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 ?
7251	(2^296361+1262)/2	89214	Stefano Morozzi	01/2020
7252	3*10^89206+13	89207	Robert Price	08/2017
7254	7*3^186960-4	89204	Lelio R Paula	08/2014
7253	(28*10^89203+47)/3	89204	Robert Price	02/2021
7255	2^296290-112133	89193	Enzo Doria	06/2014
7256	6^114620-17003	89192	Enzo Doria	02/2013
7257	(4*10^89189+41)/9	89189	Robert Price	11/2014
7258	2^296261-161181	89184	Enzo Doria	04/2013
7259	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
7260	3^186903-10	89176	Robert Price	09/2013
7261	7*10^89169-3	89170	Dmitry Domanov	11/2010
7262	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
7263	(43*10^89169+47)/9	89170	Robert Price	12/2017
7264	(10^89160+29)/3	89160	Serge Batalov	12/2014
7265	(28*10^89141-97)/3	89142	Robert Price	07/2016
7266	2^296116-734639	89140	Paul Bourdelais	04/2013
7267	(2^296101+1250)/2	89135	Stefano Morozzi	01/2020
7268	22574^8883+8883^22574	89135	Hans Havermann	08/2020
7269	6^114544-133	89133	Lelio R Paula	12/2015
7270	2^296076-113297	89128	Enzo Doria	07/2014
7271	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
7272	5*10^89118+81	89119	Robert Price	08/2017
7273	2^296037-1411	89117	Yves Minet	01/2013
7274	2^296020-2604809	89111	Enzo Doria	05/2015
7275	2^296016+81	89110	Henri Lifchitz	02/2007
7276	2^296010-11	89108	Lelio R Paula	10/2012
7277	2^295998-111911	89105	Enzo Doria	05/2014
7278	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
7279	29529^1040+1040^29529	89090	Hans Havermann	08/2020
7280	2^295939-16621	89087	Enzo Doria	04/2013
7281	2^295934-109691	89086	Enzo Doria	04/2014
7282	(2^295921+2246)/2	89081	Stefano Morozzi	01/2020
7283	(185*10^89070-11)/3	89072	Robert Price	10/2020
7284	(185*10^89063+7)/3	89065	Robert Price	02/2017
7285	2^295831+143	89055	Lelio R Paula	10/2012
7286	31^59713-30	89054	Theodore Burton	02/2007
7287	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
7288	79731!4-32	89049	Robert Price	11/2019
7290	123^42608+2	89047	Lelio R Paula	05/2013
7289	6^114433-114433^6	89047	Norbert Schneider	04/2017
7291	2^295800-459659	89045	Enzo Doria	05/2015
7292	(52*10^89037-1)/3	89039	Robert Price	02/2017
7293	(2^295782+1870)/2	89039	Stefano Morozzi	01/2020
7294	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
7295	11^85470-5850	89008	Enzo Doria	02/2013
7296	(2^295650+522)/2	89000	Stefano Morozzi	01/2020
7297	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
7298	(p(18424)#-4)/2	88985	Robert Price	09/2017
7299	2^295564-189	88974	Lelio R Paula	10/2012
7300	2^295557+73097	88972	Enzo Doria	04/2016
7301	11^85433-5760	88970	Enzo Doria	01/2013
7302	23074^7165+7165^23074	88956	Hans Havermann	08/2020
7303	(2^295479+3050)/2	88948	Stefano Morozzi	01/2020
7304	6*10^88938-91	88939	Robert Price	11/2017
7305	15^75619-88	88935	Lelio R Paula	11/2015
7306	(2^295433+2234)/2	88934	Stefano Morozzi	01/2020
7307	(15589^21211-1)/15588	88930	Serge Batalov	08/2020
7308	23776^5499+5499^23776	88929	Hans Havermann	08/2020
7309	21112^16291+16291^21112	88923	Hans Havermann	08/2020
7310	2^295385-85	88920	Lelio R Paula	10/2012
7311	2^295385-16333	88920	Enzo Doria	04/2013
7312	79617!4+32	88909	Robert Price	09/2019
7313	22077^10640+10640^22077	88903	Hans Havermann	08/2020
