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	2^338357-58921	101856	Stefano Morozzi	04/2022
8252	2^338356+94605	101856	Stefano Morozzi	09/2022
8253	2^338356+117813	101856	Stefano Morozzi	09/2022
8254	2^338358-38475	101856	Stefano Morozzi	12/2022
8255	2^338353-190291	101855	Stefano Morozzi	01/2023
8256	2^338350-152933	101854	Stefano Morozzi	01/2022
8257	2^338350+6337	101854	Stefano Morozzi	01/2022
8258	2^338350+168759	101854	Stefano Morozzi	09/2022
8261	27088^5755+5755^27088	101853	Hans Havermann	01/2019
8259	2^338347+125901	101853	Stefano Morozzi	11/2021
8260	2^338346-10643	101853	Stefano Morozzi	06/2022
8262	2^338343+152271	101852	Stefano Morozzi	12/2021
8263	2^338345+154107	101852	Stefano Morozzi	01/2022
8264	2^338342+155397	101852	Stefano Morozzi	01/2022
8265	2^338342-130767	101852	Stefano Morozzi	02/2022
8266	2^338345-30123	101852	Stefano Morozzi	02/2022
8267	2^338345+35747	101852	Stefano Morozzi	03/2022
8268	2^338345-133131	101852	Stefano Morozzi	04/2022
8269	2^338345-134559	101852	Stefano Morozzi	04/2022
8270	2^338342+170073	101852	Stefano Morozzi	11/2022
8271	2^338344+46567	101852	Stefano Morozzi	11/2022
8272	2^338344+97141	101852	Stefano Morozzi	11/2022
8273	2^338342-162213	101852	Stefano Morozzi	12/2022
8274	2^338339+2753	101851	Stefano Morozzi	12/2021
8275	2^338341+128415	101851	Stefano Morozzi	01/2022
8276	2^338338+2677	101850	Stefano Morozzi	12/2021
8277	2^338336+54607	101850	Stefano Morozzi	01/2022
8278	2^338338+109999	101850	Stefano Morozzi	03/2022
8279	2^338336+161575	101850	Stefano Morozzi	04/2022
8280	2^338335+51975	101849	Stefano Morozzi	12/2021
8281	2^338335-152607	101849	Stefano Morozzi	01/2022
8282	2^338334+55273	101849	Stefano Morozzi	01/2022
8283	2^338332+34315	101849	Stefano Morozzi	03/2022
8284	2^338335+158759	101849	Stefano Morozzi	03/2022
8285	2^338332+67621	101849	Stefano Morozzi	09/2022
8286	2^338332-66099	101849	Stefano Morozzi	01/2023
8287	2^338334-191043	101849	Stefano Morozzi	01/2023
8288	2^338331+83403	101848	Stefano Morozzi	02/2022
8289	2^338330-110865	101848	Stefano Morozzi	06/2022
8290	2^338330+71047	101848	Stefano Morozzi	11/2022
8291	2^338328-5295	101847	Stefano Morozzi	02/2022
8292	2^338327+143585	101847	Stefano Morozzi	09/2022
8293	2^338324-179667	101846	Stefano Morozzi	02/2022
8294	2^338322+21903	101846	Stefano Morozzi	11/2022
8295	2^338324+98047	101846	Stefano Morozzi	11/2022
8296	2^338323-87729	101846	Stefano Morozzi	12/2022
8297	2^338322-16667	101846	Stefano Morozzi	01/2023
8298	2^338325-142159	101846	Stefano Morozzi	02/2023
8299	2^338316-175857	101844	Stefano Morozzi	12/2021
8300	2^338318+54405	101844	Stefano Morozzi	01/2022
8301	2^338316+32961	101844	Stefano Morozzi	02/2022
8302	2^338317+68175	101844	Stefano Morozzi	09/2022
8303	2^338318-86171	101844	Stefano Morozzi	12/2022
8304	2^338315-178635	101843	Stefano Morozzi	01/2022
8305	2^338315+34899	101843	Stefano Morozzi	03/2022
8306	2^338314-106973	101843	Stefano Morozzi	03/2022
8307	2^338313+170411	101843	Stefano Morozzi	11/2022
8308	2^338315-88807	101843	Stefano Morozzi	12/2022
8309	2^338311-51799	101842	Stefano Morozzi	12/2021
8310	2^338309+157259	101842	Stefano Morozzi	02/2022
8311	2^338310+40903	101842	Stefano Morozzi	06/2022
8312	2^338309-168051	101842	Stefano Morozzi	02/2023
