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	2^338564+41965	101918	Stefano Morozzi	09/2022
8252	2^338561+121139	101918	Stefano Morozzi	11/2022
8253	2^338562+21799	101918	Stefano Morozzi	11/2022
8261	2^338559-1858777	101917	Enzo Doria	04/2016
8254	2^338558+4825	101917	Stefano Morozzi	01/2022
8255	2^338559-127935	101917	Stefano Morozzi	01/2022
8256	2^338560+154891	101917	Stefano Morozzi	01/2022
8257	2^338559+131885	101917	Stefano Morozzi	02/2022
8258	2^338558+93735	101917	Stefano Morozzi	09/2022
8259	2^338559-90957	101917	Stefano Morozzi	01/2023
8260	2^338559-190761	101917	Stefano Morozzi	01/2023
8262	2^338555+189981	101916	Stefano Morozzi	05/2022
8263	2^338553-125383	101915	Stefano Morozzi	12/2021
8264	2^338554-82821	101915	Stefano Morozzi	03/2022
8265	2^338548+76923	101914	Stefano Morozzi	12/2021
8266	2^338549+158517	101914	Stefano Morozzi	03/2022
8267	2^338549+85397	101914	Stefano Morozzi	03/2022
8268	2^338548+138121	101914	Stefano Morozzi	05/2022
8269	2^338550-110301	101914	Stefano Morozzi	06/2022
8270	2^338547+129321	101913	Stefano Morozzi	01/2022
8271	2^338547-153481	101913	Stefano Morozzi	01/2022
8272	2^338545-11059	101913	Stefano Morozzi	12/2022
8273	2^338544+107853	101912	Stefano Morozzi	02/2022
8274	2^338542+172813	101912	Stefano Morozzi	11/2022
8275	2^338544-12687	101912	Stefano Morozzi	12/2022
8276	2^338543-140677	101912	Stefano Morozzi	01/2023
8277	2^338541+152721	101911	Stefano Morozzi	01/2022
8278	2^338539+60825	101911	Stefano Morozzi	03/2022
8279	2^338539+160881	101911	Stefano Morozzi	03/2022
8280	2^338541-182523	101911	Stefano Morozzi	03/2022
8281	2^338540+87645	101911	Stefano Morozzi	04/2022
8282	2^338541+148305	101911	Stefano Morozzi	11/2022
8283	2^338541-163075	101911	Stefano Morozzi	12/2022
8284	2^338536-100785	101910	Stefano Morozzi	12/2021
8285	2^338535-51837	101910	Stefano Morozzi	12/2021
8286	2^338535-158745	101910	Stefano Morozzi	04/2022
8287	2^338536-189977	101910	Stefano Morozzi	01/2023
8288	2^338537-65623	101910	Stefano Morozzi	01/2023
8289	2^338532+39445	101909	Stefano Morozzi	05/2022
8290	2^338532+141415	101909	Stefano Morozzi	06/2022
8291	2^338532-136037	101909	Stefano Morozzi	06/2022
8292	2^338531+81081	101908	Stefano Morozzi	01/2022
8293	2^338530+59835	101908	Stefano Morozzi	03/2022
8294	2^338529+186551	101908	Stefano Morozzi	04/2022
8295	2^338531+61313	101908	Stefano Morozzi	04/2022
8296	2^338531-9277	101908	Stefano Morozzi	04/2022
8297	2^338528-92727	101908	Stefano Morozzi	02/2023
8298	2^338527+191205	101907	Stefano Morozzi	06/2022
8299	2^338525+99621	101907	Stefano Morozzi	02/2023
8300	2^338524+54421	101906	Stefano Morozzi	01/2022
8301	2^338522-155811	101906	Stefano Morozzi	02/2022
8302	2^338523-16291	101906	Stefano Morozzi	01/2023
8303	2^338522-142137	101906	Stefano Morozzi	02/2023
8304	2^338521+183131	101905	Stefano Morozzi	02/2022
8305	2^338520+34945	101905	Stefano Morozzi	03/2022
8306	2^338518-182885	101905	Stefano Morozzi	04/2022
8307	2^338518+114633	101905	Stefano Morozzi	05/2022
8308	2^338518-12621	101905	Stefano Morozzi	12/2022
8309	2^338518-187325	101905	Stefano Morozzi	12/2022
8317	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
8310	2^338517-125955	101904	Stefano Morozzi	12/2021
8311	2^338517+126437	101904	Stefano Morozzi	12/2021