7314	2^295309+59	88897	Lelio R Paula	10/2012
7315	2^295288-109799	88891	Enzo Doria	04/2014
7316	10^88888+170373	88889	Stefano Morozzi	07/2018
7317	10^88888+271399	88889	Stefano Morozzi	07/2018
7318	10^88888+375397	88889	Stefano Morozzi	07/2018
7319	10^88888+548823	88889	Stefano Morozzi	07/2018
7320	10^88888+820861	88889	Stefano Morozzi	07/2018
7321	10^88888+1206349	88889	Stefano Morozzi	07/2018
7322	10^88888+1292047	88889	Stefano Morozzi	07/2018
7323	10^88888+1456029	88889	Stefano Morozzi	07/2018
7324	10^88888-490287	88888	Patrick De Geest	09/2018
7325	2^295245+65	88878	Lelio R Paula	10/2012
7326	Padovan(727734)	88874	Eric W. Weisstein	04/2011
7327	(2^295231+1554)/2	88874	Stefano Morozzi	01/2020
7328	79585!4-32	88870	Robert Price	11/2019
7329	18^70793-17	88865	Lelio R Paula	11/2015
7330	6^114196-17573	88862	Enzo Doria	02/2013
7331	302^35829+35829^302	88857	Norbert Schneider	12/2014
7332	3^186223+16	88851	Robert Price	10/2013
7333	3*2^295139+7	88847	Lelio R Paula	08/2014
7334	3^186212-113008	88846	Enzo Doria	07/2014
7335	2*10^88844+23	88845	Robert Price	12/2020
7336	23415^6224+6224^23415	88839	Hans Havermann	08/2020
7337	87^45803-86	88836	Norbert Schneider	11/2015
7338	2^295094-110273	88833	Enzo Doria	05/2014
7339	2^295080+1869151	88828	Enzo Doria	05/2016
7340	(2^295061+2174)/2	88822	Stefano Morozzi	01/2020
7341	2^295027-113407	88812	Enzo Doria	07/2014
7342	(2*10^88808-71)/3	88808	Robert Price	01/2017
7343	(2^295009+2102)/2	88807	Stefano Morozzi	01/2020
7344	13^79722-80	88806	Lelio R Paula	11/2015
7345	21112^16077+16077^21112	88802	Hans Havermann	08/2020
7346	3^186103+104	88794	Lelio R Paula	12/2015
7347	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
7348	(4025^24631-1)/4024	88786	Serge Batalov	08/2020
7349	2^294937-115003	88785	Enzo Doria	06/2015
7350	(2^294923+3134)/2	88781	Stefano Morozzi	01/2020
7351	(15326^21211-1)/15325	88773	Serge Batalov	08/2020
7352	2551^26056+26056^2551	88766	Norbert Schneider	01/2020
7353	2^294868-109709	88765	Enzo Doria	04/2014
7354	2^294864-2985	88763	Yves Minet	09/2014
7355	(17*10^88761-41)/3	88762	Robert Price	09/2017
7356	(2^294834+2854)/2	88754	Stefano Morozzi	01/2020
7357	(2^294823+2466)/2	88751	Stefano Morozzi	01/2020
7358	(2^294764+642)/2	88733	Stefano Morozzi	01/2020
7359	2^294754+15015	88730	Lelio R Paula	10/2013
7360	(3^185951-7)/20	88720	Lelio R Paula	01/2013
7361	(2^294688+3186)/2	88710	Stefano Morozzi	01/2020
7362	(2^294673+3906)/2	88706	Stefano Morozzi	01/2020
7363	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
7364	(2^294631+2514)/2	88693	Stefano Morozzi	01/2020
7365	(10^88680+11)/3	88680	Robert Price	11/2014
7366	2*7^104928-9	88675	Lelio R Paula	10/2014
7367	11^85150+12	88675	Lelio R Paula	11/2015
7368	8*6^113951+5	88673	Lelio R Paula	10/2014
7369	(2^294549+3110)/2	88668	Stefano Morozzi	01/2020
7371	6^113940-18563	88663	Enzo Doria	03/2013
7370	38^56123-56123^38	88663	Norbert Schneider	02/2017
7372	2^294492-65	88651	Lelio R Paula	10/2012
7373	(2^294481+2822)/2	88648	Stefano Morozzi	01/2020
7374	23874^5165+5165^23874	88646	Hans Havermann	08/2020
7375	(2^294469+1466)/2	88644	Stefano Morozzi	01/2020
7376	7*10^88634-27	88635	Dylan Delgado	08/2019
7377	20^68120-53	88627	Lelio R Paula	01/2016
