Lehmer-Ramanujan Numbers

Lehmer-Ramanujan Numbers

N. Lygeros, O. Rozier

Odd prime values of the Ramanujan tau function in The Ramanujan Journal , 15/03/2013– Pdf

\|2cos(theta(p))\|	p	q	size	primality	good/bad numbers	Discovery	Program	Date	Contributors	Time	Total CPU time
0.822567	251	3	26	P	very bad (13)	Lehmer 01		1965	Lehmer
0.381879	677	3	32	P	–	LR 02		2011	LR
0.798883	971	3	33	P	bad	LR 03		2011
0.413262	983	3	33	P	bad	LR 04		2011
1.709172	47	5	37	P	very good (11)	LR 05		2011
0.690618	197	5	50	P	–	LR 06		2011
0.149742	227	11	130	P	bad	LR 07		2011
0.962083	379	11	142	P	–	LR 08		2011
1.600770	829	11	161	P	–	LR 09		2011
1.229474	607	13	184	P	–	LR 10		2011
1.099902	761	13	190	P	–	LR 11		2011
1.162514	29	31	242	P	–	LR 12		2011
0.716263	281	19	243	P	–	LR 13		2011
0.084978	439	29	407	P	–	LR 14		2011
1.709172	47	47	424	P	–	LR 15		2011
1.216486	947	41	654	P	–	LR 16		2011
1.162514	29	83	660	P	–	LR 17		2011
0.508967	811	43	671	P	bad	LR 18		2011
1.153966	613	47	706	P	very bad (17)	LR 19		2011
0.474429	89	73	772	P	very good (29)	LR 20		2011
0.642521	401	59	831	P	–	LR 21		2011
1.747589	937	59	949	P	–	LR 22		2011
0.314073	977	59	954	P	–	LR 23		2011
1.452457	773	67	1049	P	–	LR Titan 24	gp	2011
0.701505	503	73	1070	P	very good (29)	LR Titan 25	gp	2011
1.561722	787	73	1147	P	–	LR Titan 26	gp	2011
0.466280	173	103	1256	P	–	LR Titan 27	gp	2011
0.630563	421	89	1271	P	–	LR Titan 28	gp	2011
0.890666	223	101	1292	P	–	LR Titan 29	gp	2011
0.592221	239	107	1387	P	–	LR Titan 30	gp	2011
0.148174	557	109	1631	P	–	LR Titan 31	gp	2011
1.000872	11	317	1810	P	very bad (11)	LR Titan 32	gp	2011
1.162514	29	229	1834	P	–	LR Titan 33	gp	2011
0.434747	113	197	2214	P	good	LR Titan 34	gp	2011
0.568639	809	149	2367	P	very good (11)	LR Titan 35	gp	2011
0.765198	491	167	2457	P	–	LR Titan 36	gp	2011
1.179650	17	433	2924	P	–	LR Titan 37	gp	2011
0.241885	353	239	3335	P	–	LR Titan 38	gp	2011
0.886942	97	331	3606	P	–	LR Titan 39	gp	2011		31h
0.890666	223	281	3617	P	–	LR Titan 40	gp	2011		32h
0.268015	881	241	3888	P	very good (11)	LR Titan 41	primo	16/04/2013	Gérasimos	29h	59h
0.268015	881	251	4050	P	–	LR Titan 42	primo	16/04/2013	Neoklis	29h	29h
0.457445	109	373	4169	P	–	LR Titan 43	primo	16/04/2013	Olivier	11h	46h
0.630563	421	317	4561	P	–	LR Titan 44	primo	17/04/2013	Neoklis	21h	41h
1.541981	941	349	5692	P	good	LR Titan 45	primo	28/04/2013	Gérasimos
0.265111	349	409	5706	P	–	LR Titan 46	primo	19/04/2013	Olivier	44h	174h
0.363777	487	479	7066	P	–	LR Titan 47	primo	25/04/2013	Neoklis	7d	13d
0.798883	971	433	7098	P	very bad (11)	LR Titan 48	primo	20/05/2013	Dimitris
1.583644	449	547	7965	P	–	LR Titan 49	primo	23/05/2013	Olivier	5d	35d
1.649726	953	557	9111	P	good	LR Titan 50	primo	05/08/2013	Theodora
0.886942	97	887	9682	P	–	LR Titan 51	primo	26/05/2013	Keira
1.644580	857	683	11002	P	–	LR Giant 52	primo	20/07/2013	Socratis
