From the earlier drive, the following candidates reached n=200k:

[CODE]S 1024817770766811 100 166/192615 (p/ln(n) = 13.642)
S 862832795007565 100 164/199894 (13.437)
S 24014621472869 82 162/194816 (13.301)
S 24365010567297 66 161/194118 (13.222)
S 28067140916631 82 159/186843 (13.099)
S 3488826124671 58 156/181656 (12.882)
[/CODE]

And last but not least I found 3 new primes for the overall top performer:

[CODE]170 216664 1323953181459703 S 100
171 218813 1323953181459703 S 100
172 347004 1323953181459703 S 100[/CODE]

Note the huge gap between the 171st and 172nd prime. So, there might be a good chance for some of the other candidates (e.g. those yielding 166 primes at n=200k) to take over around n=300k.

Work is in progress into this direction...

[QUOTE=Thomas11;223172]From the earlier drive, the following candidates reached n=200k:

[CODE]S 1024817770766811 100 166/192615 (p/ln(n) = 13.642)
S 862832795007565 100 164/199894 (13.437)
S 24014621472869 82 162/194816 (13.301)
S 24365010567297 66 161/194118 (13.222)
S 28067140916631 82 159/186843 (13.099)
S 3488826124671 58 156/181656 (12.882)
[/CODE]

And last but not least I found 3 new primes for the overall top performer:

[CODE]170 216664 1323953181459703 S 100
171 218813 1323953181459703 S 100
172 347004 1323953181459703 S 100[/CODE]

Note the huge gap between the 171st and 172nd prime. So, there might be a good chance for some of the other candidates (e.g. those yielding 166 primes at n=200k) to take over around n=300k.

Work is in progress into this direction...[/QUOTE]

Well done Thomas, dramatic changes of fortune.

I am not processing any primes at the moment, as all three computers I had access to have burned out! It is literally too hot to process primes here. I have to carefully conserve my processing power for work, at least until I return to the UK in October, having finished 4 years in Dhaka.

Hmm, still here in Dhaka with no processing capacity. On a seriously underpowered laptop I managed the following absolute Riesel records:

R 42788306462971 60 69/819
R 42788306462971 60 70/831
R 42788306462971 60 79/1469

Robert

I have moved from Bangladesh to Afghanistan...and I will have no processing capability at all here. Such a shame. :no: One day I will be somewhere where I can really bash some cycles and resurrect this thread

Robert

I don't have a lot of capacity, just a laptop, but I think I have a new Afghan - in fact world - record for the Payam number with the most primes for n>10000

121 9793 39672235877965 R 52

The number faded badly after this...

133 37585 39672235877965 R 52

But 121 primes is definitely the best so far... beats the 119 found last year.

Best Riesel or Sierpinski, therefore absolute proth, racing records beaten by the new record holder:

111 5996 39672235877965 R 52
112 6159 39672235877965 R 52
113 6213 39672235877965 R 52
114 6218 39672235877965 R 52
115 6872 39672235877965 R 52
116 7388 39672235877965 R 52
117 7523 39672235877965 R 52
118 7600 39672235877965 R 52
119 7799 39672235877965 R 52
120 9283 39672235877965 R 52
121 9793 39672235877965 R 52

Best Riesel performance also for:

95 2906 39672235877965 R 52
96 3078 39672235877965 R 52
98 3447 39672235877965 R 52
99 3503 39672235877965 R 52
102 4463 39672235877965 R 52
103 4481 39672235877965 R 52
104 4559 39672235877965 R 52
105 4976 39672235877965 R 52
106 4985 39672235877965 R 52
107 5232 39672235877965 R 52
108 5409 39672235877965 R 52
109 5840 39672235877965 R 52
110 5953 39672235877965 R 52

Joining the Riesel hunt
 

Hello to everyone,

I just wanted to say that I was independently trying to solve the "efficient prime generation" problem for Riesel primes, but your progress is way ahead of what I got done in my "vacuum." I noticed what Payam described as his "Series A" set of numbers, but made no connection to "Series B" and the Chinese Remainder Theorem. That was nicely done!

What I do have that can contribute: a boatload of very fast hardware, 6 cores per box @ 5.2 GHz and faster.

What I need:

1. Better instructions on how to use k > 2^64. I understand you represent k = y*M(x)m but it would be so much easier if your output files just show a ready to copy/paste factored k that is over 2^64.

2. Latest versions of your software/guidelines for use. If you have some "impossibly" large E ranges you want to shoot for, tell me how to set up the programs to crank, and I will crank them full speed.

3. I have the MS Compiler, so if there are limitations (i.e. 2^27 and 2^60 were mentioned in some of your posts) I can recode with large_ints from your set of source and then redistribute the modifications.

