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 ?
7002	2^281780-114893	84825	Enzo Doria	05/2015
7001	(7654^21841-1)/7653	84825	Serge Batalov	08/2020
7003	3^177719+64	84794	Lelio R Paula	12/2015
7005	2^281675-199	84793	Lelio R Paula	08/2012
7004	2^281673-111223	84793	Enzo Doria	05/2014
7006	(4*10^84779+149)/9	84779	Robert Price	03/2017
7007	129^40167-128	84777	Norbert Schneider	01/2019
7008	(2^281622+3970)/2	84777	Stefano Morozzi	01/2020
7009	(72*10^84772-27)/9	84773	Ray Chandler	01/2011
7010	11^81398-630	84768	Enzo Doria	11/2012
7011	(25*2^281577-1)/23	84764	Lelio R Paula	02/2014
7012	20320^14819+14819^20320	84752	Hans Havermann	07/2020
7013	2^281500-455	84740	Yves Minet	03/2012
7014	10^84725+1145141919	84726	Marisa Kirisame	03/2015
7015	10^84725+142041	84726	Patrick De Geest	10/2015
7016	10^84725-138677	84725	Patrick De Geest	02/2016
7017	76^45044+75	84720	Norbert Schneider	02/2015
7018	54^48897-53	84709	Norbert Schneider	08/2014
7019	(9913*2^281377-1)/65	84706	Lelio R Paula	04/2015
7020	Phi(171124,10)/29946701/7761329021/58560344041	84700	Maksym Voznyy	11/2015
7021	2^281337-111223	84691	Enzo Doria	05/2014
7022	2^281308+54615	84683	Lelio R Paula	09/2013
7023	7*5^121144-6	84677	Lelio R Paula	10/2014
7024	(2^281270+3858)/2	84671	Stefano Morozzi	01/2020
7025	(2^281252+47)/3	84665	Lelio R Paula	01/2013
7026	11^81297-3150	84663	Enzo Doria	12/2012
7027	2^281208-303	84653	Yves Minet	02/2012
7028	197^36892-2	84648	Lelio R Paula	10/2017
7029	(21*2^281187+1)/2483	84644	Lelio R Paula	01/2013
7030	11^81247-84	84611	Lelio R Paula	10/2015
7031	(10876^20959-1)/10875	84597	Serge Batalov	08/2020
7032	2067^25516+25516^2067	84595	Norbert Schneider	11/2019
7034	17^68747-64	84590	Lelio R Paula	11/2015
7033	(2^281002+3718)/2	84590	Stefano Morozzi	01/2020
7035	5^121018-15596	84588	Enzo Doria	02/2013
7036	6^108702+7	84587	Lelio R Paula	11/2014
7037	10^84582+100677	84583	Patrick De Geest	05/2016
7038	10^84582-8001	84582	Robert Price	03/2016
7039	1828^25929+25929^1828	84580	Norbert Schneider	12/2019
7040	(2^280968+1446)/2	84580	Stefano Morozzi	01/2020
7041	3*5^121004-8	84579	Lelio R Paula	10/2014
7042	5^120996-84	84573	Lelio R Paula	10/2015
7043	(2^280896+1522)/2	84558	Stefano Morozzi	01/2020
7044	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
7045	2^280852+97681	84545	Yves Minet	08/2004
7046	2^280848-1203	84544	Lelio R Paula	09/2013
7047	5^120946-24	84538	Lelio R Paula	10/2015
7048	2^280810-2111	84533	Yves Minet	08/2013
7049	11^81161-5160	84521	Enzo Doria	01/2013
7050	2^280737-93	84511	Lelio R Paula	08/2012
7051	(2^280737+494)/2	84510	Stefano Morozzi	01/2020
7052	(2^280717+1166)/2	84504	Stefano Morozzi	01/2020
7053	2^280698+315	84499	Lelio R Paula	09/2013
7054	3^177099-340	84498	Lelio R Paula	12/2015
7055	(8201^21589-1)/8200	84493	Serge Batalov	08/2020
7056	(5*10^84469-107)/3	84470	Robert Price	01/2017
7057	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
7058	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
7059	24677^2640+2640^24677	84435	Hans Havermann	07/2020
7060	14^73660-5	84424	Lelio R Paula	11/2015
7061	(2^280405+746)/2	84411	Stefano Morozzi	01/2020
7063	(19*10^84409-61)/3	84410	Robert Price	04/2017
7062	20862^11119+11119^20862	84410	Hans Havermann	07/2020