0.944962	59	1381	13441	P	very good (11)	LR Giant 53	primo	12/10/2013	Gérasimos	83d	326d
0.109065	643	953	14703	P	–	LR Giant 54	FastECPP	01/02/2011	François	13d	313d+42d
1.153966	613	1013	15515	P	–	LR Giant 55	primo	02/09/2014	Kostas/Keira
0.822567	251	1193	15733	P	very bad (11)	LR Giant 56	FastECPP	12/03/2018	François	123d	22d
1.323747	673	1019	15834	P	–	LR Giant 57	primo	19/06/2013	Patrice	30d	892d
1.393695	79	1571	16386	P	–	LR Giant 58	primo	07/02/2014	Gérasimos
0.987446	571	1091	16526	P	–	LR Giant 59	primo	05/12/2013	Dimitris
1.441636	587	1093	16629	P	good	LR Giant 60	primo	24/05/2018	Philippe & Pierre
0.026114	821	1163	18626	P		LR Giant 61	primo	04/07/2014	Keira
1.868850	619	1297	19900	P	very good (17)	LR Giant 62	primo	07/08/2014	Patrice
0.415345	41	2297	20367	P	very bad (11)	LR Giant 63	FastECPP	06/04/2018	François	24d	321d+53d
1.333141	257	1699	22506	P	–	LR Giant 64	primo	23/04/2014	Patrice	180d	4573d
0.663405	691	1523	23770	P	–	LR Giant 65	primo	27/02/2014	André, Philippe & Pierre	238d	7179d
1.100312	157	2207	26643	P	–	LR Giant 66	FastECPP	03/04/2011	François	59d	1963d+392d
0.879617	331	2129	29492	P	–	LR Giant 67	primo	15/09/2015	André, Philippe & Pierre	559d	17888d
1.709172	47	4177	38404	P	very good (11)	LR Giant	ECPP	23/06/2022	Andreas Enge
1.403115	739	2503	39475	pp	–	LR Giant
0.266890	463	2753	40347	pp	–	LR Giant
1.631383	461	3019	44215	pp	–	LR Giant		2011
0.165452	199	4519	57125	P	good	LR Super Giant	ECPP	09/09/2022	Andreas Enge
1.829136	877	3617	58531	pp	–	LR Super Giant		2011
1.644580	857	3847	62042	pp	–	LR Super Giant		2011
0.890722	409	4423	63520	pp	–	LR Super Giant		2011
1.393695	79	6317	65920	pp	–	LR Super Giant		2011
0.661184	839	4177	67153	pp	very good (17)	LR Super Giant		2011
0.944962	59	8971	87365	pp	very good (11)	LR Super Giant		2011
0.568639	809	6029	96410	pp	–	LR Super Giant		2013
0.890666	223	9431	121795	pp	–	LR Hyper Giant		2011
1.462783	317	10331	142098	pp	–	LR Hyper Giant		2013
1.918814	103	14939	165374	pp	–	LR Hyper Giant		2013
0.109065	643	11689	180524	prp	–	LR Hyper Giant		2015
0.395585	373	15187	214796	prp	–	LR Hyper Giant		2013
0.972080	311	15787	216429	pp	–	LR Hyper Giant		2013
0.972080	311	16453	225560	pp	–	LR Hyper Giant		2013
0.415345	41	28289	250924	pp	very good (19)	LR Hyper Giant		2011
0.798883	971	15739	258571	pp	good	LR Hyper Giant		2015
0.111250	509	18947	282048	pp	–	LR Hyper Giant		2015
0.004564	907	20849	339132	pp	–	LR Hyper Giant		2016
0.768786	863	24631	397727	pp	–	LR Hyper Giant		2015
1.696603	631	32371	498503	pp	–	LR Hyper Giant		2015
1.452000	773	34961	555339	pp	–	LR Hyper Giant		2015
0.268015	881	38993	631568	pp	–	LR Hyper Giant		2015
0.413262	983	38933	640784	pp	–	LR Hyper Giant		2016
0.854653	151	56087	672156	pp	–	LR Hyper Giant		2017
1.24075	229	63499	824146	prp	–	LR Hyper Giant		2020
0.381386	181	72559	900969	prp	–	LR Hyper Giant		2018

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