I think this is fascinating stuff and I am surprised more have not joined the hunt.

That's great Sanemur.

The Riesel side lacks progress because I have no computing power. My bet is that the best k series to aim for are M(58), M(60) or M(66). There has hardly been any work done there. If you run three cores, do them in separate subdirectories.

There is already hugely efficient software out there for this hunt. It provides a lot of the k that have 100 primes at n=10000.

Download either payampentium.exe or payamathlon.exe from
[url]http://sites.google.com/site/robertgerbicz/payam[/url]

Also in.txt and progress.txt

For the in.txt file, set the parameters in all three cases as follows:

maxn 10000
hashsize 65536
sievelimit 134217728
timesave 60
boundforquickcheck 4096
vpscount 100
nashsievelimit 500

c0 1.5
c1 5.0
nash_check 1
number_of_sievebits 7
11 64
13 128
15 256
18 512
21 1024
24 2048
27 4096

smith_check 1
number_of_levels 8
11 50
18 100
25 200
36 500
57 1000
69 2000
77 3000
91 6000

These limits are there so that we can eliminate most Payams quickly. We are really only interested with k with >108 primes in the first 10,000 n to take forward from n=10000. These are the only ones that might produce competitive k in the 140 prime range.

For the 3 progress.txt files

For M(58)

c -1
E 58
iteration 9
I 21424

For M(60)

c -1
E 60
iteration 26
I 40991

For M(66)

c -1
E 66
iteration 11
I 67901

The output files give the full k value, but not the factorisation of k. This is easy enough to do though.

Keep all of the recordtable files and save the best results for each prime level found. The records currently for the three series are shown below.

Post back here batches of k that you find and any new racing records at each of the levels in the format provided in the other posts. Best to post back once you get a fair selection of k. You will get a minimum of 5 k per day per core.

Also post any results of taking any candidate forward from n=10000 in the form shown in the other posts.

[CODE]

Best m52 m58 m60 m66

1 1 1 1 1 1
2 2 2 2 2 2
3 3 3 3 3 3
4 4 4 4 4 4
5 5 5 5 5 5
6 6 6 6 6 6
7 7 7 7 7 7
8 8 8 8 8 8
9 9 9 9 9 9
10 10 10 10 10 10
11 11 11 12 12 13
12 13 13 13 14 14
13 14 14 16 16 15
14 17 18 18 17 18
15 20 20 20 20 21
16 23 23 23 24 25
17 25 25 25 27 29
18 28 28 29 31 33
19 31 31 31 33 38
20 32 32 36 38 40
21 38 40 38 40 43
22 43 44 43 46 45
23 47 47 48 50 47
24 53 53 53 54 53
25 55 58 58 57 55
26 59 61 64 59 59
27 63 65 68 63 65
28 68 68 73 78 69
29 72 75 77 84 72
30 80 80 87 85 93
31 88 88 99 88 102
32 93 93 105 94 104
33 95 95 114 97 105
34 108 108 122 112 123
35 119 119 127 122 132
36 120 120 128 128 142
37 124 124 131 135 147
38 134 134 136 143 164
39 141 148 141 153 168
40 146 152 146 154 175
41 160 162 171 160 185
42 167 173 177 167 195
43 180 187 198 180 217
44 182 193 219 182 240
45 188 220 235 188 243
46 204 234 248 204 247
47 247 247 254 249 253
48 260 260 277 262 292
49 270 270 297 275 317
50 283 293 313 283 342
51 290 313 330 290 352
52 317 360 353 317 361
53 355 370 360 355 389
54 378 378 401 387 393
55 388 392 408 388 423
56 401 424 433 401 427
57 403 438 469 403 443
58 410 439 478 410 459
59 466 466 539 477 477
60 513 517 564 513 513
61 546 546 565 565 565
62 589 589 607 596 626
63 607 607 662 631 631
64 660 660 676 660 741
65 666 720 681 666 766
66 683 745 801 683 803
67 738 764 826 738 827
68 776 799 834 776 867
69 819 856 943 819 910
70 831 871 966 831 954
71 918 931 1011 918 1007
72 933 933 1069 984 1048
73 963 963 1091 996 1060
74 1009 1021 1095 1009 1090
75 1066 1148 1122 1066 1128
76 1119 1160 1364 1119 1193
77 1164 1164 1397 1209 1272
78 1210 1325 1462 1210 1414
79 1280 1396 1472 1280 1488
80 1491 1509 1528 1560 1491
81 1531 1555 1531 1583 1577
82 1594 1626 1631 1637 1594
83 1597 1702 1756 1678 1597
84 1726 1752 1834 1758 1726
85 1847 1951 1847 1859 2028
86 1871 1964 1889 1871 2112
87 1892 2060 2004 1892 2190
88 2070 2074 2070 2107 2340
89 2193 2193 2207 2272 2398
90 2279 2379 2367 2331 2448
91 2370 2424 2370 2395 2589
92 2517 2517 2561 2578 2693
93 2640 2674 2640 3004 2826
94 2724 2724 3090 3113 3360
95 2906 2906 3232 3245 3500
96 3078 3078 3427 3307 3909
97 3324 3324 3492 3600 4420
98 3447 3447 3509 3679 5276
99 3503 3503 3638 3785 5501
100 3556 3556 4296 3836 5717
101 3943 3943 4644 4246 5813
102 4463 4463 4919 4860 6033
103 4481 4481 5443 5060 6196
104 4559 4559 5622 5127 6855
105 4976 4976 6354 5887 6974
106 4985 4985 7407 5948 7953
107 5232 5232 7618 6169 8134
108 5409 5409 7987 6346 8542
109 5840 5840 8792 7835 8858
110 5953 5953 9289 8288 9208
111 5996 5996 10117 8732 9282
112 6159 6159 11099 9129 9543
113 6213 6213 11804 9527 10116
114 6218 6218 12174 9960 10522
115 6872 6872 12443 10081 10829
116 7388 7388 13301 10082 11050
117 7523 7523 13305 10322 11438
118 7600 7600 13712 10596 12481
119 7799 7799 14127 13514 14970
120 9283 9283 14207 14175 15402
121 9793 9793 15032 14551 15740
122 12865 13875 16151 14716 16067
123 13208 16026 19604 15204 16408
124 14027 16560 20267 16619 17305
125 17542 18536 20432 18406 17542
126 18270 19533 20524 18880 18270
127 18954 20721 20775 20970 18954
128 19034 22126 24046 21065 19034
129 20795 23394 24120 22515 26039
130 20852 24653 24396 23493 27889
131 22844 25582 26136 23571 29587
132 23235 34797 26830 24250 31344
133 23248 37585 29472 27171 33192
134 23358 42691 32031 29416 33237
135 27644 45744 35816 32966 33916
136 28785 47182 36367 34259 36861
137 30128 49551 37499 41302 37127
138 30480 51246 42575 42035 37521
139 30929 52814 47388 45080 38175
140 41930 56415 48448 47148 41930
141 45117 49504 47361
142 47470 50232 47470
143 48806 55929 48806
144 49351 57795 49351
145 53717 61220 74389
146 64050 65223 75048
147 68381 69969 77931
148 70169 70169 80977
149 73685 73685 83359
150 77167 77167 84366
151 80961 80961 89497
152 84012 84012 93467
153 100101 100101 104173
154
155
156
157
158 164463 164463
159 169447 169447
160 195317 195317
161 202473 202473
162 233805 233805

