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 ?
7001	(2^261724+392705)/3/7	78786	Tony Prest / Never Odd Or Even	04/2014
7002	(2^261724+629709)/5/5	78786	Tony Prest / Never Odd Or Even	05/2014
7003	(2^261724+67397)/3/103	78785	Tony Prest / Never Odd Or Even	04/2014
7004	(2^261724+323043)/11/103	78784	Tony Prest / Never Odd Or Even	04/2014
7005	(2^261724+370143)/1289	78784	Tony Prest / Never Odd Or Even	04/2014
7006	(2^261724+560259)/5/5/73	78784	Tony Prest / Never Odd Or Even	05/2014
7007	(2^261724+64109)/3/3/3/5/5/19	78783	Tony Prest / Never Odd Or Even	04/2014
7008	(2^261724+394491)/55787	78783	Tony Prest / Never Odd Or Even	04/2014
7009	(2^261724+625897)/23/883	78783	Tony Prest / Never Odd Or Even	05/2014
7010	(2^261724+292471)/13/97/151	78782	Tony Prest / Never Odd Or Even	04/2014
7011	(2^261724+154303)/11/67/127	78782	Tony Prest / Never Odd Or Even	04/2014
7012	(2^261724+313319)/3/3/3/3/5/11/113	78782	Tony Prest / Never Odd Or Even	04/2014
7013	(2^261724+383949)/5/41/43/83	78781	Tony Prest / Never Odd Or Even	04/2014
7014	(2^261724+626567)/3/331/631	78781	Tony Prest / Never Odd Or Even	05/2014
7015	(2^261724+32987)/3/3/19/223/1031	78780	Tony Prest / Never Odd Or Even	04/2014
7016	(2^261724+5813)/3/5991397	78780	Tony Prest / Never Odd Or Even	04/2014
7017	(2^261724+13481)/3/11/239/2087	78780	Tony Prest / Never Odd Or Even	04/2014
7018	(2^261724+103399)/5/13/37/10607	78780	Tony Prest / Never Odd Or Even	04/2014
7019	(2^261724+18477)/367/65111	78780	Tony Prest / Never Odd Or Even	04/2014
7020	(2^261724+121285)/167/227/1217	78780	Tony Prest / Never Odd Or Even	04/2014
7021	(2^261724+262037)/3/3/11/23/18517	78780	Tony Prest / Never Odd Or Even	04/2014
7022	(2^261724+586157)/3/7/457/1259	78780	Tony Prest / Never Odd Or Even	05/2014
7023	(2^261724+315287)/3/45822541	78779	Tony Prest / Never Odd Or Even	04/2014
7024	(2^261724+605675)/3/3/3/103/207481	78779	Tony Prest / Never Odd Or Even	05/2014
7025	(2^261724+60031)/13/31/7024877	78778	Tony Prest / Never Odd Or Even	04/2014
7026	(2^261724+121879)/5/789433217	78778	Tony Prest / Never Odd Or Even	04/2014
7027	(2^261724+290135)/3/3/8467/9059	78778	Tony Prest / Never Odd Or Even	04/2014
7028	(2^261724+79857)/59/3847/165331	78777	Tony Prest / Never Odd Or Even	04/2014
7029	(2^261724+22883)/3/17/23/2351/10079	78777	Tony Prest / Never Odd Or Even	04/2014
7030	(2^261724+154799)/3/5/3655653719	78777	Tony Prest / Never Odd Or Even	04/2014
7031	(2^261724+391001)/3/11/17/41/43/24071	78777	Tony Prest / Never Odd Or Even	04/2014
7032	(2^261724+622383)/34843/550717	78777	Tony Prest / Never Odd Or Even	05/2014
7033	(2^261724+302829)/5/37/37/37078147	78776	Tony Prest / Never Odd Or Even	04/2014
7034	(2^261724+315837)/43/2176136243	78776	Tony Prest / Never Odd Or Even	04/2014
7035	(2^261724+582373)/53/307/311/32117	78776	Tony Prest / Never Odd Or Even	05/2014
7036	(2^261724+295283)/3/3/3/29/43/17812273	78775	Tony Prest / Never Odd Or Even	04/2014
