Very Prime Riesel and Sierpinski k

[robert44444uk]

The purpose of this thread to is post news relating to new very prime Riesel and Sierpinski k, in order that prime hunters might want to source new k's to search to high n.

A VPS (Very Prime Series) is one in which there are 100 or more primes at n=10,000 for a given k. Details of discovered k, and how to find them, are shown at

http://robert.smith44444.googlepages...umberresources

Please quote new k in the following format, k is y*M(x) where y is an integer, M(x) is the multiplier 3*5*11*13*19*29.....x, where x is the largest prime of the product of all consecutive primes less than x that have multiplicative order base 2 of p-1.

So a posting for k=1043827764761*3*5*11*13*19*29*37*53*2^n-1, which has its 100th prime at n=8888, and 103 by 10000 would be:

R 1043827764761 53 100/8888 103/10000

R=Riesel , i.e. the - series
S=Proth, i.e. the + series

You can also post near misses.

[robert44444uk]

R 1029369515711 53 100/8895 102/10000 tested to 114/20000 Unreserved
R 1636889512137 53 100/7724 104/10000 tested to 111/20000 Unreserved
R 1212241451853 53 100/8256 106/10000 tested to 110/20000 Unreserved

Near misses:

R 3053018310957 53 99/10000
R 3058988541335 53 99/10000

[robert44444uk]

R 3680068181457 53 100/7836 105/10000
R 3995993454669 53 100/9870 100/10000

Near misses:

R 3459395798073 53 99/10000
R 3726133257251 53 99/10000
R 3916647606303 53 99/10000

[roger]

Near misses:

S 2693372639 131 99/9991 100/10029 Tested to n=100,000, continuing.
S 219548216121 131 99/9915 100/10563 Tested to n=58,800, continuing.

Testing ep=131 to y=1T, currently at y=300B.

roger

[robert44444uk]

Some from E106:

R 408251547745613 107 100/8230 105/10000
R 5071829957884753 107 100/8856 101/10000
R 5858856352434629 107 100/9050 103/10000
R 101532422035567 107 100/9253 102/10000

Will take these 4 to 20000

We now have 71 Riesels which are 100/10000 or better

Near miss:

R 5731587575971897 107 99/10000

[roger]

Update: Have sieved for EP131 to 3T, and tested about half of the 2-3T candidates.

Continuing until the blasted VPS is found

No new near misses or anything yet

roger

[robert44444uk]

More from E82

R 38367867040615 83 100/6920 103/10000
R 61976585459877 83 100/8600 102/10000
R 63404089076241 83 100/8159 101/10000

[roger]

Maybe we should post here what e levels (both plus and minus) that have been tested/searched, and how far.

[robert44444uk]

Its a little complex to do that, given that the software is slightly at fault. I have taken bites out of every E level, but not systematically yet. If others join the fray, then we can work out alternative strategies. At the moment Roger you have a clear run at all of the pluses and I the minuses.

[robert44444uk]

R 1876131394595 66 100/8443 101/10000
R 1416492589021 66 100/8013 100/10000
R 1533927640019 66 100/9972 100/10000
R 1842913644031 66 100/9937 100/10000
R 1970620879533 66 100/9500 100/10000

Near miss:
R 1774116412215 66 99/10000

There are now 79 known Riesel 100+/10000 series

[roger]

As requested by robert44444uk, I'm posting my champion.txt file for ep131.

Note that e levels have different prime density, where 131 is much lower than say, 83 (takes longer to test too ).

No VPS has been found for this ep level. I'm working on correcting that Currently at y=3T.

