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	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
8252	(85*10^89375-31)/9	89376	Robert Price	11/2015
8253	9*2^296870+7	89368	Lelio R Paula	08/2014
8254	100^44683-99^44683	89366	Robert Price	07/2013
8255	2^296810+76519	89349	Enzo Doria	05/2016
8256	(2747^25981-1)/2746	89342	Serge Batalov	08/2020
8257	8^98928+7^(98928+1)	89341	Robert Price	06/2016
8259	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
8258	21832^12359+12359^21832	89337	Hans Havermann	08/2020
8260	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
8261	2^296736-432149	89327	Paul Bourdelais	05/2013
8262	2^296737-112519	89327	Enzo Doria	06/2014
8263	2^296718-3645	89322	Lelio R Paula	11/2013
8264	(2^296702+2338)/2	89316	Stefano Morozzi	01/2020
8265	2^296681-16221	89310	Enzo Doria	04/2013
8266	2^296669-16513	89307	Enzo Doria	04/2013
8267	(2^296626+1282)/2	89294	Stefano Morozzi	01/2020
8268	2^296619-16357	89292	Enzo Doria	04/2013
8269	2^296614-110051	89290	Enzo Doria	04/2014
8270	(2^296601+1730)/2	89286	Stefano Morozzi	01/2020
8271	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
8272	(2*10^89279+457)/9	89279	Robert Price	01/2017
8273	(2^296568+1222)/2	89276	Stefano Morozzi	01/2020
8274	(133*10^89273+17)/3	89275	Robert Price	11/2021
8275	15^75907-28	89274	Lelio R Paula	11/2015
8276	2^296547-37	89270	Yves Minet	01/2012
8277	2^296485+191	89251	Lelio R Paula	10/2012
8278	2^296467-75	89246	Lelio R Paula	10/2012
8279	(2^296462+1674)/2	89244	Stefano Morozzi	01/2020
8280	2^296416-109535	89231	Enzo Doria	04/2014
8281	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
8282	66^49037-65	89225	Norbert Schneider	11/2014
8283	2^296377-16245	89219	Enzo Doria	04/2013
8284	2^296372-64875	89217	Lelio R Paula	11/2013
8285	5*6^114648-7	89215	Lelio R Paula	10/2014
8286	(2^296361+1262)/2	89214	Stefano Morozzi	01/2020
8287	3*10^89206+13	89207	Robert Price	08/2017
8288	7*3^186960-4	89204	Lelio R Paula	08/2014
8289	(28*10^89203+47)/3	89204	Robert Price	02/2021
8290	2^296290-112133	89193	Enzo Doria	06/2014
8291	6^114620-17003	89192	Enzo Doria	02/2013
8292	(4*10^89189+41)/9	89189	Robert Price	11/2014
8293	2^296261-161181	89184	Enzo Doria	04/2013
8294	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
8295	3^186903-10	89176	Robert Price	09/2013
8296	7*10^89169-3	89170	Dmitry Domanov	11/2010
8297	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
8298	(43*10^89169+47)/9	89170	Robert Price	12/2017
8299	(10^89160+29)/3	89160	Serge Batalov	12/2014
8300	(28*10^89141-97)/3	89142	Robert Price	07/2016
8301	2^296116-734639	89140	Paul Bourdelais	04/2013
8302	(2^296101+1250)/2	89135	Stefano Morozzi	01/2020
8303	22574^8883+8883^22574	89135	Hans Havermann	08/2020
8304	6^114544-133	89133	Lelio R Paula	12/2015
8305	2^296076-113297	89128	Enzo Doria	07/2014
8306	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
8307	5*10^89118+81	89119	Robert Price	08/2017
8308	2^296037-1411	89117	Yves Minet	01/2013
8309	2^296020-2604809	89111	Enzo Doria	05/2015
8310	2^296016+81	89110	Henri Lifchitz	02/2007
8311	2^296010-11	89108	Lelio R Paula	10/2012
8312	2^295998-111911	89105	Enzo Doria	05/2014
8313	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