8312	2^338517-53499	101904	Stefano Morozzi	01/2022
8313	2^338515+30369	101904	Stefano Morozzi	01/2022
8314	2^338517-184623	101904	Stefano Morozzi	04/2022
8315	2^338515+89333	101904	Stefano Morozzi	05/2022
8316	2^338515+198813	101904	Stefano Morozzi	02/2023
8320	24502^14419+14419^24502	101903	Hans Havermann	01/2019
8318	2^338512-827	101903	Stefano Morozzi	12/2021
8319	2^338514-6611	101903	Stefano Morozzi	03/2022
8321	2^338509+5139	101902	Stefano Morozzi	01/2022
8322	2^338509+40205	101902	Stefano Morozzi	06/2022
8323	2^338511+19959	101902	Stefano Morozzi	09/2022
8324	2^338510-37877	101902	Stefano Morozzi	12/2022
8325	2^338507-188655	101901	Stefano Morozzi	12/2022
8326	2^338507-114457	101901	Stefano Morozzi	01/2023
8327	2^338504-152615	101900	Stefano Morozzi	01/2022
8328	2^338502-4587	101900	Stefano Morozzi	02/2022
8329	2^338502-166275	101900	Stefano Morozzi	01/2023
8330	2^338500-26865	101899	Stefano Morozzi	12/2021
8331	2^338501-177471	101899	Stefano Morozzi	12/2021
8332	2^338499-3915	101899	Stefano Morozzi	01/2022
8333	2^338501+32051	101899	Stefano Morozzi	02/2022
8334	2^338499+183533	101899	Stefano Morozzi	03/2022
8335	2^338500+35625	101899	Stefano Morozzi	03/2022
8336	2^338499+87579	101899	Stefano Morozzi	04/2022
8337	2^338498-117683	101899	Stefano Morozzi	02/2023
8340	2^338497-17041	101898	Enzo Doria	05/2013
8338	2^338497+150405	101898	Stefano Morozzi	11/2021
8339	2^338495+100533	101898	Stefano Morozzi	12/2021
8341	2^338494+36057	101897	Stefano Morozzi	03/2022
8342	2^338492+39015	101897	Stefano Morozzi	05/2022
8343	2^338494+168007	101897	Stefano Morozzi	09/2022
8344	2^338490+61149	101896	Stefano Morozzi	03/2022
8345	2^338489+161369	101896	Stefano Morozzi	04/2022
8346	2^338491+22961	101896	Stefano Morozzi	11/2022
8347	2^338487-3555	101895	Stefano Morozzi	01/2022
8348	2^338487-183129	101895	Stefano Morozzi	04/2022
8349	2^338484+128767	101894	Stefano Morozzi	01/2022
8350	2^338484-31895	101894	Stefano Morozzi	03/2022
8351	2^338483-67899	101894	Stefano Morozzi	02/2023
8352	2^338483-192129	101894	Stefano Morozzi	02/2023
8353	2^338478+10893	101893	Stefano Morozzi	03/2022
8354	2^338479+87243	101893	Stefano Morozzi	04/2022
8355	2^338479+167619	101893	Stefano Morozzi	09/2022
8356	2^338480+197503	101893	Stefano Morozzi	11/2022
8357	2^338481-11421	101893	Stefano Morozzi	12/2022
8358	2^338479-89649	101893	Stefano Morozzi	01/2023
8359	(29*34^66532-12833)/33	101893	Eric Chen	03/2023
8362	2^338475+54615	101892	Lelio R Paula	10/2016
8360	2^338475-59775	101892	Stefano Morozzi	04/2022
8361	2^338476-134237	101892	Stefano Morozzi	04/2022
8363	2^338474+100767	101891	Stefano Morozzi	11/2021
8364	2^338474+81165	101891	Stefano Morozzi	01/2022
8365	2^338474+41137	101891	Stefano Morozzi	06/2022
8366	2^338472-110445	101891	Stefano Morozzi	06/2022
8367	2^338473-89535	101891	Stefano Morozzi	01/2023
8368	2^338470+27777	101890	Stefano Morozzi	01/2022
8369	2^338468+31351	101890	Stefano Morozzi	01/2022
8370	2^338469-106339	101890	Stefano Morozzi	03/2022
8371	2^338471+187469	101890	Stefano Morozzi	04/2022
8372	2^338468+96613	101890	Stefano Morozzi	11/2022
8373	2^338469+46167	101890	Stefano Morozzi	11/2022
8374	2^338470+71527	101890	Stefano Morozzi	11/2022
8375	2^338469-112783	101890	Stefano Morozzi	12/2022
8376	2^338470-115665	101890	Stefano Morozzi	01/2023