7378	122^42477-121	88623	Norbert Schneider	10/2018
7379	2^294391-113257	88621	Enzo Doria	07/2014
7380	5^126784-15476	88619	Enzo Doria	02/2013
7381	(2^294335+554)/2	88604	Stefano Morozzi	01/2020
7382	2^294327+9	88602	Lelio R Paula	10/2012
7383	2^294320+18915	88600	Lelio R Paula	10/2013
7384	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
7385	20723^18834+18834^20723	88590	Hans Havermann	08/2020
7386	(68*10^88586-329)/9	88587	Robert Price	03/2021
7387	(2^294268+1402)/2	88584	Stefano Morozzi	01/2020
7388	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
7389	6*10^88571+77	88572	Robert Price	06/2020
7390	(2^294145+1346)/2	88547	Stefano Morozzi	01/2020
7391	(2*10^88545+7)/9	88545	Erik Branger	03/2011
7392	2^294137-133	88545	Lelio R Paula	10/2012
7393	(2^294109+3494)/2	88536	Stefano Morozzi	01/2020
7394	23515^5818+5818^23515	88529	Hans Havermann	08/2020
7395	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
7397	4^147036+147036^4+1	88525	Robert Price	04/2014
7396	22541^8458+8458^22541	88525	Hans Havermann	08/2020
7398	(14^77213-5^77213)/9	88496	Robert Price	04/2013
7399	2^293965+2793377	88493	Enzo Doria	03/2016
7400	(2^293956+3306)/2	88490	Stefano Morozzi	01/2020
7401	11^84971-150	88489	Enzo Doria	08/2012
7402	(2^293944+1066)/2	88486	Stefano Morozzi	01/2020
7403	9*10^88485+91	88486	Robert Price	10/2020
7404	48^52626-47	88478	Norbert Schneider	08/2018
7405	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
7406	11^84958-2190	88475	Enzo Doria	12/2012
7407	(2^293902+3070)/2	88474	Stefano Morozzi	01/2020
7408	2^293880-111347	88467	Enzo Doria	05/2014
7409	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
7410	10^88457+278733	88458	Patrick De Geest	07/2017
7411	10^88457-401	88457	Robert Price	06/2017
7412	(2^293834+3018)/2	88453	Stefano Morozzi	01/2020
7413	(2^293747+1626)/2	88427	Stefano Morozzi	01/2020
7414	22080^10109+10109^22080	88424	Hans Havermann	08/2020
7415	11^84908-1680	88423	Enzo Doria	12/2012
7416	(2^293703+3486)/2	88414	Stefano Morozzi	01/2020
7417	2^293679-112075	88407	Enzo Doria	06/2014
7418	6^113608-65	88405	Lelio R Paula	12/2015
7419	2^293624+82875	88390	Lelio R Paula	10/2013
7420	(2^293618+918)/2	88388	Stefano Morozzi	01/2020
7421	2^293612-112337	88387	Enzo Doria	06/2014
7422	758^30693+30693^758	88386	Norbert Schneider	05/2017
7423	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
7425	5*10^88377+77	88378	Robert Price	06/2016
7424	(2^293584+1558)/2	88378	Stefano Morozzi	01/2020
7426	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
7427	20918^16743+16743^20918	88355	Hans Havermann	08/2020
7428	(2^293499+2390)/2	88352	Stefano Morozzi	01/2020
7429	20727^18292+18292^20727	88344	Hans Havermann	08/2020
7430	2^293461-2785843	88341	Enzo Doria	03/2016
7432	2^293416-1037	88328	Yves Minet	11/2012
7431	6*10^88327+43	88328	Robert Price	07/2020
7433	25109^3292+3292^25109	88320	Hans Havermann	08/2020
7434	(2^293384-7)/3	88317	Lelio R Paula	01/2013
7435	(3^185092-5)/4	88311	Lelio R Paula	01/2013
7436	(5*10^88303-173)/3	88304	Robert Price	11/2017
7437	14^77039-57	88297	Lelio R Paula	11/2015
7438	3*10^88293-59	88294	Robert Price	10/2017
7439	5^126303+42	88283	Lelio R Paula	10/2015
7441	19^69025-18	88266	Theodore Burton	01/2006