8314	29529^1040+1040^29529	89090	Hans Havermann	08/2020
8315	2^295939-16621	89087	Enzo Doria	04/2013
8316	2^295934-109691	89086	Enzo Doria	04/2014
8317	(2^295921+2246)/2	89081	Stefano Morozzi	01/2020
8318	(185*10^89070-11)/3	89072	Robert Price	10/2020
8319	(185*10^89063+7)/3	89065	Robert Price	02/2017
8320	(8*10^89055-59)/3	89056	Robert Price	08/2021
8321	2^295831+143	89055	Lelio R Paula	10/2012
8322	31^59713-30	89054	Theodore Burton	02/2007
8323	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
8324	79731!4-32	89049	Robert Price	11/2019
8325	123^42608+2	89047	Lelio R Paula	05/2013
8326	6^114433-114433^6	89047	Norbert Schneider	04/2017
8327	2^295800-459659	89045	Enzo Doria	05/2015
8328	(52*10^89037-1)/3	89039	Robert Price	02/2017
8329	(2^295782+1870)/2	89039	Stefano Morozzi	01/2020
8330	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
8331	11^85470-5850	89008	Enzo Doria	02/2013
8332	(2^295650+522)/2	89000	Stefano Morozzi	01/2020
8333	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
8334	(p(18424)#-4)/2	88985	Robert Price	09/2017
8335	2^295564-189	88974	Lelio R Paula	10/2012
8336	2^295557+73097	88972	Enzo Doria	04/2016
8337	11^85433-5760	88970	Enzo Doria	01/2013
8338	23074^7165+7165^23074	88956	Hans Havermann	08/2020
8339	(2^295479+3050)/2	88948	Stefano Morozzi	01/2020
8340	6*10^88938-91	88939	Robert Price	11/2017
8341	15^75619-88	88935	Lelio R Paula	11/2015
8342	(2^295433+2234)/2	88934	Stefano Morozzi	01/2020
8343	(15589^21211-1)/15588	88930	Serge Batalov	08/2020
8344	23776^5499+5499^23776	88929	Hans Havermann	08/2020
8345	21112^16291+16291^21112	88923	Hans Havermann	08/2020
8346	2^295385-85	88920	Lelio R Paula	10/2012
8347	2^295385-16333	88920	Enzo Doria	04/2013
8348	(89*10^88916-377)/9	88917	Robert Price	07/2021
8349	79617!4+32	88909	Robert Price	09/2019
8350	22077^10640+10640^22077	88903	Hans Havermann	08/2020
8351	2^295309+59	88897	Lelio R Paula	10/2012
8352	2^295288-109799	88891	Enzo Doria	04/2014
8353	10^88888+170373	88889	Stefano Morozzi	07/2018
8354	10^88888+271399	88889	Stefano Morozzi	07/2018
8355	10^88888+375397	88889	Stefano Morozzi	07/2018
8356	10^88888+548823	88889	Stefano Morozzi	07/2018
8357	10^88888+820861	88889	Stefano Morozzi	07/2018
8358	10^88888+1206349	88889	Stefano Morozzi	07/2018
8359	10^88888+1292047	88889	Stefano Morozzi	07/2018
8360	10^88888+1456029	88889	Stefano Morozzi	07/2018
8361	10^88888-490287	88888	Patrick De Geest	09/2018
8362	2^295245+65	88878	Lelio R Paula	10/2012
8363	5*10^88874-37	88875	Robert Price	11/2021
8365	Padovan(727734)	88874	Eric W. Weisstein	04/2011
8364	(2^295231+1554)/2	88874	Stefano Morozzi	01/2020
8366	79585!4-32	88870	Robert Price	11/2019
8367	18^70793-17	88865	Lelio R Paula	11/2015
8368	6^114196-17573	88862	Enzo Doria	02/2013
8369	302^35829+35829^302	88857	Norbert Schneider	12/2014
8370	3^186223+16	88851	Robert Price	10/2013
8371	3*2^295139+7	88847	Lelio R Paula	08/2014
8372	3^186212-113008	88846	Enzo Doria	07/2014
8373	2*10^88844+23	88845	Robert Price	12/2020
8374	23415^6224+6224^23415	88839	Hans Havermann	08/2020
8375	87^45803-86	88836	Norbert Schneider	11/2015
8376	2^295094-110273	88833	Enzo Doria	05/2014
8377	2^295080+1869151	88828	Enzo Doria	05/2016