nth prime|n= 	y= 		type 	e value
1	1	641810301879	p	131
2	2	641810301879	p	131
3	3	2840650933081	p	131
4	4	2772154724807	p	131
5	5	2772154724807	p	131
6	9	1005717171003	p	131
7	14	1538438983039	p	131
8	17	735833438703	p	131
9	19	433185946681	p	131
10	26	2332776531909	p	131
11	30	2332776531909	p	131
12	33	2536788504417	p	131
13	42	2872822380539	p	131
14	50	2872822380539	p	131
15	56	2172948151745	p	131
16	65	2395888445905	p	131
17	69	2172948151745	p	131
18	70	2172948151745	p	131
19	79	2172948151745	p	131
20	102	2312866486441	p	131
21	106	2752757385789	p	131
22	114	2752757385789	p	131
23	115	496683804015	p	131
24	116	496683804015	p	131
25	126	2752757385789	p	131
26	145	496683804015	p	131
27	160	2651342095727	p	131
28	164	2651342095727	p	131
29	176	2651342095727	p	131
30	185	2651342095727	p	131
31	205	2651342095727	p	131
32	220	1752188272975	p	131
33	233	1752188272975	p	131
34	256	2082400108743	p	131
35	267	2082400108743	p	131
36	279	2651342095727	p	131
37	311	2651342095727	p	131
38	322	2651342095727	p	131
39	334	2651342095727	p	131
40	381	2651342095727	p	131
41	442	2651342095727	p	131
42	474	1155206085715	p	131
43	495	1155206085715	p	131
44	504	871408474377	p	131
45	523	2945274852093	p	131
46	535	2945274852093	p	131
47	588	689333657719	p	131
48	632	496683804015	p	131
49	674	410583188141	p	131
49	775	2544728821431	p	131
50	703	496683804015	p	131
51	749	496683804015	p	131
52	817	496683804015	p	131
53	872	410583188141	p	131
54	904	531404200817	p	131
55	935	410583188141	p	131
56	972	410583188141	p	131
57	992	410583188141	p	131
58	1025	496683804015	p	131
59	1284	496683804015	p	131
60	1366	900595313379	p	131
61	1404	1723839146501	p	131
62	1526	1723839146501	p	131
63	1540	1723839146501	p	131
64	1626	1723839146501	p	131
65	1642	1723839146501	p	131
66	1692	1723839146501	p	131
67	1995	2945274852093	p	131
68	2164	1179591275323	p	131
69	2224	1179591275323	p	131
70	2269	1179591275323	p	131
71	2307	1179591275323	p	131
72	2370	1179591275323	p	131
73	2395	1179591275323	p	131
74	2543	1179591275323	p	131
75	2827	1179591275323	p	131
76	3154	1179591275323	p	131
77	3446	1179591275323	p	131
78	3606	1179591275323	p	131
79	4140	1179591275323	p	131
80	4311	219548216121	p	131
81	4326	219548216121	p	131
82	4422	219548216121	p	131
83	4505	219548216121	p	131
84	5072	1748808165891	p	131
85	5079	1748808165891	p	131
86	5256	1748808165891	p	131
87	5298	1748808165891	p	131
88	5779	1748808165891	p	131
89	6334	1748808165891	p	131
90	6871	219548216121	p	131
91	7179	1748808165891	p	131
92	7186	1748808165891	p	131
93	7193	1748808165891	p	131
94	7401	1748808165891	p	131
95	7915	1748808165891	p	131
96	8108	1748808165891	p	131
97	9265	219548216121	p	131
98	9511	1179591275323	p	131
99	9915	2693372639	p	131
100	10029	2693372639	p	131
101	10175	2693372639	p	131
102	10607	2693372639	p	131
103	11197	2693372639	p	131
104	11328	219548216121	p	131
105	11873	219548216121	p	131
106	12835	219548216121	p	131
107	13741	219548216121	p	131
108	13907	219548216121	p	131
109	14294	219548216121	p	131
110	15041	219548216121	p	131
111	15568	219548216121	p	131
112	16331	219548216121	p	131
113	17439	219548216121	p	131
114	19283	219548216121	p	131
115	21819	1179591275323	p	131
116	21846	1179591275323	p	131
117	23660	1179591275323	p	131
118	24934	1179591275323	p	131
119	25998	1179591275323	p	131
120	26321	1179591275323	p	131
121	28913	1179591275323	p	131
122	34223	1179591275323	p	131
123	35094	219548216121	p	131
124	37932	1179591275323	p	131
125	38733	501092101517	p	131
126	39491	1179591275323	p	131
127	39715	1179591275323	p	131
128	43038	1179591275323	p	131
129	43404	1179591275323	p	131
130	47857	1179591275323	p	131
131	51088	1179591275323	p	131
132	63615	1179591275323	p	131
133	63756	1179591275323	p	131
134	67736	501092101517	p	131
135	69671	501092101517	p	131
136	71895	501092101517	p	131