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 ?
6751	2^338350-152933	101854	Stefano Morozzi	01/2022
6752	2^338350+6337	101854	Stefano Morozzi	01/2022
6753	2^338350+168759	101854	Stefano Morozzi	09/2022
6756	27088^5755+5755^27088	101853	Hans Havermann	01/2019
6754	2^338347+125901	101853	Stefano Morozzi	11/2021
6755	2^338346-10643	101853	Stefano Morozzi	06/2022
6757	2^338343+152271	101852	Stefano Morozzi	12/2021
6758	2^338345+154107	101852	Stefano Morozzi	01/2022
6759	2^338342+155397	101852	Stefano Morozzi	01/2022
6760	2^338342-130767	101852	Stefano Morozzi	02/2022
6761	2^338345-30123	101852	Stefano Morozzi	02/2022
6762	2^338345+35747	101852	Stefano Morozzi	03/2022
6763	2^338345-133131	101852	Stefano Morozzi	04/2022
6764	2^338345-134559	101852	Stefano Morozzi	04/2022
6765	2^338339+2753	101851	Stefano Morozzi	12/2021
6766	2^338341+128415	101851	Stefano Morozzi	01/2022
6767	2^338338+2677	101850	Stefano Morozzi	12/2021
6768	2^338336+54607	101850	Stefano Morozzi	01/2022
6769	2^338338+109999	101850	Stefano Morozzi	03/2022
6770	2^338336+161575	101850	Stefano Morozzi	04/2022
6771	2^338335+51975	101849	Stefano Morozzi	12/2021
6772	2^338335-152607	101849	Stefano Morozzi	01/2022
6773	2^338334+55273	101849	Stefano Morozzi	01/2022
6774	2^338332+34315	101849	Stefano Morozzi	03/2022
6775	2^338335+158759	101849	Stefano Morozzi	03/2022
6776	2^338332+67621	101849	Stefano Morozzi	09/2022
6777	2^338331+83403	101848	Stefano Morozzi	02/2022
6778	2^338330-110865	101848	Stefano Morozzi	06/2022
6779	2^338328-5295	101847	Stefano Morozzi	02/2022
6780	2^338327+143585	101847	Stefano Morozzi	09/2022
6781	2^338324-179667	101846	Stefano Morozzi	02/2022
6782	2^338316-175857	101844	Stefano Morozzi	12/2021
6783	2^338318+54405	101844	Stefano Morozzi	01/2022
6784	2^338316+32961	101844	Stefano Morozzi	02/2022
6785	2^338317+68175	101844	Stefano Morozzi	09/2022
6786	2^338315-178635	101843	Stefano Morozzi	01/2022
6787	2^338315+34899	101843	Stefano Morozzi	03/2022
6788	2^338314-106973	101843	Stefano Morozzi	03/2022
6789	2^338311-51799	101842	Stefano Morozzi	12/2021
6790	2^338309+157259	101842	Stefano Morozzi	02/2022
6791	2^338310+40903	101842	Stefano Morozzi	06/2022
6792	2^338308-55853	101841	Stefano Morozzi	02/2022
6793	2^338307+134871	101841	Stefano Morozzi	03/2022
6794	2^338307+19689	101841	Stefano Morozzi	09/2022
6795	2^338308+66873	101841	Stefano Morozzi	09/2022
6796	2^338304+78757	101840	Stefano Morozzi	01/2022
6797	2^338304-5807	101840	Stefano Morozzi	02/2022
6798	2^338305+110879	101840	Stefano Morozzi	03/2022
6799	2^338304+91147	101840	Stefano Morozzi	06/2022
6800	2^338299+85611	101839	Stefano Morozzi	03/2022
6801	2^338298-25571	101838	Stefano Morozzi	12/2021
6802	2^338297+35547	101838	Stefano Morozzi	03/2022
6803	2^338298+111199	101838	Stefano Morozzi	03/2022
6804	2^338294-150711	101837	Stefano Morozzi	12/2021
6805	2^338294+177597	101837	Stefano Morozzi	12/2021
6806	2^338294-177807	101837	Stefano Morozzi	01/2022
6807	2^338295-52929	101837	Stefano Morozzi	01/2022
6808	2^338293+37407	101837	Stefano Morozzi	04/2022
6809	2^338292+40573	101837	Stefano Morozzi	06/2022
6810	2^338289+30957	101836	Stefano Morozzi	01/2022
6811	2^338291+131825	101836	Stefano Morozzi	02/2022
6812	2^338291+110111	101836	Stefano Morozzi	03/2022