7037	(2^261724+27491)/3/22787/105978449	78774	Tony Prest / Never Odd Or Even	04/2014
7038	(2^261724+392751)/193813/287826689	78774	Tony Prest / Never Odd Or Even	04/2014
7039	(2^261724+328501)/7/1091/31495610519	78773	Tony Prest / Never Odd Or Even	04/2014
7040	(2^261724+111267)/19/4637/15140560427	78772	Tony Prest / Never Odd Or Even	04/2014
7041	(2^261724+572133)/127/131/73787752333	78772	Tony Prest / Never Odd Or Even	05/2014
7042	(2^261724+608733)/59/7079/18451/909151	78771	Tony Prest / Never Odd Or Even	05/2014
7043	(2^261724+255449)/3/3/5/7/1759/10177/33158869	78770	Tony Prest / Never Odd Or Even	04/2014
7044	(2^261724+99509)/3/5/5/6507271/6749659289	78769	Tony Prest / Never Odd Or Even	04/2014
7045	(2^261724+52501)/563/53939/27942831391	78769	Tony Prest / Never Odd Or Even	04/2014
7046	(2^261724+117089)/3/5/37/149/967/2027/4163741	78769	Tony Prest / Never Odd Or Even	04/2014
7047	(2^261724+372571)/1487/9209/21559/2263249	78769	Tony Prest / Never Odd Or Even	04/2014
7048	(2^261724+184549)/5/8699/44053/1409322997	78769	Tony Prest / Never Odd Or Even	04/2014
7049	(2^261724+363351)/937/159683/59523200227	78768	Tony Prest / Never Odd Or Even	04/2014
7050	(2^261724+326501)/3/43/193/263/19403/253501403	78768	Tony Prest / Never Odd Or Even	04/2014
7051	(2^261724+629477)/3/17/17/137/263/1993/16187/57347	78768	Tony Prest / Never Odd Or Even	05/2014
7052	(2^261724+94871)/3/3/13/6734017/1673425245787	78766	Tony Prest / Never Odd Or Even	04/2014
7053	(2^261724+25981)/577/1181/3643/517786334743	78766	Tony Prest / Never Odd Or Even	04/2014
7055	(23*2^261642+1)/93	78762	Lelio R Paula	10/2012
7054	(2^261724+351227)/3/3/3/3/71/13997/9595373/8193978007	78762	Tony Prest / Never Odd Or Even	04/2014
7056	(2^261724+22571)/3/7243/7321/18046081/45730741211	78761	Tony Prest / Never Odd Or Even	04/2014
7057	(2^261724+56495)/3/3/3/7/7/13/9041/512818459/23708589119	78760	Tony Prest / Never Odd Or Even	04/2014
7058	71293!4-4	78759	Robert Price	11/2019
7059	(2^261630+3582)/2	78759	Stefano Morozzi	01/2020
7060	(2^261724+604119)/5/7/7/41/14107/19681/211777/90145981/1036020834127	78750	Tony Prest / Never Odd Or Even	05/2014
7061	(2^261536+846)/2	78730	Stefano Morozzi	01/2020
7062	2^261507-2287	78722	Yves Minet	04/2009
7063	8*10^78717+39	78718	Robert Price	01/2017
7064	(78557*2^261440+1)/3	78706	Lelio R Paula	06/2014
7065	6^101128-16433	78693	Enzo Doria	02/2013
7066	20^60482+99	78689	Lelio R Paula	03/2015
7067	2^261348-110633	78674	Enzo Doria	05/2014
7068	191^34487+2	78666	Lelio R Paula	05/2013
7069	2^261305-110139	78661	Enzo Doria	04/2014
7070	(82*10^78635-1)/9	78636	Robert Price	12/2014
7071	10^78632+81	78633	Robert Price	03/2011
7072	10^78632-402693	78632	Patrick De Geest	07/2013
7073	3*10^78631+17	78632	Robert Price	03/2017
7074	2^261174-3911	78622	Yves Minet	04/2017
7075	2^261167+74843	78620	Enzo Doria	04/2016
7076	L(376121)+F(376122)	78605	Henri Lifchitz	01/2007
7077	14^68580-29	78602	Lelio R Paula	02/2015
