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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]

 robert44444uk 2008-01-27 13:45

A good week

Found the following VPS for Riesel series:

R 2502262772385 60 100/9732 100/10000
R 2781948761147 60 100/9271 100/10000
R 2342836014713 60 100/6520 109/10000 122/19093 !!! Reserved by me
R 1746492605077 60 100/8014 102/10000
R 2256305169303 60 100/9821 100/10000
R 2319747344799 60 100/9595 102/10000
R 2476995416951 60 100/9951 100/10000
R 2421745267415 60 100/9769 100/10000

Near misses:
R 1907954478839 60 99/10000
R 2002078724075 60 99/10000
R 1965188880093 60 99/10000
R 2183225888567 60 99/10000

There are now 92 known Riesel VPS

 robert44444uk 2008-01-28 12:28

Sorry for post 10 and 12, the correct multiplier M(x) is 67 and 61, and not 66 and 60 as posted.

 kar_bon 2008-01-28 13:59

i would like to make a page with all Riesel-type payams with all known primes, the searched ranges (highest n), contributor and some other datas.
currently i'm working on R 29979474409 67 (data from here [url]http://www.primepuzzles.net/puzzles/puzz_006.htm[/url]).
what i need too is the factored k (here k=29979474409=191*6217*25247) and e(67)=3*5*11*13*19*29*37*53*59*61*67.
i tested upto n=92k for now:
103 primes upto n=10k (100th at n=5968) and 129 primes at all at n=74659.
Karsten

 roger 2008-01-29 02:05

That makes sense Karsten,

AFAIK, there aren't too many people working on these series at the moment, and a formal webpage could bring in more members (and their computers :wink:)!

I'm working on the Proth side, but I'd be happy to send you my work if you include both plus and minus payam levels. (Now if I just had some VPS's :ermm:)

Good luck to you!

roger

EDIT: Also working on ep83 now. Have sieved to y=100B, and am currently testing the rest.

 kar_bon 2008-01-29 03:25

to see how i could look alike see here:
[url]www.rieselprime.org/test/SummaryRieselPayam.htm[/url]

only a first try, some background infos to display and many many more data to collect.
so i need all data i can get especially [b]all[/b] prime n!

karsten

 roger 2008-01-29 03:41

What are the highlighted and bold entries? I'm guessing the ones in a box are the 100th prime.

 kar_bon 2008-01-29 10:35

oh sure, sorry, look here for the 'syntax' i used in the summary-pages at all:
[url]www.rieselprime.org[/url] and the left menu -> "Infos Data Section (26.01.08)".
all colors and special things are described there!
karsten

 robert44444uk 2008-01-29 12:22

I think it is a good idea to start that sort of page. Up to now we have been playing around at each of the Payam levels without any real purpose other than to find VPS.

The problem is with the numbers of Riesels to put up. I have tested in excess of 10 billion y values (!!!), so putting up everything is not really feasible!!!

The VPS has the advantage of being easily understood - if there are at least 100 primes by n=100 then it is very special - that is not to say that 99/10000 is not special as well, it is only one behind. Can I suggest that the page puts all Riesel VPS up and others such as the M(163) example which are the best at their level. I have not kept records of primes found, only prime counts, so the almost 100 values would need to be run again.

A second page could capture all y*M(x) which are less than 2^40, with a slightly lower threshhold of primes by 10000, as these are of interest to the very active LLRers. It could form the basis for a future drive. I am thinking this threshhold should be maybe 85 or 90 primes by 10000.

We could also create a page for Proths - the problem here is the appetite for people to reserve values, there are 175 known VPS, tested ranges are unknown (I found many of them but did not keep a record of tests) and many have been taken to high values of n, where testing with pfgw is painfully slow. However LLR- capable Payam Proth values have not really been explored at all, to my knowledge. That would be very interesting area of exploration, using payambase.

Finally, I have kept extensive up to date records of "drag racing" Riesels, I have the best performer at each E level, and each prime found. Similar tables for Proths need to be built.

There are gaps in our knowledge. I have sketchy information on Riesels tested back in 2003 which are in my table, but for which prime information is lacking. The information on these values would need to be rebuilt.

As a side exercise it would be interesting to find the least prime Payam. I have an inkling that there are no covering sets that do not contain the small primes or primes with low order base 2. The worst performing Payam number has its first prime at about n=230, this would be an interesting search.

 kar_bon 2008-01-29 13:11

that's good to hear.
in the first step i think i could include all Riesel-VPS in that page with the information you/we got: especially the 100th prime (near misses VPS are welcome too) and/or number of primes to a level say n=10k. to get these prime n could be done time after time. reservations should also be displayed like now. then it would be helpful to make a extra page with the best candidate of every E-level with only small infos.
others information could useful: like your mentioned depth of k you searched at an E-level so noone won't do double work in that ranges.
the sierpinski-side of payam numbers could be created later (by now there're not so much results at all).
so i think i could start with the informations in this thread to extend the page and see how it looks like.
the format of report "R 1043827764761 53 100/8888 103/10000" is good, keep it, so there are infos to put in that page immediately.
Robert, i got your tables you sent me time ago. these data i can use too.
so quite now many work to do first. but you can send me more data worthly to put on!
karsten