7064	2^280388+117	84406	Lelio R Paula	08/2012
7065	2^280389-566533	84406	Paul Bourdelais	03/2013
7066	23423^4008+4008^23423	84392	Hans Havermann	07/2020
7067	(2^280340+3322)/2	84391	Stefano Morozzi	01/2020
7068	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
7069	(1897^25741-1)/1896	84378	Serge Batalov	08/2020
7071	119^40652+118	84376	Norbert Schneider	09/2018
7070	(2^280291+2274)/2	84376	Stefano Morozzi	01/2020
7072	2^280240-173	84361	Lelio R Paula	08/2012
7073	(184*10^84348-1)/3	84350	Robert Price	02/2017
7074	21068^10083+10083^21068	84348	Hans Havermann	07/2020
7075	4*10^84346+93	84347	Robert Price	01/2017
7076	7*2^280156-5	84337	Lelio R Paula	08/2014
7077	(8760^21391-1)/8759	84331	Serge Batalov	08/2020
7078	8*7^99782-3	84327	Lelio R Paula	10/2014
7079	2^280116+133	84324	Lelio R Paula	08/2012
7080	2^280118+54615	84324	Lelio R Paula	09/2013
7081	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
7082	6^108354+47	84316	Lelio R Paula	12/2015
7083	(2^280069+462)/2	84309	Stefano Morozzi	01/2020
7084	20657^12058+12058^20657	84307	Hans Havermann	07/2020
7085	10^84305+141963	84306	Patrick De Geest	07/2013
7086	10^84305-57	84305	Robert Price	05/2011
7087	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
7088	75843!4-32	84295	Robert Price	11/2019
7089	3^176648-112804	84283	Enzo Doria	06/2014
7090	6^108310+115	84282	Lelio R Paula	12/2015
7091	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
7092	6^108288-16643	84265	Enzo Doria	02/2013
7093	2^279917-58695	84264	Lelio R Paula	08/2013
7094	65^46477+36	84259	Lelio R Paula	01/2016
7095	(2^279883+3230)/2	84253	Stefano Morozzi	01/2020
7096	(2^279876+1422)/2	84251	Stefano Morozzi	01/2020
7097	2^279866-1907	84249	Yves Minet	05/2013
7098	23140^4373+4373^23140	84248	Hans Havermann	07/2020
7099	19736^18567+18567^19736	84248	Hans Havermann	07/2020
7101	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
7100	(p(17530)#+4)/2	84246	Robert Price	09/2017
7102	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
7104	18^67103-41	84233	Lelio R Paula	11/2015
7103	20^64743-43	84233	Lelio R Paula	01/2016
7105	(2^279807+2454)/2	84230	Stefano Morozzi	01/2020
7106	19717^18672+18672^19717	84216	Hans Havermann	07/2020
7107	(2^279754+3574)/2	84215	Stefano Morozzi	01/2020
7108	143^39070+39070^143	84209	Serge Batalov	05/2014
7109	11^80857-5400	84204	Enzo Doria	01/2013
7110	(2^279642+3130)/2	84181	Stefano Morozzi	01/2020
7111	(13*10^84179+161)/3	84180	Robert Price	04/2017
7112	2^279634-110405	84179	Enzo Doria	05/2014
7113	(74*10^84170+313)/9	84171	Robert Price	11/2017
7114	2^279582-1017	84163	Lelio R Paula	08/2013
7115	(22*10^84159-19)/3	84160	Robert Price	02/2017
7116	p(17513)#/2+512	84156	Robert Price	05/2017
7117	(19*10^84144-43)/3	84145	Robert Price	10/2017
7118	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
7119	11^80792-810	84137	Enzo Doria	11/2012
7120	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
7121	p(17507)#/2+32	84125	Robert Price	12/2016
7122	(1750^25939-1)/1749	84118	Serge Batalov	08/2020
7123	21485^8224+8224^21485	84116	Hans Havermann	04/2017
7124	3^176294-340	84114	Lelio R Paula	12/2015
7125	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
7126	2^279388-719	84105	Yves Minet	05/2012