7078	20603^6522+6522^20603	78588	Hans Havermann	03/2020
7079	(2^261056+646)/2	78586	Stefano Morozzi	01/2020
7080	(73*10^78576-1)/9	78577	Robert Price	01/2015
7081	(2^261020+2158)/2	78575	Stefano Morozzi	01/2020
7082	(17*2^261026-1)/40451	78574	Lelio R Paula	02/2014
7084	2^261001-195	78570	Lelio R Paula	05/2012
7083	18532^17365+17365^18532	78570	Hans Havermann	02/2020
7085	5*2^260950+9	78555	Lelio R Paula	06/2014
7086	2^260931-7605	78549	Lelio R Paula	07/2013
7087	19863^9002+9002^19863	78546	Hans Havermann	02/2020
7088	15^66778-32	78538	Lelio R Paula	02/2015
7089	(11*2^260896-1)/245	78537	Lelio R Paula	02/2014
7090	30^53166+29	78533	Norbert Schneider	03/2017
7091	lucasU(2403,1,23229)-lucasU(2403,1,23228)	78529	Mike Oakes	05/2009
7092	7*3^164574-2	78523	Lelio R Paula	06/2014
7093	18518^17385+17385^18518	78520	Hans Havermann	03/2020
7094	2^260830-112133	78518	Enzo Doria	06/2014
7095	13^70486+42	78518	Lelio R Paula	03/2015
7096	11^75386-7080	78507	Enzo Doria	01/2013
7098	(86^40583-1)/85	78506	Paul Bourdelais	08/2017
7097	(2^260790+1914)/2	78506	Stefano Morozzi	01/2020
7099	5*10^78504+11	78505	Robert Price	08/2019
7100	2^260711-58695	78482	Lelio R Paula	07/2013
7101	(2^260695+2258)/2	78477	Stefano Morozzi	01/2020
7102	2^260678-111065	78472	Enzo Doria	05/2014
7103	21560^4359+4359^21560	78466	Hans Havermann	02/2020
7104	18^62501-97	78456	Lelio R Paula	02/2015
7105	53^45498-2	78452	Lelio R Paula	08/2013
7106	(2^260549+642)/2	78433	Stefano Morozzi	01/2020
7107	(2^260527+3906)/2	78427	Stefano Morozzi	01/2020
7108	2^260513-111121	78423	Enzo Doria	05/2014
7109	37845!2-64	78412	Robert Price	06/2015
7110	2^260469-110695	78409	Enzo Doria	05/2014
7111	(11*10^78408-113)/3	78409	Robert Price	01/2017
7112	2^260447+8415	78403	Lelio R Paula	07/2013
7113	37837!2-64	78394	Robert Price	06/2015
7114	(19*2^260379-1)/53	78382	Lelio R Paula	02/2014
7115	2^260377-113233	78382	Enzo Doria	07/2014
7116	(2^260378+3750)/2	78382	Stefano Morozzi	01/2020
7118	9^82138+6^82138-2^82138	78380	Mike Oakes	08/2010
7117	69^42624+2	78380	Lelio R Paula	05/2013
7119	2^260369-1859713	78379	Enzo Doria	03/2016
7120	18634^16067+16067^18634	78374	Hans Havermann	02/2020
7121	14*10^78362+1089	78364	Jens K. Andersen	11/2007
7122	(2^260317+3542)/2	78363	Stefano Morozzi	01/2020
7123	5^112070-54	78334	Lelio R Paula	02/2015
7124	20120^7821+7821^20120	78333	Hans Havermann	03/2020
7125	(10^(239165+1)+5410^39165-1)/9	78331	Robert Price	04/2017
7126	(2^260195+3546)/2	78327	Stefano Morozzi	01/2020
7127	2^260182-113453	78323	Enzo Doria	07/2014
7128	f(16405)	78319	Robert Price	09/2017
7129	18547^16678+16678^18547	78309	Hans Havermann	02/2020
7130	(78557*2^260084+1)/519	78296	Lelio R Paula	06/2014
7132	10^78288+9^(78288+1)	78289	Robert Price	08/2016
7131	10^78288+39109	78289	Patrick De Geest	12/2016
7133	10^78288-216299	78288	Patrick De Geest	12/2016
7134	(2^260059+2430)/2	78286	Stefano Morozzi	01/2020
7135	(2^260056+1662)/2	78285	Stefano Morozzi	01/2020