PS: got anyone admin-rights to this thread? i think the posts could be deleted then if the infos are in that page and keeps this thread clear. perhaps the post #1 could be extended with more infos and link to the site (when 'official').

 kar_bon 2008-01-31 00:12

the first more data are online now. many will follow. only Riesel numbers from this thread so far.
look the link i gave in post 16.
karsten

 robert44444uk 2008-02-02 06:39

Karsten, Roger et al

I am running a huge batch of 61's and will find approx another 10 VPS. Will post these later and then will post the complete list of VPS Riesels to this forum.

Regards

Robert

 robert44444uk 2008-02-09 05:12

Sorry been out of the loop. Here is the list from last week on new Payam VPS 61's

R 4237605251199 61 100/9042 101/10000 117/20000 129/48714
R 3454244358239 61 100/6100 107/10000 115/20000
R 4484344243755 61 100/9481 104/10000 112/20000
R 2997280737989 61 100/8210 100/10000 111/20000
R 4321264026225 61 100/9470 100/10000 111/20000
R 4445595365641 61 100/9822 100/10000 111/20000
R 2853368710009 61 100/9310 101/10000 110/20000
R 2958974750767 61 100/9898 101/10000 110/20000
R 3468108555441 61 100/9882 101/10000 110/20000
R 4470681532631 61 100/8372 100/10000 110/20000
R 2916740069451 61 100/8981 103/10000 109/20000
R 3462599603041 61 100/8954 101/10000 108/20000
R 4031837397447 61 100/8706 100/10000 106/20000
R 3441114290305 61 100/9546 100/10000 104/20000

Near misses

R 3396843248155 61 99/10000
R 3590636449447 61 99/10000
R 3812607361279 61 99/10000
R 3836786856915 61 99/10000
R 4281080931105 61 99/10000

 robert44444uk 2009-09-23 15:22

Most prime series yet

I am currently reexploring payam prime series, and as of tonight I have two new enormously prime series of the form y*M(83)*2^n+1, n from 1 to infinity, y fixed and M(83) the payam multiple of 3*5*11*13*19*29*37*53*59*61*67*83.

The two series have 134 and 129 primes at n=30,000. The more prime of the two is the fastest to 134 primes ever found, with the 134th prime reached at n=27,762.

I will post more details when I get to n=100,000, if these are still performing well (148 primes or more).

 R. Gerbicz 2009-09-23 19:42

Robert, where can I find all known VPS Payam numbers?

 kar_bon 2009-09-23 23:19

[QUOTE=R. Gerbicz;190854]Robert, where can I find all known VPS Payam numbers?[/QUOTE]

i've included some of the Riesel-side with data from Robert on [url]www.rieselprime.de[/url].

 robert44444uk 2009-09-24 15:25

[QUOTE=R. Gerbicz;190854]Robert, where can I find all known VPS Payam numbers?[/QUOTE]

You might look here, it is out of date a bit, but I am the only person on the planet looking at these right now (!!!!!!!!!!!)

So I will update when I get the chance

A Study of Very Prime Payam Number Series - Word document

 robert44444uk 2009-09-24 15:26

[QUOTE=robert44444uk;190841]I am currently reexploring payam prime series, and as of tonight I have two new enormously prime series of the form y*M(83)*2^n+1, n from 1 to infinity, y fixed and M(83) the payam multiple of 3*5*11*13*19*29*37*53*59*61*67*83.

The two series have 134 and 129 primes at n=30,000. The more prime of the two is the fastest to 134 primes ever found, with the 134th prime reached at n=27,762.

I will post more details when I get to n=100,000, if these are still performing well (148 primes or more).[/QUOTE]

Not performing well from 30K to 43K but will persist

 R. Gerbicz 2009-09-27 00:45

I'm writing a code in gmp for the problem.

 robert44444uk 2009-09-27 04:12

[QUOTE=R. Gerbicz;191196]I'm writing a code in gmp for the problem.[/QUOTE]

Brilliant!!! love to understand your approach.

 R. Gerbicz 2009-09-28 17:43

Now I completed my code: have a look at my site: [URL="http://robert.gerbicz.googlepages.com/payam"]http://robert.gerbicz.googlepages.com/payam[/URL]
This is all in one program, contains many type of sieves to speed up the code, but only one fermat test for the primality (so there is a very small chance that the correct number of primes is smaller than the displayed value).

When tested I found the following (new?) solutions (I stopped my programs, tested only E=52, not much about one-two day of computation).

