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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
9751	2^338932+92995	102029	Stefano Morozzi	09/2022
9752	2^338931+97001	102029	Stefano Morozzi	11/2022
9753	2^338932-165453	102029	Stefano Morozzi	01/2023
9754	2^338933-40899	102029	Stefano Morozzi	01/2023
9755	2^338928+2367	102028	Stefano Morozzi	12/2021
9756	2^338927+52779	102028	Stefano Morozzi	01/2022
9757	2^338927-79539	102028	Stefano Morozzi	02/2022
9758	2^338929+60819	102028	Stefano Morozzi	03/2022
9759	2^338928-156959	102028	Stefano Morozzi	03/2022
9760	2^338927-63919	102028	Stefano Morozzi	12/2022
9761	2^338925+106631	102027	Stefano Morozzi	01/2022
9762	2^338926+80235	102027	Stefano Morozzi	01/2022
9763	2^338926+41607	102027	Stefano Morozzi	09/2022
9764	2^338925+195435	102027	Stefano Morozzi	11/2022
9765	2^338924-92885	102027	Stefano Morozzi	02/2023
9766	2^338922-27291	102026	Stefano Morozzi	12/2021
9767	2^338919-103849	102025	Stefano Morozzi	01/2022
9768	2^338919+130221	102025	Stefano Morozzi	01/2022
9769	2^338918-91967	102025	Stefano Morozzi	02/2023
9770	2^338917+561057	102025	Boyan Hu	03/2024
9771	2^338914-79121	102024	Stefano Morozzi	02/2022
9772	2^338916+134047	102024	Stefano Morozzi	03/2022
9773	2^338914-11315	102024	Stefano Morozzi	12/2022
9774	2^338910+81027	102023	Stefano Morozzi	01/2022
9775	2^338912+179821	102023	Stefano Morozzi	01/2022
9776	2^338909+100769	102022	Stefano Morozzi	11/2021
9777	2^338908-100839	102022	Stefano Morozzi	12/2021
9778	2^338909-25951	102022	Stefano Morozzi	12/2021
9779	2^338909+66845	102022	Stefano Morozzi	09/2022
9780	2^338907+73509	102022	Stefano Morozzi	11/2022
9781	2^338906-25823	102021	Stefano Morozzi	12/2021
9782	2^338904+75951	102021	Stefano Morozzi	12/2021
9783	2^338906+6685	102021	Stefano Morozzi	01/2022
9784	2^338905+160365	102021	Stefano Morozzi	03/2022
9785	2^338906+92617	102021	Stefano Morozzi	09/2022
9786	2^338904+47065	102021	Stefano Morozzi	11/2022
9787	2^338905+70427	102021	Stefano Morozzi	11/2022
9788	2^338905-163975	102021	Stefano Morozzi	12/2022
9789	2^338903+4155	102020	Stefano Morozzi	01/2022
9790	2^338901+55571	102020	Stefano Morozzi	01/2022
9791	2^338901-55479	102020	Stefano Morozzi	02/2022
9792	2^338903+33555	102020	Stefano Morozzi	03/2022
9793	2^338901+39777	102020	Stefano Morozzi	05/2022
9794	2^338903+165981	102020	Stefano Morozzi	06/2022
9795	2^338901-34863	102020	Stefano Morozzi	06/2022
9796	2^338899-150051	102019	Stefano Morozzi	12/2021
9797	2^338899+125951	102019	Stefano Morozzi	12/2021
9798	2^338898+179623	102019	Stefano Morozzi	01/2022
9799	2^338899-154467	102019	Stefano Morozzi	02/2022
9800	2^338898-60753	102019	Stefano Morozzi	06/2022
9801	2^338898+68635	102019	Stefano Morozzi	09/2022
9802	2^338897-85963	102019	Stefano Morozzi	12/2022
9803	2^338898+174129	102019	Stefano Morozzi	02/2023
9804	2^338894-133295	102018	Stefano Morozzi	04/2022
9805	2^338894+165573	102018	Stefano Morozzi	06/2022
9806	2^338894-60957	102018	Stefano Morozzi	06/2022
9807	2^338894-89463	102018	Stefano Morozzi	01/2023
9817	2^338891-18885	102017	Enzo Doria	05/2013
9808	2^338891+26499	102017	Stefano Morozzi	12/2021
9809	2^338891-2625	102017	Stefano Morozzi	12/2021
9810	2^338893+128727	102017	Stefano Morozzi	01/2022
9811	2^338890-52965	102017	Stefano Morozzi	01/2022