7136	5^111997+36	78283	Lelio R Paula	02/2015
7137	(2^260017+1602)/2	78273	Stefano Morozzi	01/2020
7138	(2^260017+2162)/2	78273	Stefano Morozzi	01/2020
7139	(21^59183+1)/22	78252	Paul Bourdelais	03/2010
7140	(88*10^78242-7)/9	78243	Robert Price	11/2014
7141	2*6^100547+7	78242	Lelio R Paula	10/2014
7142	(2^259913+3470)/2	78242	Stefano Morozzi	01/2020
7143	(2^259885+3726)/2	78233	Stefano Morozzi	01/2020
7144	2^259860-111089	78226	Enzo Doria	05/2014
7145	18226^18359+18359^18226	78223	Norbert Schneider	02/2020
7146	(2^259833+3342)/2	78218	Stefano Morozzi	01/2020
7147	37^49875-2	78215	Lelio R Paula	09/2013
7148	(13*10^78213+401)/9	78214	Robert Price	10/2017
7149	7*5^111893-4	78211	Lelio R Paula	10/2014
7150	(11*2^259809-1)/1437	78209	Lelio R Paula	02/2014
7151	7^92511-6	78181	Theodore Burton	11/2005
7152	(3^163859-4)/253	78179	Lelio R Paula	10/2012
7153	(2^259689+1346)/2	78174	Stefano Morozzi	01/2020
7154	(27*2^259666-1)/625691	78163	Lelio R Paula	02/2014
7155	(2^259642+3202)/2	78160	Stefano Morozzi	01/2020
7156	(2^259624+442)/2	78155	Stefano Morozzi	01/2020
7157	3*10^78146+17	78147	Robert Price	03/2017
7158	(2^259594+1558)/2	78146	Stefano Morozzi	01/2020
7159	(576^28307+1)/577	78137	Richard Fischer	01/2018
7160	2^259503+74333	78119	Enzo Doria	04/2016
7161	(2^259503+2438)/2	78118	Stefano Morozzi	01/2020
7162	(31*2^259504-1)/13365	78116	Lelio R Paula	02/2014
7164	(58547^16384+1)/2	78111	Lelio R Paula	11/2011
7163	6^100379+13	78111	Lelio R Paula	03/2015
7165	2^259469-109909	78108	Enzo Doria	04/2014
7166	15^66413-26	78108	Lelio R Paula	02/2015
7167	7^92410-9266	78096	Mike Oakes	02/2010
7168	2^259398+75799	78087	Enzo Doria	04/2016
7169	2^259394+1876189	78086	Enzo Doria	07/2016
7170	PIPrime(78073)	78073	Eric W. Weisstein	07/2006
7171	5*2^259344-7	78072	Lelio R Paula	06/2014
7172	(2^259347+990)/2	78071	Stefano Morozzi	01/2020
7173	14^68097-87	78048	Lelio R Paula	02/2015
7174	2^259233-475573	78037	Paul Bourdelais	03/2013
7175	181^34554-2	78012	Lelio R Paula	10/2017
7176	3^163500-28	78010	Robert Price	12/2013
7177	(65*10^77992+691)/9	77993	Robert Price	08/2016
7178	(2^259035+3930)/2	77978	Stefano Morozzi	01/2020
7179	2^259013-112591	77971	Enzo Doria	06/2014
7181	7*10^77969-11	77970	Robert Price	10/2017
7180	(2^259011+2430)/2	77970	Stefano Morozzi	01/2020
7182	6^100193-100193^6	77966	Norbert Schneider	04/2017
7183	(2^258974+2638)/2	77959	Stefano Morozzi	01/2020
7184	24214^1657+1657^24214	77953	Hans Havermann	03/2020
7185	(2^258945+674)/2	77950	Stefano Morozzi	01/2020
7186	(2^258939+2450)/2	77949	Stefano Morozzi	01/2020
7187	18090^18307+18307^18090	77941	Norbert Schneider	02/2020
7188	2^258863-110235	77926	Enzo Doria	05/2014
7189	2^258852+1605	77923	Lelio R Paula	06/2013
7190	10^77919-123456789	77919	Robert Price	02/2020
7191	(11*10^77909+49)/3	77910	Robert Price	05/2016
7192	2*7^92187-9	77908	Lelio R Paula	10/2014
7193	2^258763-110155	77896	Enzo Doria	04/2014
