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 ?
8251	2^338448+187167	101883	Stefano Morozzi	04/2022
8252	2^338446-160115	101883	Stefano Morozzi	06/2022
8253	2^338447-164157	101883	Stefano Morozzi	01/2023
8254	2^338447-191001	101883	Stefano Morozzi	01/2023
8255	2^338444+127623	101882	Stefano Morozzi	12/2021
8256	2^338443-113827	101882	Stefano Morozzi	12/2022
8257	2^338441-5893	101881	Stefano Morozzi	02/2022
8258	2^338439-162565	101881	Stefano Morozzi	12/2022
8259	2^338436+153657	101880	Stefano Morozzi	01/2022
8260	2^338437-153159	101880	Stefano Morozzi	01/2022
8261	2^338436-83783	101880	Stefano Morozzi	04/2022
8262	2^338435+89109	101880	Stefano Morozzi	05/2022
8263	2^338435+13871	101880	Stefano Morozzi	05/2022
8264	2^338436+149691	101880	Stefano Morozzi	02/2023
8265	2^338434+81537	101879	Stefano Morozzi	01/2022
8266	2^338432+33495	101879	Stefano Morozzi	03/2022
8267	2^338432-7043	101879	Stefano Morozzi	03/2022
8268	2^338433-32629	101879	Stefano Morozzi	03/2022
8269	2^338430-9903	101878	Stefano Morozzi	04/2022
8277	2^338426-19797	101877	Enzo Doria	06/2013
8270	2^338427-77797	101877	Stefano Morozzi	01/2022
8271	2^338427-178687	101877	Stefano Morozzi	01/2022
8272	2^338428-54873	101877	Stefano Morozzi	02/2022
8273	2^338425+41357	101877	Stefano Morozzi	06/2022
8274	2^338428+90855	101877	Stefano Morozzi	06/2022
8275	2^338428-39807	101877	Stefano Morozzi	01/2023
8276	2^338425-192381	101877	Stefano Morozzi	02/2023
8278	2^338422-188787	101876	Stefano Morozzi	12/2022
8279	2^338423-187755	101876	Stefano Morozzi	12/2022
8280	2^338422-115865	101876	Stefano Morozzi	01/2023
8281	2^338420-178829	101875	Stefano Morozzi	01/2022
8282	2^338421-105423	101875	Stefano Morozzi	02/2022
8283	2^338419-82761	101875	Stefano Morozzi	03/2022
8284	2^338420+193143	101875	Stefano Morozzi	09/2022
8285	2^338419+199641	101875	Stefano Morozzi	02/2023
8286	2^338420-143103	101875	Stefano Morozzi	02/2023
8287	2^338418-50903	101874	Stefano Morozzi	12/2021
8288	2^338418+158355	101874	Stefano Morozzi	02/2022
8289	2^338418+159339	101874	Stefano Morozzi	03/2022
8290	2^338416+14953	101874	Stefano Morozzi	05/2022
8291	2^338416+166051	101874	Stefano Morozzi	06/2022
8292	2^338418-138765	101874	Stefano Morozzi	12/2022
8293	2^338417+49737	101874	Stefano Morozzi	02/2023
8294	2^338413-125919	101873	Stefano Morozzi	12/2021
8295	2^338414+26083	101873	Stefano Morozzi	12/2021
8296	2^338412-152379	101873	Stefano Morozzi	12/2021
8297	2^338413+54797	101873	Stefano Morozzi	01/2022
8298	2^338412+157951	101873	Stefano Morozzi	02/2022
8299	2^338414+81627	101873	Stefano Morozzi	02/2022
8300	2^338413+133679	101873	Stefano Morozzi	03/2022
8301	2^338413+197735	101873	Stefano Morozzi	11/2022
8302	2^338413-114301	101873	Stefano Morozzi	01/2023
8303	11*32^67682+395	101873	Eric Chen	04/2023
8304	2^338409-52183	101872	Stefano Morozzi	12/2021
8305	2^338411-3789	101872	Stefano Morozzi	01/2022
8306	2^338409+173237	101872	Stefano Morozzi	11/2022
8307	2^338406-184175	101871	Stefano Morozzi	04/2022
8308	2^338405+94451	101871	Stefano Morozzi	09/2022
8309	2^338406-161217	101871	Stefano Morozzi	12/2022
8310	2^338406+199929	101871	Stefano Morozzi	02/2023
8311	2^338404+55717	101870	Stefano Morozzi	01/2022
8312	2^338403+36261	101870	Stefano Morozzi	04/2022