9812	2^338892-55467	102017	Stefano Morozzi	02/2022
9813	2^338892-83393	102017	Stefano Morozzi	04/2022
9814	2^338893+13649	102017	Stefano Morozzi	05/2022
9815	2^338892+117957	102017	Stefano Morozzi	09/2022
9816	2^338892-14643	102017	Stefano Morozzi	01/2023
9818	2^338887+154029	102016	Stefano Morozzi	01/2022
9819	2^338889-104293	102016	Stefano Morozzi	02/2022
9820	2^338887+147741	102016	Stefano Morozzi	11/2022
9821	2^338889+195975	102016	Stefano Morozzi	11/2022
9822	2^338889-117873	102016	Stefano Morozzi	02/2023
9823	2^338886+177159	102015	Stefano Morozzi	12/2021
9824	2^338885+40425	102015	Stefano Morozzi	06/2022
9825	2^338884-13053	102015	Stefano Morozzi	12/2022
9826	2^338885-112569	102015	Stefano Morozzi	12/2022
9827	2^338880+11341	102014	Stefano Morozzi	03/2022
9828	2^338880-160383	102014	Stefano Morozzi	06/2022
9829	2^338880-161627	102014	Stefano Morozzi	12/2022
9830	2^338879-1059	102013	Stefano Morozzi	12/2021
9831	2^338879-54525	102013	Stefano Morozzi	02/2022
9832	2^338877-82813	102013	Stefano Morozzi	03/2022
9833	2^338878-185883	102013	Stefano Morozzi	06/2022
9834	2^338879-60355	102013	Stefano Morozzi	06/2022
9835	2^338878+43719	102013	Stefano Morozzi	09/2022
9836	2^338879+122049	102013	Stefano Morozzi	11/2022
9837	2^338874-15063	102012	Stefano Morozzi	01/2023
9838	2^338874+148993	102012	Stefano Morozzi	02/2023
9839	2^338871+7679	102011	Stefano Morozzi	02/2022
9840	2^338872+61141	102011	Stefano Morozzi	03/2022
9841	2^338872-183923	102011	Stefano Morozzi	04/2022
9842	2^338873+19527	102011	Stefano Morozzi	09/2022
9843	2^338870+70719	102011	Stefano Morozzi	11/2022
9844	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
9845	2^338870-37571	102011	Stefano Morozzi	12/2022
9846	2^338872-138573	102011	Stefano Morozzi	12/2022
9847	2^338873-63843	102011	Stefano Morozzi	12/2022
9848	2^338868-5985	102010	Stefano Morozzi	02/2022
9849	2^338867+38079	102010	Stefano Morozzi	05/2022
9850	2^338868+140437	102010	Stefano Morozzi	06/2022
9851	2^338868-110175	102010	Stefano Morozzi	06/2022
9852	2^338868+123337	102010	Stefano Morozzi	11/2022
9853	2^338867-13327	102010	Stefano Morozzi	12/2022
9854	2^338868-11279	102010	Stefano Morozzi	12/2022
9855	2^338868-115685	102010	Stefano Morozzi	01/2023
9856	2^338864+158191	102009	Stefano Morozzi	02/2022
9857	2^338865-39699	102009	Stefano Morozzi	01/2023
9858	2^338865-40789	102009	Stefano Morozzi	01/2023
9859	2^338862+60433	102008	Stefano Morozzi	03/2022
9860	2^338861-9453	102008	Stefano Morozzi	04/2022
9861	2^338861+98067	102008	Stefano Morozzi	11/2022
9862	2^338862+146545	102008	Stefano Morozzi	11/2022
9863	2^338863-186207	102008	Stefano Morozzi	12/2022
9864	2^338860-41429	102008	Stefano Morozzi	01/2023
9865	2^338862-115833	102008	Stefano Morozzi	01/2023
9866	2^338863+74259	102008	Stefano Morozzi	02/2023
9867	2^338863-193017	102008	Stefano Morozzi	02/2023
9868	2^338858-190185	102007	Stefano Morozzi	01/2023
9869	2^338855+102141	102006	Stefano Morozzi	12/2021
9870	2^338856-27173	102006	Stefano Morozzi	12/2021
9871	2^338856-102839	102006	Stefano Morozzi	01/2022
9872	2^338855+79629	102006	Stefano Morozzi	01/2022
9873	2^338856+47755	102006	Stefano Morozzi	11/2022
9874	2^338850+27987	102005	Stefano Morozzi	01/2022
9875	2^338853+111791	102005	Stefano Morozzi	04/2022
