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 ?
9751	2^338545-11059	101913	Stefano Morozzi	12/2022
9752	2^338544+107853	101912	Stefano Morozzi	02/2022
9753	2^338542+172813	101912	Stefano Morozzi	11/2022
9754	2^338544-12687	101912	Stefano Morozzi	12/2022
9755	2^338543-140677	101912	Stefano Morozzi	01/2023
9756	2^338541+152721	101911	Stefano Morozzi	01/2022
9757	2^338539+60825	101911	Stefano Morozzi	03/2022
9758	2^338539+160881	101911	Stefano Morozzi	03/2022
9759	2^338541-182523	101911	Stefano Morozzi	03/2022
9760	2^338540+87645	101911	Stefano Morozzi	04/2022
9761	2^338541+148305	101911	Stefano Morozzi	11/2022
9762	2^338541-163075	101911	Stefano Morozzi	12/2022
9763	2^338536-100785	101910	Stefano Morozzi	12/2021
9764	2^338535-51837	101910	Stefano Morozzi	12/2021
9765	2^338535-158745	101910	Stefano Morozzi	04/2022
9766	2^338536-189977	101910	Stefano Morozzi	01/2023
9767	2^338537-65623	101910	Stefano Morozzi	01/2023
9768	2^338532+39445	101909	Stefano Morozzi	05/2022
9769	2^338532+141415	101909	Stefano Morozzi	06/2022
9770	2^338532-136037	101909	Stefano Morozzi	06/2022
9771	2^338531+81081	101908	Stefano Morozzi	01/2022
9772	2^338530+59835	101908	Stefano Morozzi	03/2022
9773	2^338529+186551	101908	Stefano Morozzi	04/2022
9774	2^338531+61313	101908	Stefano Morozzi	04/2022
9775	2^338531-9277	101908	Stefano Morozzi	04/2022
9776	2^338528-92727	101908	Stefano Morozzi	02/2023
9777	2^338527+191205	101907	Stefano Morozzi	06/2022
9778	2^338525+99621	101907	Stefano Morozzi	02/2023
9779	2^338524+54421	101906	Stefano Morozzi	01/2022
9780	2^338522-155811	101906	Stefano Morozzi	02/2022
9781	2^338523-16291	101906	Stefano Morozzi	01/2023
9782	2^338522-142137	101906	Stefano Morozzi	02/2023
9783	2^338521+183131	101905	Stefano Morozzi	02/2022
9784	2^338520+34945	101905	Stefano Morozzi	03/2022
9785	2^338518-182885	101905	Stefano Morozzi	04/2022
9786	2^338518+114633	101905	Stefano Morozzi	05/2022
9787	2^338518-12621	101905	Stefano Morozzi	12/2022
9788	2^338518-187325	101905	Stefano Morozzi	12/2022
9796	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
9789	2^338517-125955	101904	Stefano Morozzi	12/2021
9790	2^338517+126437	101904	Stefano Morozzi	12/2021
9791	2^338517-53499	101904	Stefano Morozzi	01/2022
9792	2^338515+30369	101904	Stefano Morozzi	01/2022
9793	2^338517-184623	101904	Stefano Morozzi	04/2022
9794	2^338515+89333	101904	Stefano Morozzi	05/2022
9795	2^338515+198813	101904	Stefano Morozzi	02/2023
9799	24502^14419+14419^24502	101903	Hans Havermann	01/2019
9797	2^338512-827	101903	Stefano Morozzi	12/2021
9798	2^338514-6611	101903	Stefano Morozzi	03/2022
9800	2^338509+5139	101902	Stefano Morozzi	01/2022
9801	2^338509+40205	101902	Stefano Morozzi	06/2022
9802	2^338511+19959	101902	Stefano Morozzi	09/2022
9803	2^338510-37877	101902	Stefano Morozzi	12/2022
9804	2^338507-188655	101901	Stefano Morozzi	12/2022
9805	2^338507-114457	101901	Stefano Morozzi	01/2023
9806	2^338504-152615	101900	Stefano Morozzi	01/2022
9807	2^338502-4587	101900	Stefano Morozzi	02/2022
9808	2^338502-166275	101900	Stefano Morozzi	01/2023
9809	2^338500-26865	101899	Stefano Morozzi	12/2021
9810	2^338501-177471	101899	Stefano Morozzi	12/2021
9811	2^338499-3915	101899	Stefano Morozzi	01/2022
9812	2^338501+32051	101899	Stefano Morozzi	02/2022