6813	2^338290-156423	101836	Stefano Morozzi	03/2022
6814	2^338291-157845	101836	Stefano Morozzi	03/2022
6815	2^338290+69243	101836	Stefano Morozzi	09/2022
6816	2^338288+26623	101835	Stefano Morozzi	12/2021
6817	2^338286+33325	101835	Stefano Morozzi	02/2022
6818	2^338287+132633	101835	Stefano Morozzi	02/2022
6819	2^338287+157149	101835	Stefano Morozzi	02/2022
6820	2^338288-107193	101835	Stefano Morozzi	03/2022
6821	2^338286-83333	101835	Stefano Morozzi	04/2022
6822	2^338287+114425	101835	Stefano Morozzi	05/2022
6823	2^338288+194403	101835	Stefano Morozzi	09/2022
6824	2^338285+82131	101834	Stefano Morozzi	02/2022
6825	2^338284-104217	101834	Stefano Morozzi	02/2022
6826	2^338282-84533	101834	Stefano Morozzi	04/2022
6827	2^338283+67545	101834	Stefano Morozzi	09/2022
6834	2^338280-19745	101833	Enzo Doria	06/2013
6828	2^338279-125947	101833	Stefano Morozzi	12/2021
6829	2^338280-50343	101833	Stefano Morozzi	12/2021
6830	2^338279+133331	101833	Stefano Morozzi	02/2022
6831	2^338281-54561	101833	Stefano Morozzi	02/2022
6832	2^338280+192063	101833	Stefano Morozzi	09/2022
6833	2^338281+18971	101833	Stefano Morozzi	09/2022
6835	2^338278+188215	101832	Stefano Morozzi	05/2022
6836	2^338273+181101	101831	Stefano Morozzi	01/2022
6837	2^338275+32909	101831	Stefano Morozzi	02/2022
6838	2^338272+166431	101831	Stefano Morozzi	06/2022
6839	2^338270-135725	101830	Stefano Morozzi	06/2022
6840	2^338266+110665	101829	Stefano Morozzi	03/2022
6841	2^338267+110481	101829	Stefano Morozzi	03/2022
6842	2^338265-154893	101828	Stefano Morozzi	02/2022
6843	2^338264+163611	101828	Stefano Morozzi	05/2022
6844	2^338256+5223	101826	Stefano Morozzi	01/2022
6845	2^338257+178425	101826	Stefano Morozzi	01/2022
6846	2^338256-180569	101826	Stefano Morozzi	02/2022
6847	2^338257-5965	101826	Stefano Morozzi	02/2022
6848	2^338258-9225	101826	Stefano Morozzi	04/2022
6849	2^338255-127021	101825	Stefano Morozzi	12/2021
6850	2^338253+159005	101825	Stefano Morozzi	03/2022
6851	2^338253+64817	101825	Stefano Morozzi	05/2022
6852	2^338254-85403	101825	Stefano Morozzi	06/2022
6853	2^338254+142947	101825	Stefano Morozzi	09/2022
6854	2^338251+78975	101824	Stefano Morozzi	01/2022
6855	2^338252-178709	101824	Stefano Morozzi	01/2022
6856	2^338252+129703	101824	Stefano Morozzi	01/2022
6857	2^338252+132285	101824	Stefano Morozzi	02/2022
6858	2^338251-33381	101824	Stefano Morozzi	04/2022
6859	2^338245-134755	101822	Stefano Morozzi	04/2022
6860	2^338244-59219	101822	Stefano Morozzi	04/2022
6868	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
6861	2^338241+1391	101821	Stefano Morozzi	12/2021
6862	2^338242+151195	101821	Stefano Morozzi	12/2021
6863	2^338240-152495	101821	Stefano Morozzi	12/2021
6864	2^338240+81745	101821	Stefano Morozzi	02/2022
6865	2^338241-155551	101821	Stefano Morozzi	02/2022
6866	2^338242-108237	101821	Stefano Morozzi	04/2022
6867	2^338242+43045	101821	Stefano Morozzi	09/2022
6869	2^338238-126735	101820	Stefano Morozzi	12/2021
6870	2^338238+183855	101820	Stefano Morozzi	03/2022
6871	2^338238+141013	101820	Stefano Morozzi	06/2022
6872	2^338234-80925	101819	Stefano Morozzi	02/2022
6873	2^338234-154593	101819	Stefano Morozzi	02/2022
6874	2^338235-131787	101819	Stefano Morozzi	03/2022
6875	2^338233+89781	101819	Stefano Morozzi	05/2022
6881	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