9876	2^338852+145797	102005	Stefano Morozzi	11/2022
9877	2^338852-88497	102005	Stefano Morozzi	12/2022
9878	2^338850+124843	102005	Stefano Morozzi	02/2023
9879	2^338853-167695	102005	Stefano Morozzi	02/2023
9880	2^338847+176013	102004	Stefano Morozzi	12/2021
9881	2^338847-2365	102004	Stefano Morozzi	12/2021
9882	2^338848+158941	102004	Stefano Morozzi	03/2022
9883	2^338848+16671	102004	Stefano Morozzi	06/2022
9884	2^338847-35061	102004	Stefano Morozzi	06/2022
9885	2^338848+145063	102004	Stefano Morozzi	11/2022
9886	2^338847-61885	102004	Stefano Morozzi	12/2022
9887	2^338845+135831	102003	Stefano Morozzi	03/2022
9888	2^338846+85695	102003	Stefano Morozzi	03/2022
9889	2^338845+186525	102003	Stefano Morozzi	04/2022
9890	2^338846-163473	102003	Stefano Morozzi	12/2022
9891	2^338844-16077	102003	Stefano Morozzi	01/2023
9892	2^338844-165143	102003	Stefano Morozzi	01/2023
9893	2^338843-127261	102002	Stefano Morozzi	12/2021
9894	2^338843+107205	102002	Stefano Morozzi	02/2022
9895	2^338842-33185	102002	Stefano Morozzi	04/2022
9896	2^338842+14227	102002	Stefano Morozzi	05/2022
9897	2^338842+147973	102002	Stefano Morozzi	11/2022
9905	8*10^102000+51	102001	Robert Price	08/2019
9898	2^338838+150837	102001	Stefano Morozzi	11/2021
9899	2^338838+141397	102001	Stefano Morozzi	06/2022
9900	2^338839+194363	102001	Stefano Morozzi	09/2022
9901	2^338838+95637	102001	Stefano Morozzi	11/2022
9902	2^338839+171545	102001	Stefano Morozzi	11/2022
9903	2^338837-40071	102001	Stefano Morozzi	01/2023
9904	2^338838-90251	102001	Stefano Morozzi	01/2023
9906	2^338835-150625	102000	Stefano Morozzi	12/2021
9907	2^338834-32877	102000	Stefano Morozzi	04/2022
9911	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
9908	2^338833-100905	101999	Stefano Morozzi	12/2021
9909	2^338831+54419	101999	Stefano Morozzi	01/2022
9910	2^338831-63687	101999	Stefano Morozzi	12/2022
9919	2^338829-113239	101998	Enzo Doria	07/2014
9920	2^338828-113297	101998	Enzo Doria	07/2014
9912	2^338830+25017	101998	Stefano Morozzi	11/2021
9913	2^338831+321	101998	Stefano Morozzi	11/2021
9914	2^338827-26197	101998	Stefano Morozzi	12/2021
9915	2^338829+52727	101998	Stefano Morozzi	01/2022
9916	2^338827-55461	101998	Stefano Morozzi	02/2022
9917	2^338828-65859	101998	Stefano Morozzi	01/2023
9918	2^338829+99365	101998	Stefano Morozzi	02/2023
9921	2^338825-27453	101997	Stefano Morozzi	12/2021
9922	2^338824+89355	101997	Stefano Morozzi	05/2022
9923	2^338825-10995	101997	Stefano Morozzi	06/2022
9924	2^338824+149865	101997	Stefano Morozzi	02/2023
9925	2^338822+111175	101996	Stefano Morozzi	03/2022
9926	2^338822+187819	101996	Stefano Morozzi	04/2022
9927	2^338823+139545	101996	Stefano Morozzi	05/2022
9928	2^338823-184905	101996	Stefano Morozzi	06/2022
9929	2^338821-38919	101996	Stefano Morozzi	12/2022
9930	2^338820+41317	101995	Stefano Morozzi	06/2022
9931	2^338817+46019	101995	Stefano Morozzi	11/2022
9932	2^338820+148083	101995	Stefano Morozzi	11/2022
9933	2^338817-163251	101995	Stefano Morozzi	12/2022
9934	2^338819-63705	101995	Stefano Morozzi	12/2022
9935	2^338817-92509	101995	Stefano Morozzi	02/2023
9936	2^338815+151175	101994	Stefano Morozzi	12/2021
9937	2^338814-30011	101994	Stefano Morozzi	02/2022
9938	2^338814+12309	101994	Stefano Morozzi	04/2022