8313	2^338308-55853	101841	Stefano Morozzi	02/2022
8314	2^338307+134871	101841	Stefano Morozzi	03/2022
8315	2^338307+19689	101841	Stefano Morozzi	09/2022
8316	2^338308+66873	101841	Stefano Morozzi	09/2022
8317	2^338306+124399	101841	Stefano Morozzi	02/2023
8318	2^338306-91913	101841	Stefano Morozzi	02/2023
8319	2^338304+78757	101840	Stefano Morozzi	01/2022
8320	2^338304-5807	101840	Stefano Morozzi	02/2022
8321	2^338305+110879	101840	Stefano Morozzi	03/2022
8322	2^338304+91147	101840	Stefano Morozzi	06/2022
8323	2^338304-64475	101840	Stefano Morozzi	01/2023
8324	2^338299+85611	101839	Stefano Morozzi	03/2022
8325	2^338299-189985	101839	Stefano Morozzi	01/2023
8326	2^338298-25571	101838	Stefano Morozzi	12/2021
8327	2^338297+35547	101838	Stefano Morozzi	03/2022
8328	2^338298+111199	101838	Stefano Morozzi	03/2022
8329	2^338297+145455	101838	Stefano Morozzi	11/2022
8330	2^338297-166285	101838	Stefano Morozzi	01/2023
8331	2^338294-150711	101837	Stefano Morozzi	12/2021
8332	2^338294+177597	101837	Stefano Morozzi	12/2021
8333	2^338294-177807	101837	Stefano Morozzi	01/2022
8334	2^338295-52929	101837	Stefano Morozzi	01/2022
8335	2^338293+37407	101837	Stefano Morozzi	04/2022
8336	2^338292+40573	101837	Stefano Morozzi	06/2022
8337	2^338294+172425	101837	Stefano Morozzi	11/2022
8338	2^338293-191799	101837	Stefano Morozzi	02/2023
8339	2^338289+30957	101836	Stefano Morozzi	01/2022
8340	2^338291+131825	101836	Stefano Morozzi	02/2022
8341	2^338291+110111	101836	Stefano Morozzi	03/2022
8342	2^338290-156423	101836	Stefano Morozzi	03/2022
8343	2^338291-157845	101836	Stefano Morozzi	03/2022
8344	2^338290+69243	101836	Stefano Morozzi	09/2022
8345	2^338291-189327	101836	Stefano Morozzi	01/2023
8346	2^338291+74079	101836	Stefano Morozzi	02/2023
8347	2^338288+26623	101835	Stefano Morozzi	12/2021
8348	2^338286+33325	101835	Stefano Morozzi	02/2022
8349	2^338287+132633	101835	Stefano Morozzi	02/2022
8350	2^338287+157149	101835	Stefano Morozzi	02/2022
8351	2^338288-107193	101835	Stefano Morozzi	03/2022
8352	2^338286-83333	101835	Stefano Morozzi	04/2022
8353	2^338287+114425	101835	Stefano Morozzi	05/2022
8354	2^338288+194403	101835	Stefano Morozzi	09/2022
8355	2^338288-113177	101835	Stefano Morozzi	12/2022
8356	2^338288-65747	101835	Stefano Morozzi	01/2023
8357	2^338285+82131	101834	Stefano Morozzi	02/2022
8358	2^338284-104217	101834	Stefano Morozzi	02/2022
8359	2^338282-84533	101834	Stefano Morozzi	04/2022
8360	2^338283+67545	101834	Stefano Morozzi	09/2022
8361	2^338283-65439	101834	Stefano Morozzi	01/2023
8370	2^338280-19745	101833	Enzo Doria	06/2013
8362	2^338279-125947	101833	Stefano Morozzi	12/2021
8363	2^338280-50343	101833	Stefano Morozzi	12/2021
8364	2^338279+133331	101833	Stefano Morozzi	02/2022
8365	2^338281-54561	101833	Stefano Morozzi	02/2022
8366	2^338280+192063	101833	Stefano Morozzi	09/2022
8367	2^338281+18971	101833	Stefano Morozzi	09/2022
8368	2^338281-186711	101833	Stefano Morozzi	12/2022
8369	2^338281-91273	101833	Stefano Morozzi	01/2023
8371	2^338278+188215	101832	Stefano Morozzi	05/2022
8372	2^338273+181101	101831	Stefano Morozzi	01/2022
8373	2^338275+32909	101831	Stefano Morozzi	02/2022
8374	2^338272+166431	101831	Stefano Morozzi	06/2022
8375	2^338272+22011	101831	Stefano Morozzi	11/2022
8376	2^338275+148271	101831	Stefano Morozzi	11/2022