8313	2^338402-34431	101870	Stefano Morozzi	04/2022
8314	2^338404-159215	101870	Stefano Morozzi	04/2022
8315	2^338403+18363	101870	Stefano Morozzi	09/2022
8316	2^338403+170235	101870	Stefano Morozzi	11/2022
8317	2^338399+23045	101869	Stefano Morozzi	11/2022
8318	2^338399-65535	101869	Stefano Morozzi	01/2023
8319	2^338395-127449	101868	Stefano Morozzi	12/2021
8320	2^338398-127637	101868	Stefano Morozzi	01/2022
8321	2^338398-166533	101868	Stefano Morozzi	01/2023
8322	2^338394+100317	101867	Stefano Morozzi	11/2021
8323	2^338393-152749	101867	Stefano Morozzi	01/2022
8324	2^338393+163025	101867	Stefano Morozzi	04/2022
8325	2^338393+89229	101867	Stefano Morozzi	05/2022
8326	2^338393+99647	101867	Stefano Morozzi	02/2023
8327	2^338394-192471	101867	Stefano Morozzi	02/2023
8328	2^338390+76627	101866	Stefano Morozzi	12/2021
8329	2^338389-85081	101866	Stefano Morozzi	06/2022
8330	2^338390+148113	101866	Stefano Morozzi	11/2022
8331	2^338389-14253	101866	Stefano Morozzi	01/2023
8332	2^338390-114297	101866	Stefano Morozzi	01/2023
8333	2^338391-64225	101866	Stefano Morozzi	01/2023
8334	2^338389-16971	101866	Stefano Morozzi	02/2023
8335	2^338387-75685	101865	Stefano Morozzi	12/2021
8336	2^338388-53459	101865	Stefano Morozzi	01/2022
8337	2^338388-36575	101865	Stefano Morozzi	12/2022
8338	2^338385-190311	101865	Stefano Morozzi	01/2023
8339	2^338384+131563	101864	Stefano Morozzi	01/2022
8340	2^338382+109069	101864	Stefano Morozzi	03/2022
8341	2^338384+168987	101864	Stefano Morozzi	09/2022
8342	2^338383-42367	101864	Stefano Morozzi	02/2023
8343	2^338380+77125	101863	Stefano Morozzi	12/2021
8344	2^338381-35539	101863	Stefano Morozzi	06/2022
8345	2^338378-125841	101862	Stefano Morozzi	12/2021
8346	2^338375+27815	101862	Stefano Morozzi	01/2022
8347	2^338375-28509	101862	Stefano Morozzi	01/2022
8348	2^338375+29985	101862	Stefano Morozzi	01/2022
8349	2^338377+157881	101862	Stefano Morozzi	02/2022
8350	2^338375+59589	101862	Stefano Morozzi	03/2022
8351	2^338378+36399	101862	Stefano Morozzi	04/2022
8352	2^338378-159773	101862	Stefano Morozzi	04/2022
8353	2^338378+14883	101862	Stefano Morozzi	05/2022
8354	2^338376+140173	101862	Stefano Morozzi	06/2022
8355	2^338375+18761	101862	Stefano Morozzi	09/2022
8356	2^338373-75103	101861	Stefano Morozzi	12/2021
8357	2^338372+128877	101861	Stefano Morozzi	01/2022
8358	2^338374-28731	101861	Stefano Morozzi	01/2022
8359	2^338374-128427	101861	Stefano Morozzi	01/2022
8360	2^338372+37875	101861	Stefano Morozzi	04/2022
8361	2^338373+161541	101861	Stefano Morozzi	04/2022
8362	2^338374+37759	101861	Stefano Morozzi	04/2022
8363	2^338372+93235	101861	Stefano Morozzi	09/2022
8364	2^338373-63273	101861	Stefano Morozzi	12/2022
8365	2^338369+29427	101860	Stefano Morozzi	01/2022
8366	2^338370+179133	101860	Stefano Morozzi	01/2022
8367	2^338369+131501	101860	Stefano Morozzi	01/2022
8368	2^338369+181649	101860	Stefano Morozzi	02/2022
8369	2^338370-4787	101860	Stefano Morozzi	02/2022
8370	2^338371-133491	101860	Stefano Morozzi	04/2022
8371	2^338371+42023	101860	Stefano Morozzi	09/2022
8372	2^338371+145323	101860	Stefano Morozzi	11/2022
8373	2^338371-138145	101860	Stefano Morozzi	12/2022
8380	2^338368-20369	101859	Enzo Doria	06/2013
8381	2^338366+74179	101859	Enzo Doria	04/2016
8374	2^338366+53853	101859	Stefano Morozzi	01/2022