7127	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
7128	(2^279343+578)/2	84091	Stefano Morozzi	01/2020
7129	2^279332-110447	84088	Enzo Doria	05/2014
7130	2^279320+7	84084	Lelio R Paula	06/2012
7131	127^39966-2	84081	Lelio R Paula	10/2017
7132	(2^279299+2490)/2	84078	Stefano Morozzi	01/2020
7133	(2^279301+1694)/2	84078	Stefano Morozzi	01/2020
7134	(2^279285+962)/2	84073	Stefano Morozzi	01/2020
7135	(2^279269+1122)/2	84069	Stefano Morozzi	01/2020
7136	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
7137	2^279218-111347	84053	Enzo Doria	05/2014
7138	35^54435+2	84052	Lelio R Paula	05/2013
7139	(2^279176+2998)/2	84041	Stefano Morozzi	01/2020
7140	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
7141	20996^10059+10059^20996	84038	Hans Havermann	05/2017
7142	97*10^84033-3	84035	Robert Price	01/2017
7143	(2^279153+1326)/2	84034	Stefano Morozzi	01/2020
7144	(2^279155+3534)/2	84034	Stefano Morozzi	01/2020
7145	21234^9067+9067^21234	84033	Hans Havermann	05/2017
7146	(134569^16384+1)/2	84033	Richard Fischer	06/2018
7147	(5858^22303-1)/5857	84029	Serge Batalov	08/2020
7148	2^279095-109717	84016	Enzo Doria	04/2014
7149	(2^279054+1438)/2	84004	Stefano Morozzi	01/2020
7150	14^73282-99	83991	Lelio R Paula	11/2015
7151	21457^8200+8200^21457	83979	Hans Havermann	06/2017
7152	89*10^83976-7	83978	Robert Price	03/2017
7153	2^278955+173	83974	Lelio R Paula	06/2012
7154	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
7155	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
7156	5^120076-14846	83930	Enzo Doria	02/2013
7157	(85*10^83921-1)/3	83923	Robert Price	07/2017
7158	(2^278770-3)/23	83917	Lelio R Paula	12/2012
7159	(10^83916+449)/9	83916	Serge Batalov	12/2014
7161	2^278715+99	83902	Lelio R Paula	06/2012
7160	(132109^16384+1)/2	83902	Richard Fischer	05/2018
7162	40235!2-2^40235	83899	Robert Price	09/2015
7163	2^278698-171	83897	Lelio R Paula	06/2012
7164	(19*10^83894-43)/3	83895	Robert Price	10/2017
7165	6^107802+25	83887	Lelio R Paula	12/2015
7166	8*10^83880+39	83881	Robert Price	01/2017
7167	(58*10^83878+23)/9	83879	Robert Price	09/2015
7168	7^99244-90	83871	Lelio R Paula	10/2015
7169	(2^278601+1674)/2	83867	Stefano Morozzi	01/2020
7170	2^278554+4257	83854	Lelio R Paula	08/2013
7171	2^278504-109619	83839	Enzo Doria	04/2014
7172	2^278499+1870433	83837	Enzo Doria	05/2016
7173	(2^278487+570)/2	83833	Stefano Morozzi	01/2020
7174	105^41475+104	83829	Norbert Schneider	11/2016
7175	15^71276-68	83828	Lelio R Paula	11/2015
7176	2^278464-216413	83827	Enzo Doria	04/2013
7177	(2^278440+1602)/2	83819	Stefano Morozzi	01/2020
7178	(76*10^83816-211)/9	83817	Robert Price	10/2017
7179	(2^278429+1950)/2	83816	Stefano Morozzi	01/2020
7180	(2^278428+1750)/2	83815	Stefano Morozzi	01/2020
7181	(8*10^83811-101)/3	83812	Robert Price	10/2017
7182	2^278400+40755	83807	Lelio R Paula	08/2013
7183	(2^278394+3718)/2	83805	Stefano Morozzi	01/2020
7184	(2^278388+3586)/2	83803	Stefano Morozzi	01/2020
7185	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
7186	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
7187	19551^19268+19268^19551	83773	Hans Havermann	05/2017
7188	20625^11522+11522^20625	83770	Hans Havermann	05/2017
7189	(44*10^83768-791)/9	83769	Robert Price	10/2017