8377	2^338467-25665	101889	Stefano Morozzi	12/2021
8378	2^338465+152139	101889	Stefano Morozzi	12/2021
8379	2^338466-28643	101889	Stefano Morozzi	01/2022
8380	2^338465+181517	101889	Stefano Morozzi	01/2022
8381	2^338466+115917	101889	Stefano Morozzi	06/2022
8382	2^338465-88291	101889	Stefano Morozzi	12/2022
8383	2^338464-104009	101888	Stefano Morozzi	02/2022
8384	2^338463+185169	101888	Stefano Morozzi	03/2022
8385	2^338464+60595	101888	Stefano Morozzi	03/2022
8386	2^338464-66377	101888	Stefano Morozzi	01/2023
8387	2^338458+60273	101887	Stefano Morozzi	03/2022
8388	2^338461+135867	101887	Stefano Morozzi	03/2022
8389	2^338455-4621	101886	Stefano Morozzi	02/2022
8390	2^338457+187827	101886	Stefano Morozzi	04/2022
8391	2^338455+173349	101886	Stefano Morozzi	11/2022
8392	2^338454+133737	101885	Stefano Morozzi	03/2022
8393	2^338454-158501	101885	Stefano Morozzi	04/2022
8394	2^338454-184217	101885	Stefano Morozzi	04/2022
8395	2^338453+164451	101885	Stefano Morozzi	05/2022
8396	2^338452-136137	101885	Stefano Morozzi	12/2022
8397	2^338450+106275	101884	Stefano Morozzi	01/2022
8398	2^338450+168439	101884	Stefano Morozzi	09/2022
8399	(133*10^101881+17)/3	101883	Robert Price	11/2021
8400	2^338445-80461	101883	Stefano Morozzi	02/2022
8401	2^338446-131211	101883	Stefano Morozzi	02/2022
8402	2^338448+187167	101883	Stefano Morozzi	04/2022
8403	2^338446-160115	101883	Stefano Morozzi	06/2022
8404	2^338447-164157	101883	Stefano Morozzi	01/2023
8405	2^338447-191001	101883	Stefano Morozzi	01/2023
8406	2^338444+127623	101882	Stefano Morozzi	12/2021
8407	2^338443-113827	101882	Stefano Morozzi	12/2022
8408	2^338441-5893	101881	Stefano Morozzi	02/2022
8409	2^338439-162565	101881	Stefano Morozzi	12/2022
8410	2^338436+153657	101880	Stefano Morozzi	01/2022
8411	2^338437-153159	101880	Stefano Morozzi	01/2022
8412	2^338436-83783	101880	Stefano Morozzi	04/2022
8413	2^338435+89109	101880	Stefano Morozzi	05/2022
8414	2^338435+13871	101880	Stefano Morozzi	05/2022
8415	2^338436+149691	101880	Stefano Morozzi	02/2023
8416	2^338434+81537	101879	Stefano Morozzi	01/2022
8417	2^338432+33495	101879	Stefano Morozzi	03/2022
8418	2^338432-7043	101879	Stefano Morozzi	03/2022
8419	2^338433-32629	101879	Stefano Morozzi	03/2022
8420	2^338430-9903	101878	Stefano Morozzi	04/2022
8428	2^338426-19797	101877	Enzo Doria	06/2013
8421	2^338427-77797	101877	Stefano Morozzi	01/2022
8422	2^338427-178687	101877	Stefano Morozzi	01/2022
8423	2^338428-54873	101877	Stefano Morozzi	02/2022
8424	2^338425+41357	101877	Stefano Morozzi	06/2022
8425	2^338428+90855	101877	Stefano Morozzi	06/2022
8426	2^338428-39807	101877	Stefano Morozzi	01/2023
8427	2^338425-192381	101877	Stefano Morozzi	02/2023
8429	2^338422-188787	101876	Stefano Morozzi	12/2022
8430	2^338423-187755	101876	Stefano Morozzi	12/2022
8431	2^338422-115865	101876	Stefano Morozzi	01/2023
8432	2^338420-178829	101875	Stefano Morozzi	01/2022
8433	2^338421-105423	101875	Stefano Morozzi	02/2022
8434	2^338419-82761	101875	Stefano Morozzi	03/2022
8435	2^338420+193143	101875	Stefano Morozzi	09/2022
8436	2^338419+199641	101875	Stefano Morozzi	02/2023
8437	2^338420-143103	101875	Stefano Morozzi	02/2023
8438	2^338418-50903	101874	Stefano Morozzi	12/2021
8439	2^338418+158355	101874	Stefano Morozzi	02/2022