8375	2^338365-31665	101859	Stefano Morozzi	03/2022
8376	2^338368-156345	101859	Stefano Morozzi	03/2022
8377	2^338366-159867	101859	Stefano Morozzi	04/2022
8378	2^338368-63509	101859	Stefano Morozzi	12/2022
8379	2^338365-190975	101859	Stefano Morozzi	01/2023
8382	2^338362-180845	101858	Stefano Morozzi	02/2022
8383	2^338364-155769	101858	Stefano Morozzi	02/2022
8384	2^338362+142843	101858	Stefano Morozzi	09/2022
8385	2^338362+170019	101858	Stefano Morozzi	11/2022
8386	2^338361-100875	101857	Stefano Morozzi	12/2021
8387	2^338361+154169	101857	Stefano Morozzi	01/2022
8388	2^338359-189645	101857	Stefano Morozzi	01/2023
8389	2^338356+101271	101856	Stefano Morozzi	12/2021
8390	2^338356+53383	101856	Stefano Morozzi	01/2022
8391	2^338355+59393	101856	Stefano Morozzi	03/2022
8392	2^338356+60775	101856	Stefano Morozzi	03/2022
8393	2^338356-106257	101856	Stefano Morozzi	03/2022
8394	2^338357-58921	101856	Stefano Morozzi	04/2022
8395	2^338356+94605	101856	Stefano Morozzi	09/2022
8396	2^338356+117813	101856	Stefano Morozzi	09/2022
8397	2^338358-38475	101856	Stefano Morozzi	12/2022
8398	2^338353-190291	101855	Stefano Morozzi	01/2023
8399	2^338350-152933	101854	Stefano Morozzi	01/2022
8400	2^338350+6337	101854	Stefano Morozzi	01/2022
8401	2^338350+168759	101854	Stefano Morozzi	09/2022
8404	27088^5755+5755^27088	101853	Hans Havermann	01/2019
8402	2^338347+125901	101853	Stefano Morozzi	11/2021
8403	2^338346-10643	101853	Stefano Morozzi	06/2022
8405	2^338343+152271	101852	Stefano Morozzi	12/2021
8406	2^338345+154107	101852	Stefano Morozzi	01/2022
8407	2^338342+155397	101852	Stefano Morozzi	01/2022
8408	2^338342-130767	101852	Stefano Morozzi	02/2022
8409	2^338345-30123	101852	Stefano Morozzi	02/2022
8410	2^338345+35747	101852	Stefano Morozzi	03/2022
8411	2^338345-133131	101852	Stefano Morozzi	04/2022
8412	2^338345-134559	101852	Stefano Morozzi	04/2022
8413	2^338342+170073	101852	Stefano Morozzi	11/2022
8414	2^338344+46567	101852	Stefano Morozzi	11/2022
8415	2^338344+97141	101852	Stefano Morozzi	11/2022
8416	2^338342-162213	101852	Stefano Morozzi	12/2022
8417	2^338339+2753	101851	Stefano Morozzi	12/2021
8418	2^338341+128415	101851	Stefano Morozzi	01/2022
8419	2^338338+2677	101850	Stefano Morozzi	12/2021
8420	2^338336+54607	101850	Stefano Morozzi	01/2022
8421	2^338338+109999	101850	Stefano Morozzi	03/2022
8422	2^338336+161575	101850	Stefano Morozzi	04/2022
8423	2^338335+51975	101849	Stefano Morozzi	12/2021
8424	2^338335-152607	101849	Stefano Morozzi	01/2022
8425	2^338334+55273	101849	Stefano Morozzi	01/2022
8426	2^338332+34315	101849	Stefano Morozzi	03/2022
8427	2^338335+158759	101849	Stefano Morozzi	03/2022
8428	2^338332+67621	101849	Stefano Morozzi	09/2022
8429	2^338332-66099	101849	Stefano Morozzi	01/2023
8430	2^338334-191043	101849	Stefano Morozzi	01/2023
8431	2^338331+83403	101848	Stefano Morozzi	02/2022
8432	2^338330-110865	101848	Stefano Morozzi	06/2022
8433	2^338330+71047	101848	Stefano Morozzi	11/2022
8434	2^338328-5295	101847	Stefano Morozzi	02/2022
8435	2^338327+143585	101847	Stefano Morozzi	09/2022
8436	2^338324-179667	101846	Stefano Morozzi	02/2022
8437	2^338322+21903	101846	Stefano Morozzi	11/2022
8438	2^338324+98047	101846	Stefano Morozzi	11/2022
8439	2^338323-87729	101846	Stefano Morozzi	12/2022