9813	2^338499+183533	101899	Stefano Morozzi	03/2022
9814	2^338500+35625	101899	Stefano Morozzi	03/2022
9815	2^338499+87579	101899	Stefano Morozzi	04/2022
9816	2^338498-117683	101899	Stefano Morozzi	02/2023
9819	2^338497-17041	101898	Enzo Doria	05/2013
9817	2^338497+150405	101898	Stefano Morozzi	11/2021
9818	2^338495+100533	101898	Stefano Morozzi	12/2021
9820	2^338494+36057	101897	Stefano Morozzi	03/2022
9821	2^338492+39015	101897	Stefano Morozzi	05/2022
9822	2^338494+168007	101897	Stefano Morozzi	09/2022
9823	2^338490+61149	101896	Stefano Morozzi	03/2022
9824	2^338489+161369	101896	Stefano Morozzi	04/2022
9825	2^338491+22961	101896	Stefano Morozzi	11/2022
9826	2^338487-3555	101895	Stefano Morozzi	01/2022
9827	2^338487-183129	101895	Stefano Morozzi	04/2022
9828	2^338484+128767	101894	Stefano Morozzi	01/2022
9829	2^338484-31895	101894	Stefano Morozzi	03/2022
9830	2^338483-67899	101894	Stefano Morozzi	02/2023
9831	2^338483-192129	101894	Stefano Morozzi	02/2023
9832	2^338478+10893	101893	Stefano Morozzi	03/2022
9833	2^338479+87243	101893	Stefano Morozzi	04/2022
9834	2^338479+167619	101893	Stefano Morozzi	09/2022
9835	2^338480+197503	101893	Stefano Morozzi	11/2022
9836	2^338481-11421	101893	Stefano Morozzi	12/2022
9837	2^338479-89649	101893	Stefano Morozzi	01/2023
9838	(29*34^66532-12833)/33	101893	Eric Chen	03/2023
9841	2^338475+54615	101892	Lelio R Paula	10/2016
9839	2^338475-59775	101892	Stefano Morozzi	04/2022
9840	2^338476-134237	101892	Stefano Morozzi	04/2022
9842	2^338474+100767	101891	Stefano Morozzi	11/2021
9843	2^338474+81165	101891	Stefano Morozzi	01/2022
9844	2^338474+41137	101891	Stefano Morozzi	06/2022
9845	2^338472-110445	101891	Stefano Morozzi	06/2022
9846	2^338473-89535	101891	Stefano Morozzi	01/2023
9847	2^338470+27777	101890	Stefano Morozzi	01/2022
9848	2^338468+31351	101890	Stefano Morozzi	01/2022
9849	2^338469-106339	101890	Stefano Morozzi	03/2022
9850	2^338471+187469	101890	Stefano Morozzi	04/2022
9851	2^338468+96613	101890	Stefano Morozzi	11/2022
9852	2^338469+46167	101890	Stefano Morozzi	11/2022
9853	2^338470+71527	101890	Stefano Morozzi	11/2022
9854	2^338469-112783	101890	Stefano Morozzi	12/2022
9855	2^338470-115665	101890	Stefano Morozzi	01/2023
9856	2^338467-25665	101889	Stefano Morozzi	12/2021
9857	2^338465+152139	101889	Stefano Morozzi	12/2021
9858	2^338466-28643	101889	Stefano Morozzi	01/2022
9859	2^338465+181517	101889	Stefano Morozzi	01/2022
9860	2^338466+115917	101889	Stefano Morozzi	06/2022
9861	2^338465-88291	101889	Stefano Morozzi	12/2022
9862	2^338464-104009	101888	Stefano Morozzi	02/2022
9863	2^338463+185169	101888	Stefano Morozzi	03/2022
9864	2^338464+60595	101888	Stefano Morozzi	03/2022
9865	2^338464-66377	101888	Stefano Morozzi	01/2023
9866	2^338458+60273	101887	Stefano Morozzi	03/2022
9867	2^338461+135867	101887	Stefano Morozzi	03/2022
9868	2^338455-4621	101886	Stefano Morozzi	02/2022
9869	2^338457+187827	101886	Stefano Morozzi	04/2022
9870	2^338455+173349	101886	Stefano Morozzi	11/2022
9871	2^338454+133737	101885	Stefano Morozzi	03/2022
9872	2^338454-158501	101885	Stefano Morozzi	04/2022
9873	2^338454-184217	101885	Stefano Morozzi	04/2022
9874	2^338453+164451	101885	Stefano Morozzi	05/2022
9875	2^338452-136137	101885	Stefano Morozzi	12/2022
