Proth 2 3k-value

Proth numbers k•2ⁿ+1 where k-value is a multiple of 3.

The column "Index" contains the index of the k-value: [math]\displaystyle{ Index\ =\ {k\ +\ 3 \over 6} }[/math]

Table

There are 89 sequences in this Wiki:

k	Index	Count	Nash	Max n
3	1	50	2132	22021811
9	2	66	2297	5200000
15	3	65	2873	9000000
21	4	48	2374	9000000
27	5	49	2142	10000000
33	6	41	1960	9000000
39	7	88	3219	9000000
45	8	57	2581	9000000
51	9	63	3076	5200000
63	11	71	3116	5200000
93	16	67	3116	5200000
129	22	39	2357	5200000
165	28	109	5158	5200000
177	30	77	3473	5200000
207	35	69	3570	5200000
255	43	67	2629	5200000
261	44	96	4016	5200000
297	50	36	1682	5000000
345	58	92	4308	5000000
417	70	81	3454	4500000
435	73	95	4603	4500000
453	76	55	2586	4500000
513	86	62	2665	4500000
555	93	102	4497	4500000
579	97	32	1918	4000000
615	103	64	2908	4000000
639	107	85	3560	4000000
699	117	49	1894	4000000
759	127	39	2127	3640000
765	128	87	4734	3640000
789	132	45	2515	3640000
801	134	32	1434	3640000
831	139	33	2035	3640000
915	153	54	2802	3640000
933	156	76	3148	3640000
1023	171	83	3931	3640000
1065	178	80	4065	3640000
1071	179	67	3090	3640000
1149	192	38	2261	3640000
1323	221	73	3226	2000000
1461	244	32	1347	2000000
1479	247	55	3237	2000000
1575	263	72	4003	2000000
2187	365	41	2141	2000000
2379	397	29	1696	2000000
2943	491	22	1135	2000000
3207	535	59	2518	2000000
3267	545	40	2071	2000000
3375	563	48	2702	3486000
3777	630	61	3246	2000000
4119	687	23	1352	2000000
4665	778	55	2280	2000000
5193	866	54	2405	2000000
5307	885	58	3348	2000000
5505	918	57	3173	2000000
5703	951	19	851	2000000
5823	971	39	2254	2000000
6219	1037	39	1826	2000000
6807	1135	32	1805	2000000
6843	1141	36	2407	2000000
7233	1206	43	2694	2000000
8139	1357	29	1062	2000000
9267	1545	10	498	2000000
9609	1602	34	2106	2000000
9777	1630	22	1485	2000000
12321	2054	46	2495	300000
15735	2623	35	2954	50000
19683	3281	32	1802	4000000
23451	3909	17	1223	100000
32247	5375	23	1736	100000
42717	7120	7	893	100000
48495	8083	51	3088	1200000
53133	8856	18	1475	50000
60357	10060	34	2209	100000
60849	10142	22	1368	100000
66741	11124	9	811	50000
67275	11213	25	3481	1000
84363	14061	28	1624	100000
85287	14215	20	1630	100000
95283	15881	27	1489	50000
1089927	181655	27	1888	1000000
2441205	406868	106	6132	500000
84966861	14161144	30	2140	150000
314159265	52359878	57	466	314159
577294575	96215763	144	6655	50000
2003663613	333943936	39	2762	195000
1527888802614951	254648133769159	28	2929	10000
32268186233370440249391495	-3.6641581263172E+17	177	7953	340000
945561887392230553579269135	-1.1482867194984E+18	169	8431	600000

Proth primes

Miscellaneous

Proth prime Sierpiński problem Least n (k≤12)

Tables

1-300 300-2000 2000-4000 4000-6000 6000-8000 8000-10000 104-105 105-106 106-107 107-108 108-109 109-1010 1010-∞

Categories

1-300 300-2000 2000-4000 4000-6000 6000-8000 8000-10000 104-105 105-106 106-107 107-108 108-109 109-1010 1010-∞

Others

3k 15k 2145k 2805k 0 primes 100+ primes Sierpiński numbers Missing ranges

Other categories

Sierpiński numbers Missing ranges Low weight Count 0

Other bases

3 4 5 6 7 11 999