8440	2^338322-16667	101846	Stefano Morozzi	01/2023
8441	2^338325-142159	101846	Stefano Morozzi	02/2023
8442	2^338316-175857	101844	Stefano Morozzi	12/2021
8443	2^338318+54405	101844	Stefano Morozzi	01/2022
8444	2^338316+32961	101844	Stefano Morozzi	02/2022
8445	2^338317+68175	101844	Stefano Morozzi	09/2022
8446	2^338318-86171	101844	Stefano Morozzi	12/2022
8447	2^338315-178635	101843	Stefano Morozzi	01/2022
8448	2^338315+34899	101843	Stefano Morozzi	03/2022
8449	2^338314-106973	101843	Stefano Morozzi	03/2022
8450	2^338313+170411	101843	Stefano Morozzi	11/2022
8451	2^338315-88807	101843	Stefano Morozzi	12/2022
8452	2^338311-51799	101842	Stefano Morozzi	12/2021
8453	2^338309+157259	101842	Stefano Morozzi	02/2022
8454	2^338310+40903	101842	Stefano Morozzi	06/2022
8455	2^338309-168051	101842	Stefano Morozzi	02/2023
8456	2^338308-55853	101841	Stefano Morozzi	02/2022
8457	2^338307+134871	101841	Stefano Morozzi	03/2022
8458	2^338307+19689	101841	Stefano Morozzi	09/2022
8459	2^338308+66873	101841	Stefano Morozzi	09/2022
8460	2^338306+124399	101841	Stefano Morozzi	02/2023
8461	2^338306-91913	101841	Stefano Morozzi	02/2023
8462	2^338304+78757	101840	Stefano Morozzi	01/2022
8463	2^338304-5807	101840	Stefano Morozzi	02/2022
8464	2^338305+110879	101840	Stefano Morozzi	03/2022
8465	2^338304+91147	101840	Stefano Morozzi	06/2022
8466	2^338304-64475	101840	Stefano Morozzi	01/2023
8467	2^338299+85611	101839	Stefano Morozzi	03/2022
8468	2^338299-189985	101839	Stefano Morozzi	01/2023
8469	2^338298-25571	101838	Stefano Morozzi	12/2021
8470	2^338297+35547	101838	Stefano Morozzi	03/2022
8471	2^338298+111199	101838	Stefano Morozzi	03/2022
8472	2^338297+145455	101838	Stefano Morozzi	11/2022
8473	2^338297-166285	101838	Stefano Morozzi	01/2023
8474	2^338294-150711	101837	Stefano Morozzi	12/2021
8475	2^338294+177597	101837	Stefano Morozzi	12/2021
8476	2^338294-177807	101837	Stefano Morozzi	01/2022
8477	2^338295-52929	101837	Stefano Morozzi	01/2022
8478	2^338293+37407	101837	Stefano Morozzi	04/2022
8479	2^338292+40573	101837	Stefano Morozzi	06/2022
8480	2^338294+172425	101837	Stefano Morozzi	11/2022
8481	2^338293-191799	101837	Stefano Morozzi	02/2023
8482	2^338289+30957	101836	Stefano Morozzi	01/2022
8483	2^338291+131825	101836	Stefano Morozzi	02/2022
8484	2^338291+110111	101836	Stefano Morozzi	03/2022
8485	2^338290-156423	101836	Stefano Morozzi	03/2022
8486	2^338291-157845	101836	Stefano Morozzi	03/2022
8487	2^338290+69243	101836	Stefano Morozzi	09/2022
8488	2^338291-189327	101836	Stefano Morozzi	01/2023
8489	2^338291+74079	101836	Stefano Morozzi	02/2023
8490	2^338288+26623	101835	Stefano Morozzi	12/2021
8491	2^338286+33325	101835	Stefano Morozzi	02/2022
8492	2^338287+132633	101835	Stefano Morozzi	02/2022
8493	2^338287+157149	101835	Stefano Morozzi	02/2022
8494	2^338288-107193	101835	Stefano Morozzi	03/2022
8495	2^338286-83333	101835	Stefano Morozzi	04/2022
8496	2^338287+114425	101835	Stefano Morozzi	05/2022
8497	2^338288+194403	101835	Stefano Morozzi	09/2022
8498	2^338288-113177	101835	Stefano Morozzi	12/2022
8499	2^338288-65747	101835	Stefano Morozzi	01/2023
8500	2^338285+82131	101834	Stefano Morozzi	02/2022

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Probable Primes Top 10000

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