7190	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
7191	2^278235-49	83758	Lelio R Paula	06/2012
7192	23543^3610+3610^23543	83755	Hans Havermann	05/2017
7194	18^66711-91	83741	Lelio R Paula	11/2015
7193	4*10^83740-89	83741	Robert Price	08/2017
7195	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
7196	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
7197	4*7^99059-9	83716	Lelio R Paula	10/2014
7198	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
7199	2^278077+1867211	83710	Enzo Doria	03/2016
7200	(85*10^83708+203)/9	83709	Robert Price	09/2020
7201	2^278059-27	83705	Lelio R Paula	06/2012
7202	214^35917+35917^214	83702	Norbert Schneider	12/2014
7203	(23*10^83693+7)/3	83694	Robert Price	10/2015
7204	85^43375-2	83689	Lelio R Paula	09/2013
7205	5*3^175360+4	83669	Lelio R Paula	07/2014
7206	(23^61441-1)/22	83665	Robert Price	01/2012
7207	20091^14596+14596^20091	83664	Hans Havermann	03/2017
7208	2^277907-110629	83659	Enzo Doria	05/2014
7209	19522^19283+19283^19522	83656	Hans Havermann	04/2017
7210	(2^277881+2570)/2	83651	Stefano Morozzi	01/2020
7211	8*5^119664-3	83643	Lelio R Paula	10/2014
7212	8*3^175299-7	83640	Lelio R Paula	07/2014
7213	(26*10^83638-413)/9	83639	Robert Price	10/2017
7214	3^175250+22	83616	Robert Price	12/2013
7216	11^80285+30	83609	Lelio R Paula	10/2015
7215	26870^1293+1293^26870	83609	Hans Havermann	03/2017
7217	(6730^21841-1)/6729	83604	Serge Batalov	08/2020
7218	(2828^24223-1)/2827	83602	Serge Batalov	08/2020
7219	2^277691+1874423	83594	Enzo Doria	06/2016
7220	13^75022-60	83571	Lelio R Paula	11/2015
7221	(2^277593+2622)/2	83564	Stefano Morozzi	01/2020
7222	14^72905-51	83559	Lelio R Paula	11/2015
7223	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
7224	5^119532-12	83550	Lelio R Paula	10/2015
7225	6^107358-16253	83541	Enzo Doria	02/2013
7226	2^277478-460211	83530	Enzo Doria	06/2015
7227	(2^277474+814)/2	83528	Stefano Morozzi	01/2020
7228	(22*10^83525-7)/3	83526	Erik Branger	09/2014
7229	(30^56543+1)/31	83520	Robert Price	07/2013
7230	2^277417-460783	83511	Paul Bourdelais	04/2013
7231	(2^277404+3582)/2	83507	Stefano Morozzi	01/2020
7232	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
7233	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
7234	21368^8085+8085^21368	83500	Hans Havermann	04/2017
7235	(2^277353+3750)/2	83492	Stefano Morozzi	01/2020
7236	(2^277348+3538)/2	83490	Stefano Morozzi	01/2020
7237	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
7238	5^119439-66	83485	Lelio R Paula	10/2015
7239	(14*10^83471-101)/3	83472	Robert Price	04/2017
7240	5*6^107263+7	83468	Lelio R Paula	10/2014
7241	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
7242	2^277244-175709	83459	Hans Havermann	10/2018
7243	(2^277230+1450)/2	83455	Stefano Morozzi	01/2020
7244	(2^277232+3658)/2	83455	Stefano Morozzi	01/2020
7245	17^67796-92	83420	Lelio R Paula	11/2015
7246	2^277106-110057	83418	Enzo Doria	04/2014
7247	6^107200-19	83418	Lelio R Paula	12/2015
7248	11^80096-1830	83412	Enzo Doria	12/2012
7249	3^174801+56	83402	Lelio R Paula	12/2015
7250	2^277033-111973	83396	Enzo Doria	05/2014

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Probable Primes Top 10000

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