[/CODE]

Hi Robert,

Thanks for the quick reply! I will get right on it.

A few things that might help nomenclature-wise, which you guys can either agree to use or ignore :grin:

1. Your p/ln(n) which is your prime count per natural log of the exponent, I would just call that something like "d" for the prime density.

2. Instead of writing 100/5734 for noting when a particular k hits the 100th prime, why not just create a "100 weight indicator", maybe call it the "hectoprime" (abbreviated "h") and then divide the exponent by 100? Like 57.34 in the example here.

3. We need some sort of way to describe the quasi-primorials from "Series A" better. You know, the 3*5*11*13*19*53 numbers that skip primes now and then depending on where you are searching. I don't like using M(x) since the M could be confused with the Mersenne Prime. Maybe use something like k = y * Q(p) where Q(p) is the Quasi-primorial in question.

Just trying to make a small contribution to the project.

[QUOTE=robert44444uk;277253]
The Riesel side lacks progress because I have no computing power. My bet is that the best k series to aim for are M(58), M(60) or M(66). There has hardly been any work done there. If you run three cores, do them in separate subdirectories.
[/QUOTE]

I started the project on one of my 4.0 GHz machines right now (which is also sieving close to 40T on another sparse prime generator I am looking at and also running 2 other LLRs) and I will migrate it to the "monster" once it is done with a complex rendering that should take it all weekend. I had no idea you would respond so quickly :smile:

Looks like in the 800/sec and 900/sec range for 2 of them.

1. Don't really use now. This was Phil Carmody's measure. The measure is not straight line in any case, tending to increase for Payam numbers as n increases.

2. We do it that way so that I can keep the drag racing records up to date.

3. There are papers out there now that use the y and M(x) nomenclature, so will probably stick to that.

Happy hunting! I think it is going to be just you and me for a while. Think Thomas11 has moved on to new grounds, but he did find over 3,000 very prime k, and has the overall record with 171 primes. If you have lots of cores, then you can really get the Riesel side to match.