8377	2^338270-135725	101830	Stefano Morozzi	06/2022
8378	2^338269-136951	101830	Stefano Morozzi	12/2022
8379	2^338270-192701	101830	Stefano Morozzi	02/2023
8380	2^338271-42831	101830	Stefano Morozzi	02/2023
8381	2^338266+110665	101829	Stefano Morozzi	03/2022
8382	2^338267+110481	101829	Stefano Morozzi	03/2022
8383	2^338267-166035	101829	Stefano Morozzi	01/2023
8384	2^338265-154893	101828	Stefano Morozzi	02/2022
8385	2^338264+163611	101828	Stefano Morozzi	05/2022
8386	2^338263-62767	101828	Stefano Morozzi	12/2022
8387	2^338261-188119	101827	Stefano Morozzi	12/2022
8388	2^338259-40327	101827	Stefano Morozzi	01/2023
8389	2^338256+5223	101826	Stefano Morozzi	01/2022
8390	2^338257+178425	101826	Stefano Morozzi	01/2022
8391	2^338256-180569	101826	Stefano Morozzi	02/2022
8392	2^338257-5965	101826	Stefano Morozzi	02/2022
8393	2^338258-9225	101826	Stefano Morozzi	04/2022
8394	2^338255-127021	101825	Stefano Morozzi	12/2021
8395	2^338253+159005	101825	Stefano Morozzi	03/2022
8396	2^338253+64817	101825	Stefano Morozzi	05/2022
8397	2^338254-85403	101825	Stefano Morozzi	06/2022
8398	2^338254+142947	101825	Stefano Morozzi	09/2022
8399	2^338253+121095	101825	Stefano Morozzi	11/2022
8400	2^338254+196725	101825	Stefano Morozzi	11/2022
8401	2^338254-91007	101825	Stefano Morozzi	01/2023
8402	2^338251+78975	101824	Stefano Morozzi	01/2022
8403	2^338252-178709	101824	Stefano Morozzi	01/2022
8404	2^338252+129703	101824	Stefano Morozzi	01/2022
8405	2^338252+132285	101824	Stefano Morozzi	02/2022
8406	2^338251-33381	101824	Stefano Morozzi	04/2022
8407	2^338252-13805	101824	Stefano Morozzi	12/2022
8408	2^338245-134755	101822	Stefano Morozzi	04/2022
8409	2^338244-59219	101822	Stefano Morozzi	04/2022
8410	2^338244-64703	101822	Stefano Morozzi	01/2023
8418	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
8411	2^338241+1391	101821	Stefano Morozzi	12/2021
8412	2^338242+151195	101821	Stefano Morozzi	12/2021
8413	2^338240-152495	101821	Stefano Morozzi	12/2021
8414	2^338240+81745	101821	Stefano Morozzi	02/2022
8415	2^338241-155551	101821	Stefano Morozzi	02/2022
8416	2^338242-108237	101821	Stefano Morozzi	04/2022
8417	2^338242+43045	101821	Stefano Morozzi	09/2022
8419	2^338238-126735	101820	Stefano Morozzi	12/2021
8420	2^338238+183855	101820	Stefano Morozzi	03/2022
8421	2^338238+141013	101820	Stefano Morozzi	06/2022
8422	2^338237+97227	101820	Stefano Morozzi	11/2022
8423	2^338238+48429	101820	Stefano Morozzi	11/2022
8424	2^338234-80925	101819	Stefano Morozzi	02/2022
8425	2^338234-154593	101819	Stefano Morozzi	02/2022
8426	2^338235-131787	101819	Stefano Morozzi	03/2022
8427	2^338233+89781	101819	Stefano Morozzi	05/2022
8428	2^338235+169971	101819	Stefano Morozzi	11/2022
8429	2^338233-113875	101819	Stefano Morozzi	12/2022
8436	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
8430	2^338232-175539	101818	Stefano Morozzi	12/2021
8431	2^338231+57345	101818	Stefano Morozzi	02/2022
8432	2^338232+36097	101818	Stefano Morozzi	03/2022
8433	2^338230+137403	101818	Stefano Morozzi	04/2022
8434	2^338231-59569	101818	Stefano Morozzi	04/2022
8435	2^338230-86633	101818	Stefano Morozzi	12/2022
8437	2^338228+159247	101817	Stefano Morozzi	03/2022
8438	2^338227-12631	101817	Stefano Morozzi	12/2022
8439	(34*10^101815+191)/9	101816	Robert Price	08/2021