9876	2^338450+106275	101884	Stefano Morozzi	01/2022
9877	2^338450+168439	101884	Stefano Morozzi	09/2022
9878	(133*10^101881+17)/3	101883	Robert Price	11/2021
9879	2^338445-80461	101883	Stefano Morozzi	02/2022
9880	2^338446-131211	101883	Stefano Morozzi	02/2022
9881	2^338448+187167	101883	Stefano Morozzi	04/2022
9882	2^338446-160115	101883	Stefano Morozzi	06/2022
9883	2^338447-164157	101883	Stefano Morozzi	01/2023
9884	2^338447-191001	101883	Stefano Morozzi	01/2023
9885	2^338444+127623	101882	Stefano Morozzi	12/2021
9886	2^338443-113827	101882	Stefano Morozzi	12/2022
9887	2^338441-5893	101881	Stefano Morozzi	02/2022
9888	2^338439-162565	101881	Stefano Morozzi	12/2022
9889	2^338436+153657	101880	Stefano Morozzi	01/2022
9890	2^338437-153159	101880	Stefano Morozzi	01/2022
9891	2^338436-83783	101880	Stefano Morozzi	04/2022
9892	2^338435+89109	101880	Stefano Morozzi	05/2022
9893	2^338435+13871	101880	Stefano Morozzi	05/2022
9894	2^338436+149691	101880	Stefano Morozzi	02/2023
9895	2^338434+81537	101879	Stefano Morozzi	01/2022
9896	2^338432+33495	101879	Stefano Morozzi	03/2022
9897	2^338432-7043	101879	Stefano Morozzi	03/2022
9898	2^338433-32629	101879	Stefano Morozzi	03/2022
9899	2^338430-9903	101878	Stefano Morozzi	04/2022
9907	2^338426-19797	101877	Enzo Doria	06/2013
9900	2^338427-77797	101877	Stefano Morozzi	01/2022
9901	2^338427-178687	101877	Stefano Morozzi	01/2022
9902	2^338428-54873	101877	Stefano Morozzi	02/2022
9903	2^338425+41357	101877	Stefano Morozzi	06/2022
9904	2^338428+90855	101877	Stefano Morozzi	06/2022
9905	2^338428-39807	101877	Stefano Morozzi	01/2023
9906	2^338425-192381	101877	Stefano Morozzi	02/2023
9908	2^338422-188787	101876	Stefano Morozzi	12/2022
9909	2^338423-187755	101876	Stefano Morozzi	12/2022
9910	2^338422-115865	101876	Stefano Morozzi	01/2023
9911	2^338420-178829	101875	Stefano Morozzi	01/2022
9912	2^338421-105423	101875	Stefano Morozzi	02/2022
9913	2^338419-82761	101875	Stefano Morozzi	03/2022
9914	2^338420+193143	101875	Stefano Morozzi	09/2022
9915	2^338419+199641	101875	Stefano Morozzi	02/2023
9916	2^338420-143103	101875	Stefano Morozzi	02/2023
9917	2^338418-50903	101874	Stefano Morozzi	12/2021
9918	2^338418+158355	101874	Stefano Morozzi	02/2022
9919	2^338418+159339	101874	Stefano Morozzi	03/2022
9920	2^338416+14953	101874	Stefano Morozzi	05/2022
9921	2^338416+166051	101874	Stefano Morozzi	06/2022
9922	2^338418-138765	101874	Stefano Morozzi	12/2022
9923	2^338417+49737	101874	Stefano Morozzi	02/2023
9924	2^338413-125919	101873	Stefano Morozzi	12/2021
9925	2^338414+26083	101873	Stefano Morozzi	12/2021
9926	2^338412-152379	101873	Stefano Morozzi	12/2021
9927	2^338413+54797	101873	Stefano Morozzi	01/2022
9928	2^338412+157951	101873	Stefano Morozzi	02/2022
9929	2^338414+81627	101873	Stefano Morozzi	02/2022
9930	2^338413+133679	101873	Stefano Morozzi	03/2022
9931	2^338413+197735	101873	Stefano Morozzi	11/2022
9932	2^338413-114301	101873	Stefano Morozzi	01/2023
9933	11*32^67682+395	101873	Eric Chen	04/2023
9934	2^338409-52183	101872	Stefano Morozzi	12/2021
9935	2^338411-3789	101872	Stefano Morozzi	01/2022
9936	2^338409+173237	101872	Stefano Morozzi	11/2022
9937	2^338406-184175	101871	Stefano Morozzi	04/2022
9938	2^338405+94451	101871	Stefano Morozzi	09/2022
9939	2^338406-161217	101871	Stefano Morozzi	12/2022