8440	2^338418+159339	101874	Stefano Morozzi	03/2022
8441	2^338416+14953	101874	Stefano Morozzi	05/2022
8442	2^338416+166051	101874	Stefano Morozzi	06/2022
8443	2^338418-138765	101874	Stefano Morozzi	12/2022
8444	2^338417+49737	101874	Stefano Morozzi	02/2023
8445	2^338413-125919	101873	Stefano Morozzi	12/2021
8446	2^338414+26083	101873	Stefano Morozzi	12/2021
8447	2^338412-152379	101873	Stefano Morozzi	12/2021
8448	2^338413+54797	101873	Stefano Morozzi	01/2022
8449	2^338412+157951	101873	Stefano Morozzi	02/2022
8450	2^338414+81627	101873	Stefano Morozzi	02/2022
8451	2^338413+133679	101873	Stefano Morozzi	03/2022
8452	2^338413+197735	101873	Stefano Morozzi	11/2022
8453	2^338413-114301	101873	Stefano Morozzi	01/2023
8454	11*32^67682+395	101873	Eric Chen	04/2023
8455	2^338409-52183	101872	Stefano Morozzi	12/2021
8456	2^338411-3789	101872	Stefano Morozzi	01/2022
8457	2^338409+173237	101872	Stefano Morozzi	11/2022
8458	2^338406-184175	101871	Stefano Morozzi	04/2022
8459	2^338405+94451	101871	Stefano Morozzi	09/2022
8460	2^338406-161217	101871	Stefano Morozzi	12/2022
8461	2^338406+199929	101871	Stefano Morozzi	02/2023
8462	2^338404+55717	101870	Stefano Morozzi	01/2022
8463	2^338403+36261	101870	Stefano Morozzi	04/2022
8464	2^338402-34431	101870	Stefano Morozzi	04/2022
8465	2^338404-159215	101870	Stefano Morozzi	04/2022
8466	2^338403+18363	101870	Stefano Morozzi	09/2022
8467	2^338403+170235	101870	Stefano Morozzi	11/2022
8468	2^338399+23045	101869	Stefano Morozzi	11/2022
8469	2^338399-65535	101869	Stefano Morozzi	01/2023
8470	2^338395-127449	101868	Stefano Morozzi	12/2021
8471	2^338398-127637	101868	Stefano Morozzi	01/2022
8472	2^338398-166533	101868	Stefano Morozzi	01/2023
8473	2^338394+100317	101867	Stefano Morozzi	11/2021
8474	2^338393-152749	101867	Stefano Morozzi	01/2022
8475	2^338393+163025	101867	Stefano Morozzi	04/2022
8476	2^338393+89229	101867	Stefano Morozzi	05/2022
8477	2^338393+99647	101867	Stefano Morozzi	02/2023
8478	2^338394-192471	101867	Stefano Morozzi	02/2023
8479	2^338390+76627	101866	Stefano Morozzi	12/2021
8480	2^338389-85081	101866	Stefano Morozzi	06/2022
8481	2^338390+148113	101866	Stefano Morozzi	11/2022
8482	2^338389-14253	101866	Stefano Morozzi	01/2023
8483	2^338390-114297	101866	Stefano Morozzi	01/2023
8484	2^338391-64225	101866	Stefano Morozzi	01/2023
8485	2^338389-16971	101866	Stefano Morozzi	02/2023
8486	2^338387-75685	101865	Stefano Morozzi	12/2021
8487	2^338388-53459	101865	Stefano Morozzi	01/2022
8488	2^338388-36575	101865	Stefano Morozzi	12/2022
8489	2^338385-190311	101865	Stefano Morozzi	01/2023
8490	2^338384+131563	101864	Stefano Morozzi	01/2022
8491	2^338382+109069	101864	Stefano Morozzi	03/2022
8492	2^338384+168987	101864	Stefano Morozzi	09/2022
8493	2^338383-42367	101864	Stefano Morozzi	02/2023
8494	2^338380+77125	101863	Stefano Morozzi	12/2021
8495	2^338381-35539	101863	Stefano Morozzi	06/2022
8496	2^338378-125841	101862	Stefano Morozzi	12/2021
8497	2^338375+27815	101862	Stefano Morozzi	01/2022
8498	2^338375-28509	101862	Stefano Morozzi	01/2022
8499	2^338375+29985	101862	Stefano Morozzi	01/2022
8500	2^338377+157881	101862	Stefano Morozzi	02/2022

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Probable Primes Top 10000

(295932 PRPs in the top)