8440	2^338224+185461	101816	Stefano Morozzi	03/2022
8441	2^338224+62295	101816	Stefano Morozzi	04/2022
8442	2^338225+162645	101816	Stefano Morozzi	04/2022
8443	2^338223+144209	101816	Stefano Morozzi	09/2022
8450	6^130841+103	101815	Lelio R Paula	10/2016
8444	2^338220+150405	101815	Stefano Morozzi	11/2021
8445	2^338219-4147	101815	Stefano Morozzi	01/2022
8446	2^338221+83391	101815	Stefano Morozzi	02/2022
8447	2^338221+62937	101815	Stefano Morozzi	04/2022
8448	2^338220-65697	101815	Stefano Morozzi	01/2023
8449	2^338220-139505	101815	Stefano Morozzi	01/2023
8451	2^338216+77473	101814	Stefano Morozzi	12/2021
8452	2^338218+155299	101814	Stefano Morozzi	01/2022
8453	2^338217-134745	101814	Stefano Morozzi	04/2022
8454	2^338218+73507	101814	Stefano Morozzi	11/2022
8455	2^338213-125631	101813	Stefano Morozzi	12/2021
8456	2^338215+25845	101813	Stefano Morozzi	12/2021
8457	2^338210-153537	101812	Stefano Morozzi	01/2022
8458	2^338209+60915	101812	Stefano Morozzi	03/2022
8459	2^338211-57297	101812	Stefano Morozzi	03/2022
8460	2^338211-110257	101812	Stefano Morozzi	06/2022
8461	2^338211+71549	101812	Stefano Morozzi	11/2022
8462	2^338208-178787	101811	Stefano Morozzi	01/2022
8463	2^338208+106153	101811	Stefano Morozzi	01/2022
8464	2^338207+16499	101811	Stefano Morozzi	06/2022
8465	2^338205+102471	101810	Stefano Morozzi	12/2021
8466	2^338199-176377	101809	Stefano Morozzi	12/2021
8467	2^338201-151233	101809	Stefano Morozzi	12/2021
8468	2^338202-152061	101809	Stefano Morozzi	12/2021
8469	2^338202+133785	101809	Stefano Morozzi	03/2022
8470	2^338200+135643	101809	Stefano Morozzi	03/2022
8471	2^338202+14169	101809	Stefano Morozzi	05/2022
8472	2^338202-85211	101809	Stefano Morozzi	06/2022
8473	2^338200+74265	101809	Stefano Morozzi	02/2023
8474	2^338196+121147	101808	Stefano Morozzi	11/2022
8475	2^338196+73551	101808	Stefano Morozzi	11/2022
8476	2^338194-175845	101807	Stefano Morozzi	12/2021
8477	2^338195+56771	101807	Stefano Morozzi	02/2022
8478	2^338195+162365	101807	Stefano Morozzi	04/2022
8479	2^338194+67497	101807	Stefano Morozzi	09/2022
8480	2^338193-116335	101807	Stefano Morozzi	01/2023
8481	2^338194-15585	101807	Stefano Morozzi	01/2023
8482	2^338192+130387	101806	Stefano Morozzi	01/2022
8483	2^338190+89359	101806	Stefano Morozzi	05/2022
8484	2^338189+144605	101806	Stefano Morozzi	09/2022
8485	2^338190-113537	101806	Stefano Morozzi	12/2022
8486	2^338186+127245	101805	Stefano Morozzi	12/2021
8487	2^338186-130013	101805	Stefano Morozzi	02/2022
8488	2^338186+39235	101805	Stefano Morozzi	05/2022
8489	2^338185+77315	101804	Stefano Morozzi	12/2021
8490	2^338185+102519	101804	Stefano Morozzi	12/2021
8491	2^338183-76539	101804	Stefano Morozzi	12/2021
8492	2^338185+104489	101804	Stefano Morozzi	01/2022
8493	2^338179+35361	101803	Stefano Morozzi	03/2022
8494	2^338181+64235	101803	Stefano Morozzi	05/2022
8495	2^338181+94047	101803	Stefano Morozzi	09/2022
8496	2^338180+146131	101803	Stefano Morozzi	11/2022
8497	2^338179+123399	101803	Stefano Morozzi	11/2022
8498	2^338182-42425	101803	Stefano Morozzi	02/2023
8499	2^338177+51807	101802	Stefano Morozzi	12/2021
8500	2^338177+107385	101802	Stefano Morozzi	02/2022

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Probable Primes Top 10000

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