6876	2^338232-175539	101818	Stefano Morozzi	12/2021
6877	2^338231+57345	101818	Stefano Morozzi	02/2022
6878	2^338232+36097	101818	Stefano Morozzi	03/2022
6879	2^338230+137403	101818	Stefano Morozzi	04/2022
6880	2^338231-59569	101818	Stefano Morozzi	04/2022
6882	2^338228+159247	101817	Stefano Morozzi	03/2022
6883	(34*10^101815+191)/9	101816	Robert Price	08/2021
6884	2^338224+185461	101816	Stefano Morozzi	03/2022
6885	2^338224+62295	101816	Stefano Morozzi	04/2022
6886	2^338225+162645	101816	Stefano Morozzi	04/2022
6887	2^338223+144209	101816	Stefano Morozzi	09/2022
6892	6^130841+103	101815	Lelio R Paula	10/2016
6888	2^338220+150405	101815	Stefano Morozzi	11/2021
6889	2^338219-4147	101815	Stefano Morozzi	01/2022
6890	2^338221+83391	101815	Stefano Morozzi	02/2022
6891	2^338221+62937	101815	Stefano Morozzi	04/2022
6893	2^338216+77473	101814	Stefano Morozzi	12/2021
6894	2^338218+155299	101814	Stefano Morozzi	01/2022
6895	2^338217-134745	101814	Stefano Morozzi	04/2022
6896	2^338213-125631	101813	Stefano Morozzi	12/2021
6897	2^338215+25845	101813	Stefano Morozzi	12/2021
6898	2^338210-153537	101812	Stefano Morozzi	01/2022
6899	2^338209+60915	101812	Stefano Morozzi	03/2022
6900	2^338211-57297	101812	Stefano Morozzi	03/2022
6901	2^338211-110257	101812	Stefano Morozzi	06/2022
6902	2^338208-178787	101811	Stefano Morozzi	01/2022
6903	2^338208+106153	101811	Stefano Morozzi	01/2022
6904	2^338207+16499	101811	Stefano Morozzi	06/2022
6905	2^338205+102471	101810	Stefano Morozzi	12/2021
6906	2^338199-176377	101809	Stefano Morozzi	12/2021
6907	2^338201-151233	101809	Stefano Morozzi	12/2021
6908	2^338202-152061	101809	Stefano Morozzi	12/2021
6909	2^338202+133785	101809	Stefano Morozzi	03/2022
6910	2^338200+135643	101809	Stefano Morozzi	03/2022
6911	2^338202+14169	101809	Stefano Morozzi	05/2022
6912	2^338202-85211	101809	Stefano Morozzi	06/2022
6913	2^338194-175845	101807	Stefano Morozzi	12/2021
6914	2^338195+56771	101807	Stefano Morozzi	02/2022
6915	2^338195+162365	101807	Stefano Morozzi	04/2022
6916	2^338194+67497	101807	Stefano Morozzi	09/2022
6917	2^338192+130387	101806	Stefano Morozzi	01/2022
6918	2^338190+89359	101806	Stefano Morozzi	05/2022
6919	2^338189+144605	101806	Stefano Morozzi	09/2022
6920	2^338186+127245	101805	Stefano Morozzi	12/2021
6921	2^338186-130013	101805	Stefano Morozzi	02/2022
6922	2^338186+39235	101805	Stefano Morozzi	05/2022
6923	2^338185+77315	101804	Stefano Morozzi	12/2021
6924	2^338185+102519	101804	Stefano Morozzi	12/2021
6925	2^338183-76539	101804	Stefano Morozzi	12/2021
6926	2^338185+104489	101804	Stefano Morozzi	01/2022
6927	2^338179+35361	101803	Stefano Morozzi	03/2022
6928	2^338181+64235	101803	Stefano Morozzi	05/2022
6929	2^338181+94047	101803	Stefano Morozzi	09/2022
6930	2^338177+51807	101802	Stefano Morozzi	12/2021
6931	2^338177+107385	101802	Stefano Morozzi	02/2022
6932	2^338178+34287	101802	Stefano Morozzi	03/2022
6933	2^338178+184207	101802	Stefano Morozzi	03/2022
6934	2^338177-108901	101802	Stefano Morozzi	04/2022
6935	2^338177+141569	101802	Stefano Morozzi	06/2022
6936	2^338175+25161	101801	Stefano Morozzi	11/2021
6937	2^338173-27901	101801	Stefano Morozzi	01/2022
6938	2^338169-155965	101800	Stefano Morozzi	02/2022
6939	2^338166+183237	101799	Stefano Morozzi	02/2022