8378	(2^295061+2174)/2	88822	Stefano Morozzi	01/2020
8379	2^295027-113407	88812	Enzo Doria	07/2014
8380	(2*10^88808-71)/3	88808	Robert Price	01/2017
8381	(2^295009+2102)/2	88807	Stefano Morozzi	01/2020
8382	13^79722-80	88806	Lelio R Paula	11/2015
8383	21112^16077+16077^21112	88802	Hans Havermann	08/2020
8384	3^186103+104	88794	Lelio R Paula	12/2015
8385	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
8386	(4025^24631-1)/4024	88786	Serge Batalov	08/2020
8387	2^294937-115003	88785	Enzo Doria	06/2015
8388	(2^294923+3134)/2	88781	Stefano Morozzi	01/2020
8389	(15326^21211-1)/15325	88773	Serge Batalov	08/2020
8390	2551^26056+26056^2551	88766	Norbert Schneider	01/2020
8391	2^294868-109709	88765	Enzo Doria	04/2014
8392	2^294864-2985	88763	Yves Minet	09/2014
8393	(17*10^88761-41)/3	88762	Robert Price	09/2017
8394	(2^294834+2854)/2	88754	Stefano Morozzi	01/2020
8395	(2^294823+2466)/2	88751	Stefano Morozzi	01/2020
8396	(2^294764+642)/2	88733	Stefano Morozzi	01/2020
8397	2^294754+15015	88730	Lelio R Paula	10/2013
8398	(3^185951-7)/20	88720	Lelio R Paula	01/2013
8399	(2^294688+3186)/2	88710	Stefano Morozzi	01/2020
8400	(2^294673+3906)/2	88706	Stefano Morozzi	01/2020
8401	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
8402	(2^294631+2514)/2	88693	Stefano Morozzi	01/2020
8403	(10^88680+11)/3	88680	Robert Price	11/2014
8404	2*7^104928-9	88675	Lelio R Paula	10/2014
8405	11^85150+12	88675	Lelio R Paula	11/2015
8406	8*6^113951+5	88673	Lelio R Paula	10/2014
8407	(2^294549+3110)/2	88668	Stefano Morozzi	01/2020
8408	6^113940-18563	88663	Enzo Doria	03/2013
8409	38^56123-56123^38	88663	Norbert Schneider	02/2017
8410	2^294492-65	88651	Lelio R Paula	10/2012
8411	(2^294481+2822)/2	88648	Stefano Morozzi	01/2020
8412	23874^5165+5165^23874	88646	Hans Havermann	08/2020
8413	(2^294469+1466)/2	88644	Stefano Morozzi	01/2020
8414	7*10^88634-27	88635	Dylan Delgado	08/2019
8415	20^68120-53	88627	Lelio R Paula	01/2016
8416	122^42477-121	88623	Norbert Schneider	10/2018
8417	2^294391-113257	88621	Enzo Doria	07/2014
8418	5^126784-15476	88619	Enzo Doria	02/2013
8419	(2^294335+554)/2	88604	Stefano Morozzi	01/2020
8420	2^294327+9	88602	Lelio R Paula	10/2012
8421	2^294320+18915	88600	Lelio R Paula	10/2013
8422	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
8423	20723^18834+18834^20723	88590	Hans Havermann	08/2020
8424	(68*10^88586-329)/9	88587	Robert Price	03/2021
8425	(2^294268+1402)/2	88584	Stefano Morozzi	01/2020
8426	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
8427	6*10^88571+77	88572	Robert Price	06/2020
8428	2^294224-933075	88571	Paul Bourdelais	04/2021
8429	(2^294145+1346)/2	88547	Stefano Morozzi	01/2020
8430	(2*10^88545+7)/9	88545	Erik Branger	03/2011
8431	2^294137-133	88545	Lelio R Paula	10/2012
8432	(2^294109+3494)/2	88536	Stefano Morozzi	01/2020
8433	23515^5818+5818^23515	88529	Hans Havermann	08/2020
8434	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
8435	4^147036+147036^4+1	88525	Robert Price	04/2014
8436	22541^8458+8458^22541	88525	Hans Havermann	08/2020
8437	(14^77213-5^77213)/9	88496	Robert Price	04/2013
8438	2^293965+2793377	88493	Enzo Doria	03/2016
8439	(2^293956+3306)/2	88490	Stefano Morozzi	01/2020
