^338845+186525	102003	Stefano Morozzi	04/2022
7663	2^338846-163473	102003	Stefano Morozzi	12/2022
7664	2^338844-16077	102003	Stefano Morozzi	01/2023
7665	2^338844-165143	102003	Stefano Morozzi	01/2023
7666	2^338843-127261	102002	Stefano Morozzi	12/2021
7667	2^338843+107205	102002	Stefano Morozzi	02/2022
7668	2^338842-33185	102002	Stefano Morozzi	04/2022
7669	2^338842+14227	102002	Stefano Morozzi	05/2022
7670	2^338842+147973	102002	Stefano Morozzi	11/2022
7678	8*10^102000+51	102001	Robert Price	08/2019
7671	2^338838+150837	102001	Stefano Morozzi	11/2021
7672	2^338838+141397	102001	Stefano Morozzi	06/2022
7673	2^338839+194363	102001	Stefano Morozzi	09/2022
7674	2^338838+95637	102001	Stefano Morozzi	11/2022
7675	2^338839+171545	102001	Stefano Morozzi	11/2022
7676	2^338837-40071	102001	Stefano Morozzi	01/2023
7677	2^338838-90251	102001	Stefano Morozzi	01/2023
7679	2^338835-150625	102000	Stefano Morozzi	12/2021
7680	2^338834-32877	102000	Stefano Morozzi	04/2022
7684	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
7681	2^338833-100905	101999	Stefano Morozzi	12/2021
7682	2^338831+54419	101999	Stefano Morozzi	01/2022
7683	2^338831-63687	101999	Stefano Morozzi	12/2022
7692	2^338829-113239	101998	Enzo Doria	07/2014
7693	2^338828-113297	101998	Enzo Doria	07/2014
7685	2^338830+25017	101998	Stefano Morozzi	11/2021
7686	2^338831+321	101998	Stefano Morozzi	11/2021
7687	2^338827-26197	101998	Stefano Morozzi	12/2021
7688	2^338829+52727	101998	Stefano Morozzi	01/2022
7689	2^338827-55461	101998	Stefano Morozzi	02/2022
7690	2^338828-65859	101998	Stefano Morozzi	01/2023
7691	2^338829+99365	101998	Stefano Morozzi	02/2023
7694	2^338825-27453	101997	Stefano Morozzi	12/2021
7695	2^338824+89355	101997	Stefano Morozzi	05/2022
7696	2^338825-10995	101997	Stefano Morozzi	06/2022
7697	2^338824+149865	101997	Stefano Morozzi	02/2023
7698	2^338822+111175	101996	Stefano Morozzi	03/2022
7699	2^338822+187819	101996	Stefano Morozzi	04/2022
7700	2^338823+139545	101996	Stefano Morozzi	05/2022
7701	2^338823-184905	101996	Stefano Morozzi	06/2022
7702	2^338821-38919	101996	Stefano Morozzi	12/2022
7703	2^338820+41317	101995	Stefano Morozzi	06/2022
7704	2^338817+46019	101995	Stefano Morozzi	11/2022
7705	2^338820+148083	101995	Stefano Morozzi	11/2022
7706	2^338817-163251	101995	Stefano Morozzi	12/2022
7707	2^338819-63705	101995	Stefano Morozzi	12/2022
7708	2^338817-92509	101995	Stefano Morozzi	02/2023
7709	2^338815+151175	101994	Stefano Morozzi	12/2021
7710	2^338814-30011	101994	Stefano Morozzi	02/2022
7711	2^338814+12309	101994	Stefano Morozzi	04/2022
7712	2^338816-60647	101994	Stefano Morozzi	06/2022
7713	2^338816+171043	101994	Stefano Morozzi	11/2022
7714	2^338814-11513	101994	Stefano Morozzi	12/2022
7715	2^338811-126999	101993	Stefano Morozzi	12/2021
7716	2^338811+131621	101993	Stefano Morozzi	02/2022
7717	2^338812-107637	101993	Stefano Morozzi	03/2022
7718	2^338813+192725	101993	Stefano Morozzi	09/2022
7719	2^338812+94731	101993	Stefano Morozzi	11/2022
7720	2^338813+49205	101993	Stefano Morozzi	02/2023
7721	2^338809-152755	101992	Stefano Morozzi	01/2022
7722	2^338808+156531	101992	Stefano Morozzi	01/2022
7723	2^338808+7885	101992	Stefano Morozzi	02/2022
7724	2^338808-105797	101992	Stefano Morozzi	02/2022
7725	2^338807-35899	101992	Stefano Morozzi	06/2022
7726	2^338808-89175	101992	Stefano Morozzi	01/2023
7727	2^338808-91475	101992	Stefano Morozzi	01/2023
7728	2^338805+29879	101991	Stefano Morozzi	01/2022
7729	2^338805+157925	101991	Stefano Morozzi	02/2022
7730	2^338804-6809	101991	Stefano Morozzi	03/2022
7731	2^338806-157095	101991	Stefano Morozzi	03/2022
7732	2^338804-133173	101991	Stefano Morozzi	04/2022
7733	2^338805-115189	101991	Stefano Morozzi	01/2023
7734	2^338802+150403	101990	Stefano Morozzi	11/2021
7735	2^338801+154587	101990	Stefano Morozzi	01/2022
7736	2^338802-180603	101990	Stefano Morozzi	02/2022
7737	2^338803-31921	101990	Stefano Morozzi	03/2022
7738	2^338803-81735	101990	Stefano Morozzi	03/2022
7739	2^338803+195141	101990	Stefano Morozzi	11/2022
7740	2^338800+160141	101989	Stefano Morozzi	03/2022
7741	2^338797-82489	101989	Stefano Morozzi	03/2022
7746	2^338796+93	101988	Donovan Johnson	06/2008
7742	2^338795+455	101988	Stefano Morozzi	11/2021
7743	2^338795-102075	101988	Stefano Morozzi	12/2021
7744	2^338794-3483	101988	Stefano Morozzi	01/2022
7745	2^338796+179641	101988	Stefano Morozzi	01/2022
7747	2^338793-5155	101987	Stefano Morozzi	02/2022
7748	2^338793+111107	101987	Stefano Morozzi	03/2022
7749	2^338791+112083	101987	Stefano Morozzi	04/2022
7750	2^338792-85097	101987	Stefano Morozzi	06/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(295532 PRPs in the top)