9940	2^338406+199929	101871	Stefano Morozzi	02/2023
9941	2^338404+55717	101870	Stefano Morozzi	01/2022
9942	2^338403+36261	101870	Stefano Morozzi	04/2022
9943	2^338402-34431	101870	Stefano Morozzi	04/2022
9944	2^338404-159215	101870	Stefano Morozzi	04/2022
9945	2^338403+18363	101870	Stefano Morozzi	09/2022
9946	2^338403+170235	101870	Stefano Morozzi	11/2022
9947	2^338399+23045	101869	Stefano Morozzi	11/2022
9948	2^338399-65535	101869	Stefano Morozzi	01/2023
9949	2^338395-127449	101868	Stefano Morozzi	12/2021
9950	2^338398-127637	101868	Stefano Morozzi	01/2022
9951	2^338398-166533	101868	Stefano Morozzi	01/2023
9952	2^338394+100317	101867	Stefano Morozzi	11/2021
9953	2^338393-152749	101867	Stefano Morozzi	01/2022
9954	2^338393+163025	101867	Stefano Morozzi	04/2022
9955	2^338393+89229	101867	Stefano Morozzi	05/2022
9956	2^338393+99647	101867	Stefano Morozzi	02/2023
9957	2^338394-192471	101867	Stefano Morozzi	02/2023
9958	2^338390+76627	101866	Stefano Morozzi	12/2021
9959	2^338389-85081	101866	Stefano Morozzi	06/2022
9960	2^338390+148113	101866	Stefano Morozzi	11/2022
9961	2^338389-14253	101866	Stefano Morozzi	01/2023
9962	2^338390-114297	101866	Stefano Morozzi	01/2023
9963	2^338391-64225	101866	Stefano Morozzi	01/2023
9964	2^338389-16971	101866	Stefano Morozzi	02/2023
9965	2^338387-75685	101865	Stefano Morozzi	12/2021
9966	2^338388-53459	101865	Stefano Morozzi	01/2022
9967	2^338388-36575	101865	Stefano Morozzi	12/2022
9968	2^338385-190311	101865	Stefano Morozzi	01/2023
9969	2^338384+131563	101864	Stefano Morozzi	01/2022
9970	2^338382+109069	101864	Stefano Morozzi	03/2022
9971	2^338384+168987	101864	Stefano Morozzi	09/2022
9972	2^338383-42367	101864	Stefano Morozzi	02/2023
9973	2^338380+77125	101863	Stefano Morozzi	12/2021
9974	2^338381-35539	101863	Stefano Morozzi	06/2022
9975	2^338378-125841	101862	Stefano Morozzi	12/2021
9976	2^338375+27815	101862	Stefano Morozzi	01/2022
9977	2^338375-28509	101862	Stefano Morozzi	01/2022
9978	2^338375+29985	101862	Stefano Morozzi	01/2022
9979	2^338377+157881	101862	Stefano Morozzi	02/2022
9980	2^338375+59589	101862	Stefano Morozzi	03/2022
9981	2^338378+36399	101862	Stefano Morozzi	04/2022
9982	2^338378-159773	101862	Stefano Morozzi	04/2022
9983	2^338378+14883	101862	Stefano Morozzi	05/2022
9984	2^338376+140173	101862	Stefano Morozzi	06/2022
9985	2^338375+18761	101862	Stefano Morozzi	09/2022
9986	2^338373-75103	101861	Stefano Morozzi	12/2021
9987	2^338372+128877	101861	Stefano Morozzi	01/2022
9988	2^338374-28731	101861	Stefano Morozzi	01/2022
9989	2^338374-128427	101861	Stefano Morozzi	01/2022
9990	2^338372+37875	101861	Stefano Morozzi	04/2022
9991	2^338373+161541	101861	Stefano Morozzi	04/2022
9992	2^338374+37759	101861	Stefano Morozzi	04/2022
9993	2^338372+93235	101861	Stefano Morozzi	09/2022
9994	2^338373-63273	101861	Stefano Morozzi	12/2022
9995	2^338369+29427	101860	Stefano Morozzi	01/2022
9996	2^338370+179133	101860	Stefano Morozzi	01/2022
9997	2^338369+131501	101860	Stefano Morozzi	01/2022
9998	2^338369+181649	101860	Stefano Morozzi	02/2022
9999	2^338370-4787	101860	Stefano Morozzi	02/2022
10000	2^338371-133491	101860	Stefano Morozzi	04/2022

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PRP Records

Probable Primes Top 10000

(301737 PRPs in the top)