8440	11^84971-150	88489	Enzo Doria	08/2012
8441	(2^293944+1066)/2	88486	Stefano Morozzi	01/2020
8442	9*10^88485+91	88486	Robert Price	10/2020
8443	48^52626-47	88478	Norbert Schneider	08/2018
8444	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
8445	11^84958-2190	88475	Enzo Doria	12/2012
8446	(2^293902+3070)/2	88474	Stefano Morozzi	01/2020
8447	2^293880-111347	88467	Enzo Doria	05/2014
8448	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
8449	10^88457+278733	88458	Patrick De Geest	07/2017
8450	10^88457-401	88457	Robert Price	06/2017
8451	(2^293834+3018)/2	88453	Stefano Morozzi	01/2020
8452	(2^293747+1626)/2	88427	Stefano Morozzi	01/2020
8453	22080^10109+10109^22080	88424	Hans Havermann	08/2020
8454	11^84908-1680	88423	Enzo Doria	12/2012
8455	(2^293703+3486)/2	88414	Stefano Morozzi	01/2020
8456	2^293679-112075	88407	Enzo Doria	06/2014
8457	6^113608-65	88405	Lelio R Paula	12/2015
8458	2^293624+82875	88390	Lelio R Paula	10/2013
8459	(2^293618+918)/2	88388	Stefano Morozzi	01/2020
8460	2^293612-112337	88387	Enzo Doria	06/2014
8461	758^30693+30693^758	88386	Norbert Schneider	05/2017
8462	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
8463	5*10^88377+77	88378	Robert Price	06/2016
8464	(2^293584+1558)/2	88378	Stefano Morozzi	01/2020
8465	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
8466	20918^16743+16743^20918	88355	Hans Havermann	08/2020
8467	(2^293499+2390)/2	88352	Stefano Morozzi	01/2020
8468	20727^18292+18292^20727	88344	Hans Havermann	08/2020
8470	2^293461-2785843	88341	Enzo Doria	03/2016
8469	(31*10^88340+257)/9	88341	Robert Price	12/2021
8472	2^293416-1037	88328	Yves Minet	11/2012
8471	6*10^88327+43	88328	Robert Price	07/2020
8473	25109^3292+3292^25109	88320	Hans Havermann	08/2020
8474	(2^293384-7)/3	88317	Lelio R Paula	01/2013
8475	(3^185092-5)/4	88311	Lelio R Paula	01/2013
8476	(5*10^88303-173)/3	88304	Robert Price	11/2017
8477	14^77039-57	88297	Lelio R Paula	11/2015
8478	3*10^88293-59	88294	Robert Price	10/2017
8479	5^126303+42	88283	Lelio R Paula	10/2015
8480	19^69025-18	88266	Theodore Burton	01/2006
8481	140^41128+139	88266	Norbert Schneider	04/2019
8482	5*10^88261-3	88262	Dmitry Domanov	11/2010
8483	(2^293195+2238)/2	88261	Stefano Morozzi	01/2020
8484	8^97731-7^(97731-1)	88260	Robert Price	04/2016
8485	5*10^88254+59	88255	Robert Price	09/2016
8486	4*3^184968-7	88253	Lelio R Paula	08/2014
8487	34*10^88251-9	88253	Robert Price	06/2020
8488	7^104426+88	88251	Lelio R Paula	10/2015
8489	2^293142+99	88245	Lelio R Paula	10/2012
8490	11^84736-2130	88244	Enzo Doria	12/2012
8491	23884^4945+4945^23884	88232	Hans Havermann	08/2020
8492	22080^9907+9907^22080	88231	Hans Havermann	08/2020
8493	(10^110315+1)/(10^22063+1)/5824812682167648578460281641	88225	Makoto Kamada	04/2019
8494	2^293068-89	88223	Lelio R Paula	10/2012
8495	2126^26511+26511^2126	88218	Norbert Schneider	02/2020
8496	2^293014-109655	88207	Enzo Doria	04/2014
8497	8*7^104371-3	88205	Lelio R Paula	10/2014
8498	2^292995-2145	88201	Lelio R Paula	10/2013
8499	28534^1233+1233^28534	88198	Hans Havermann	08/2020
8500	5*10^88182+77	88183	Robert Price	06/2016

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PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)