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-   -   Very Prime Riesel and Sierpinski k (https://www.mersenneforum.org/showthread.php?t=9755)

 robert44444uk 2007-12-17 11:02

Very Prime Riesel and Sierpinski k

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

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 2007-12-20 04:44

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 2007-12-23 07:16

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 2007-12-23 21:03

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 2008-01-06 11:53

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 2008-01-15 02:19

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

Continuing until the blasted VPS is found :furious: :grin:

No new near misses or anything yet :sad:

roger

 robert44444uk 2008-01-15 11:20

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 2008-01-17 04:42

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

 robert44444uk 2008-01-18 07:56

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 2008-01-19 06:19

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 2008-01-19 23:04

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 :rolleyes:).

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

[CODE]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[/CODE]

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