9939	2^338816-60647	101994	Stefano Morozzi	06/2022
9940	2^338816+171043	101994	Stefano Morozzi	11/2022
9941	2^338814-11513	101994	Stefano Morozzi	12/2022
9942	2^338811-126999	101993	Stefano Morozzi	12/2021
9943	2^338811+131621	101993	Stefano Morozzi	02/2022
9944	2^338812-107637	101993	Stefano Morozzi	03/2022
9945	2^338813+192725	101993	Stefano Morozzi	09/2022
9946	2^338812+94731	101993	Stefano Morozzi	11/2022
9947	2^338813+49205	101993	Stefano Morozzi	02/2023
9948	2^338809-152755	101992	Stefano Morozzi	01/2022
9949	2^338808+156531	101992	Stefano Morozzi	01/2022
9950	2^338808+7885	101992	Stefano Morozzi	02/2022
9951	2^338808-105797	101992	Stefano Morozzi	02/2022
9952	2^338807-35899	101992	Stefano Morozzi	06/2022
9953	2^338808-89175	101992	Stefano Morozzi	01/2023
9954	2^338808-91475	101992	Stefano Morozzi	01/2023
9955	2^338805+29879	101991	Stefano Morozzi	01/2022
9956	2^338805+157925	101991	Stefano Morozzi	02/2022
9957	2^338804-6809	101991	Stefano Morozzi	03/2022
9958	2^338806-157095	101991	Stefano Morozzi	03/2022
9959	2^338804-133173	101991	Stefano Morozzi	04/2022
9960	2^338805-115189	101991	Stefano Morozzi	01/2023
9961	2^338802+150403	101990	Stefano Morozzi	11/2021
9962	2^338801+154587	101990	Stefano Morozzi	01/2022
9963	2^338802-180603	101990	Stefano Morozzi	02/2022
9964	2^338803-31921	101990	Stefano Morozzi	03/2022
9965	2^338803-81735	101990	Stefano Morozzi	03/2022
9966	2^338803+195141	101990	Stefano Morozzi	11/2022
9967	2^338800+160141	101989	Stefano Morozzi	03/2022
9968	2^338797-82489	101989	Stefano Morozzi	03/2022
9973	2^338796+93	101988	Donovan Johnson	06/2008
9969	2^338795+455	101988	Stefano Morozzi	11/2021
9970	2^338795-102075	101988	Stefano Morozzi	12/2021
9971	2^338794-3483	101988	Stefano Morozzi	01/2022
9972	2^338796+179641	101988	Stefano Morozzi	01/2022
9974	2^338793-5155	101987	Stefano Morozzi	02/2022
9975	2^338793+111107	101987	Stefano Morozzi	03/2022
9976	2^338791+112083	101987	Stefano Morozzi	04/2022
9977	2^338792-85097	101987	Stefano Morozzi	06/2022
9978	(61*10^101986+47)/9	101987	Robert Price	07/2022
9979	2^338787+53309	101986	Stefano Morozzi	01/2022
9980	2^338787-153817	101986	Stefano Morozzi	01/2022
9981	2^338789+56229	101986	Stefano Morozzi	01/2022
9982	2^338790+6429	101986	Stefano Morozzi	01/2022
9983	2^338788+131701	101986	Stefano Morozzi	02/2022
9984	2^338785+104639	101985	Stefano Morozzi	01/2022
9985	2^338784+37591	101985	Stefano Morozzi	04/2022
9986	2^338786-9831	101985	Stefano Morozzi	04/2022
9987	2^338783+109065	101984	Stefano Morozzi	03/2022
9988	2^338779+86711	101983	Stefano Morozzi	04/2022
9989	2^338778+113589	101983	Stefano Morozzi	05/2022
9990	2^338775-30369	101982	Stefano Morozzi	02/2022
9991	2^338774+159135	101982	Stefano Morozzi	03/2022
9992	2^338776+113001	101982	Stefano Morozzi	04/2022
9993	2^338774+117039	101982	Stefano Morozzi	09/2022
9994	2^338775+167109	101982	Stefano Morozzi	09/2022
9995	2^338774+147595	101982	Stefano Morozzi	11/2022
9996	2^338772+42733	101981	Stefano Morozzi	09/2022
9997	2^338771-138805	101981	Stefano Morozzi	12/2022
9998	2^338768-181007	101980	Stefano Morozzi	02/2022
9999	2^338768+108807	101980	Stefano Morozzi	03/2022
10000	2^338767+169155	101980	Stefano Morozzi	09/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(303322 PRPs in the top)