6940	2^338168-157835	101799	Stefano Morozzi	03/2022
6941	2^338166+137107	101799	Stefano Morozzi	04/2022
6942	2^338165-152139	101798	Stefano Morozzi	12/2021
6943	2^338163-178947	101798	Stefano Morozzi	02/2022
6944	2^338159-127575	101797	Stefano Morozzi	12/2021
6945	2^338161+154259	101797	Stefano Morozzi	01/2022
6946	2^338160+139947	101797	Stefano Morozzi	05/2022
6947	2^338160+191815	101797	Stefano Morozzi	09/2022
6948	2^338156-75269	101796	Stefano Morozzi	12/2021
6949	2^338156-151247	101796	Stefano Morozzi	12/2021
6950	2^338156+103273	101796	Stefano Morozzi	01/2022
6951	2^338156+167053	101796	Stefano Morozzi	09/2022
6952	2^338158+69303	101796	Stefano Morozzi	09/2022
6953	2^338155+132621	101795	Stefano Morozzi	02/2022
6954	2^338155-82605	101795	Stefano Morozzi	03/2022
6955	2^338155-182631	101795	Stefano Morozzi	03/2022
6956	2^338155+187755	101795	Stefano Morozzi	04/2022
6957	2^338154-83975	101795	Stefano Morozzi	04/2022
6958	2^338154+163759	101795	Stefano Morozzi	05/2022
6959	2^338152-25767	101794	Stefano Morozzi	12/2021
6960	2^338152+181927	101794	Stefano Morozzi	02/2022
6961	2^338151+60779	101794	Stefano Morozzi	03/2022
6962	2^338151+189149	101794	Stefano Morozzi	05/2022
6963	2^338147+29343	101793	Stefano Morozzi	01/2022
6964	2^338148+130803	101793	Stefano Morozzi	01/2022
6965	2^338146+166167	101793	Stefano Morozzi	06/2022
6966	2^338149-185073	101793	Stefano Morozzi	06/2022
6967	2^338149+41757	101793	Stefano Morozzi	09/2022
6968	2^338144+180697	101792	Stefano Morozzi	01/2022
6969	2^338143+8589	101792	Stefano Morozzi	02/2022
6970	2^338143-55611	101792	Stefano Morozzi	02/2022
6971	2^338143+60623	101792	Stefano Morozzi	03/2022
6972	2^338141-77301	101791	Stefano Morozzi	12/2021
6973	2^338141+157145	101791	Stefano Morozzi	02/2022
6974	2^338140+84745	101791	Stefano Morozzi	03/2022
6975	2^338140+90073	101791	Stefano Morozzi	05/2022
6976	2^338139-134719	101790	Stefano Morozzi	04/2022
6977	2^338133+1445	101789	Stefano Morozzi	12/2021
6978	2^338132+105643	101788	Stefano Morozzi	01/2022
6979	2^338131+181871	101788	Stefano Morozzi	02/2022
6980	2^338132-184539	101788	Stefano Morozzi	04/2022
6981	2^338128+128953	101787	Stefano Morozzi	01/2022
6982	2^338127+11021	101787	Stefano Morozzi	03/2022
6983	2^338127+192935	101787	Stefano Morozzi	09/2022
6984	2^338123-25959	101786	Stefano Morozzi	12/2021
6985	2^338124-180765	101786	Stefano Morozzi	02/2022
6986	2^338125-7129	101786	Stefano Morozzi	03/2022
6990	2^338122-20117	101785	Enzo Doria	06/2013
6991	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
6987	2^338122+32799	101785	Stefano Morozzi	02/2022
6988	2^338120+166411	101785	Stefano Morozzi	06/2022
6989	2^338122+90705	101785	Stefano Morozzi	06/2022
6992	2^338117+103761	101784	Stefano Morozzi	01/2022
6993	2^338118+53817	101784	Stefano Morozzi	01/2022
6994	2^338116+82585	101784	Stefano Morozzi	02/2022
6995	2^338118+39483	101784	Stefano Morozzi	05/2022
6996	2^338115+61083	101783	Stefano Morozzi	03/2022
6997	2^338110-175365	101782	Stefano Morozzi	12/2021
6998	2^338110-3963	101782	Stefano Morozzi	01/2022
6999	2^338112+155061	101782	Stefano Morozzi	01/2022
7000	2^338112+137335	101782	Stefano Morozzi	04/2022

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Probable Primes Top 10000

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