7194	(2^258738+1062)/2	77888	Stefano Morozzi	01/2020
7195	2^258694-110387	77875	Enzo Doria	05/2014
7196	11^74773-94	77869	Lelio R Paula	02/2015
7197	6^100067+125	77868	Lelio R Paula	03/2015
7198	15^66205+8	77864	Lelio R Paula	07/2014
7199	(2^258637+17)/18605003	77851	Stefano Morozzi	03/2020
7200	5^111373-18136	77847	Enzo Doria	05/2014
7201	(2^258566+1974)/2	77836	Stefano Morozzi	01/2020
7202	2^258524-109877	77824	Enzo Doria	04/2014
7203	(2^258515+3914)/2	77821	Stefano Morozzi	01/2020
7204	6^100002-16643	77817	Enzo Doria	02/2013
7205	(13*10^77811+347)/9	77812	Robert Price	10/2017
7206	65^42916+28	77803	Lelio R Paula	01/2016
7207	(2^258405+3302)/2	77788	Stefano Morozzi	01/2020
7208	(89*10^77781-17)/9	77782	Robert Price	11/2015
7209	2^258382-110405	77781	Enzo Doria	05/2014
7211	5^111278-14996	77780	Enzo Doria	02/2013
7210	(2^258378+2314)/2	77780	Stefano Morozzi	01/2020
7212	14^67862+61	77779	Lelio R Paula	02/2015
7213	10^77777+48483	77778	Patrick De Geest	11/2010
7214	10^77777-183243	77777	Patrick De Geest	11/2010
7215	(27*2^258352+1)/43	77772	Lelio R Paula	08/2012
7216	(2^258294+2454)/2	77754	Stefano Morozzi	01/2020
7217	337^30756-10002	77740	Enzo Doria	07/2012
7218	10^77726+99	77727	Robert Price	03/2011
7219	10^77726-85947	77726	Patrick De Geest	06/2013
7220	89^39870-2	77723	Lelio R Paula	08/2013
7221	7^91966-32	77721	Lelio R Paula	02/2015
7222	35^50327+2	77709	Lelio R Paula	05/2013
7223	24^56298+23	77704	Norbert Schneider	12/2016
7224	(2^258128+3502)/2	77704	Stefano Morozzi	01/2020
7226	(2^258105+78557)/19	77697	Lelio R Paula	10/2012
7225	(2^258102+2842)/2	77697	Stefano Morozzi	01/2020
7227	2^258079+179	77690	Lelio R Paula	03/2012
7228	2^258062-113111	77685	Enzo Doria	07/2014
7229	(2^258022+2422)/2	77673	Stefano Morozzi	01/2020
7230	10^77669+123456789	77670	Robert Price	10/2019
7231	10^77669+59127	77670	Patrick De Geest	12/2019
7232	10^77669-109103	77669	Patrick De Geest	12/2019
7233	(2^258002+3822)/2	77667	Stefano Morozzi	01/2020
7234	80^40807-79	77660	Norbert Schneider	03/2015
7235	70385!4-4	77658	Robert Price	11/2019
7236	(10^77637+359)/9	77637	Serge Batalov	12/2014
7237	2^257862-165	77625	Lelio R Paula	03/2012
7238	(25*2^257853+1)/3	77623	Lelio R Paula	07/2012
7239	(2^257832+1362)/2	77615	Stefano Morozzi	01/2020
7240	(2^257869+1)/(3*18645362967379)	77613	Henri Lifchitz	04/2005
7241	6^99728+71	77604	Lelio R Paula	01/2015
7242	2^257778-112767	77599	Enzo Doria	06/2014
7243	(31*2^257771+1)/537	77596	Lelio R Paula	07/2012
7244	(2^257762+2214)/2	77594	Stefano Morozzi	01/2020
7245	2^257729-73	77585	Lelio R Paula	03/2012
7246	(2^257728+1890)/2	77584	Stefano Morozzi	01/2020
7248	2^257689-63	77573	Lelio R Paula	03/2012
7247	(47*10^77572+493)/9	77573	Robert Price	11/2017
7249	(78557*2^257665+1)/6108725	77564	Lelio R Paula	06/2014
7250	(3^162563+8)/2885	77559	Lelio R Paula	10/2012

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Probable Primes Top 10000

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