7440	140^41128+139	88266	Norbert Schneider	04/2019
7442	5*10^88261-3	88262	Dmitry Domanov	11/2010
7443	(2^293195+2238)/2	88261	Stefano Morozzi	01/2020
7444	8^97731-7^(97731-1)	88260	Robert Price	04/2016
7445	5*10^88254+59	88255	Robert Price	09/2016
7447	4*3^184968-7	88253	Lelio R Paula	08/2014
7446	34*10^88251-9	88253	Robert Price	06/2020
7448	7^104426+88	88251	Lelio R Paula	10/2015
7449	2^293142+99	88245	Lelio R Paula	10/2012
7450	11^84736-2130	88244	Enzo Doria	12/2012
7451	23884^4945+4945^23884	88232	Hans Havermann	08/2020
7452	22080^9907+9907^22080	88231	Hans Havermann	08/2020
7453	(10^110315+1)/(10^22063+1)/5824812682167648578460281641	88225	Makoto Kamada	04/2019
7454	2^293068-89	88223	Lelio R Paula	10/2012
7455	2126^26511+26511^2126	88218	Norbert Schneider	02/2020
7456	2^293014-109655	88207	Enzo Doria	04/2014
7457	8*7^104371-3	88205	Lelio R Paula	10/2014
7458	2^292995-2145	88201	Lelio R Paula	10/2013
7459	28534^1233+1233^28534	88198	Hans Havermann	08/2020
7460	5*10^88182+77	88183	Robert Price	06/2016
7462	2^292929+43877	88181	Donovan Johnson	04/2005
7461	6^113321+131	88181	Lelio R Paula	12/2015
7463	(2^292919+3366)/2	88178	Stefano Morozzi	01/2020
7464	2^292904-583949	88173	Paul Bourdelais	04/2013
7465	2^292894-111851	88170	Enzo Doria	05/2014
7466	2^292872-2797349	88164	Enzo Doria	03/2016
7467	(2^292864+1042)/2	88161	Stefano Morozzi	01/2020
7468	2^292860-109685	88160	Enzo Doria	04/2014
7469	9*6^113288-5	88157	Lelio R Paula	10/2014
7470	(2^292735+2166)/2	88122	Stefano Morozzi	01/2020
7471	(2^292735+2346)/2	88122	Stefano Morozzi	01/2020
7472	(2^292705+1934)/2	88113	Stefano Morozzi	01/2020
7473	(2*10^88112-23)/3	88112	Robert Price	09/2017
7474	29622^943+943^29622	88111	Hans Havermann	08/2020
7475	(73*10^88105+17)/9	88106	Robert Price	10/2015
7476	(2^292673+3026)/2	88104	Stefano Morozzi	01/2020
7477	11^84588+78	88090	Lelio R Paula	11/2015
7478	(265*10^88077+11)/3	88079	Robert Price	03/2017
7479	91^44959-90^44959	88077	Robert Price	07/2015
7480	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
7481	1316^28233+28233^1316	88066	Norbert Schneider	07/2020
7482	(2^292543+2234)/2	88064	Stefano Morozzi	01/2020
7483	(10^88020+101)/3	88020	Robert Price	04/2016
7485	52^51285-51	88006	Norbert Schneider	09/2018
7484	21002^15501+15501^21002	88006	Hans Havermann	08/2020
7486	20466^19951+19951^20466	88004	Hans Havermann	08/2020
7487	(2^292324+2346)/2	87998	Stefano Morozzi	01/2020
7488	21634^11683+11683^21634	87998	Hans Havermann	08/2020
7489	(6340^23143-1)/6339	87988	Serge Batalov	08/2020
7490	20674^18013+18013^20674	87980	Hans Havermann	08/2020
7491	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
7492	(424*10^87930-1)/9	87932	Robert Price	11/2017
7493	(2^292100+3070)/2	87931	Stefano Morozzi	01/2020
7494	p(18225)#/2+128	87929	Robert Price	04/2017
7495	(10607^21841-1)/10606	87919	Serge Batalov	08/2020
7496	(2^292047+1550)/2	87915	Stefano Morozzi	01/2020
7497	4*6^112977+7	87914	Lelio R Paula	10/2014
7498	(2^292016+1062)/2	87906	Stefano Morozzi	01/2020
7499	(11359^21673-1)/11358	87888	Serge Batalov	08/2020
7500	14^76677+69	87882	Lelio R Paula	11/2015

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Probable Primes Top 10000

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