(for these riesels lost the data when it hits the 100th prime.)
R 279853706635 52 100/10000 K=648615843039215090325
R 1498340918709 52 105/10000 K=3472698896270561741355
R 1238363638869 52 102/10000 K=2870150569996671516555

S 1067246716655 52 100/7771 103/10000 K=2473553547592864962225
S 2000762814915 52 100/9824 100/10000 K=4637160163149703256925
S 740179134037 52 100/9739 100/10000 K=1715510288558036485515
S 732686633037 52 100/6580 105/10000 K=1698144948248552890515
S 2524404303887 52 100/6046 104/10000 K=5850801997320093221265
S 982750260367 52 100/8532 101/10000 K=2277716440812829166865
S 864230647989 52 100/9769 100/10000 K=2003023998023424902955
S 197278850743 52 100/7259 105/10000 K=457232421993138948585

You need two files to use it (it will ask no additional input) in.txt contains various parameters for the problem. progress.txt has got only 4 values:
c, where c=1 (sierpinski) or c=-1 (riesel),

the E value,

the iteration number (this is counter of the outer cycle) iteration=0 solves the problem for the first about 3*10^12 K values, iteration=1 solves it in the (3*10^12,6*10^12) interval and so on.

But this would take days to complete an iteration so there is an inner cycle to divide one iteration to 120960 subproblems, this is the I value, by giving it the program will start from this I value. When I reaches 120960 then iteration will be bigger by one, and I=0.

The in.txt file is a little more complicated, there are some obvious parameters. Note that I'm computing also the Nash weight for the sequence, because by this I can predict the number of remaining primes, I'm using a weaker form (not to lost a solution): #(total number of primes found so far)+c0*#(expected number of primes from Nash)+c1. Increasing the c0,c1 value makes the sieve slower, but you can find a little more sequence. Balance this. If n reaches various number then I'm using a different sieve depth: number_of_sievebits is the levels for sieve, currently this is 7, and the offset:
11 64
13 128
15 256
18 512
21 1024
24 2048
27 4096
so sieving up to 2^11 if n=64 reached,..., up to 2^27 if n=4096 reached. Note that this is also the sievelimit=2^27.

Your heuristic check is also included (as smith check), the table is exactly what I found at your site (currently this means 8 levels).

Optimize these (you can change the number of levels, but use increasing order when you describe the levels). By setting zero for nash_check or smith_check you can disable these checks in the code.

By boundforquickcheck I make an additional quick elimination using many primes up to this bound. Currently this value should be good. Setting this very high is pointless (elminates very few sequences and takes time).

nashsievelimit is 500 currently. Note that this equals to the initial sieve depth. So if there is no Nash check, then not lower this value.

timesave 60. Saves the E,c,iteration,I values in progress.txt in every 60 seconds, but only if we are not checking a sequence, so it means that there will be a save only after half an hour if we are checking a very good payam.

In results.txt file I also save every vps numbers. The code is valid for E>=52.
Ask if you don't understand something.

 robert44444uk 2009-09-29 07:06

Gosh, a new toy..thank you so much Robert, I will give this a go, that is for sure.

The list of payam VPS for Sierpinski, before R Gerbicz's discoveries, is:

[CODE]

Rank E y n p=primes p/ln(n) 100 p at n= Notes

1 59 708477982733 353045 169 13.230 7815
2 59 201456540759 137581 152 12.847 6929
3 107 224425208891 105413 148 12.797 7884 Done as 101-24013497351337
4 83 8648987274287 53961 139 12.757 7874
5 83 2266756289325 51015 138 12.731 7034
6 59 520294740741 123329 149 12.710 7970
7 67 2158430601663 174566 153 12.676 5496
8 53 748868434461 113183 147 12.632 4584
9 67 4217062025887 170000 152 12.621 6634
10 59 241489693273 126324 147 12.514 8938
11 67 3830573300695 113977 145 12.453 6063
12 59 49564242661 116957 144 12.340 5774 Done as 53- 2924290316999
13 67 244078509453 100112 142 12.333 9459
14 67 3274457656551 128894 145 12.323 8422
15 67 1691908298101 110287 143 12.316 6356
16 59 748236995639 128980 144 12.237 6592
17 59 33936630553 96274 140 12.200 7515 Done as 53-2002261202627
18 83 491867720503 88968 139 12.197 8064
19 101 21475115323671 124388 143 12.190 9589
20 101 95527332753853 112374 141 12.124 9694
21 53 1108828374241 126708 142 12.085 3258
22 101 100848501131179 135522 142 12.017 8240
23 67 4169065599069 97356 138 12.014 9413
24 61 761114361105 165526 144 11.983 9591
25 53 2088021538507 121242 140 11.960 6029
26 83 1198899076961 46968 128 11.899 7326
27 101 154597862545015 85569 135 11.887 8916
28 101 192982750577891 125493 139 11.840 7193
29 53 2793145615989 70337 132 11.827 5621
30 83 16606496583 40100 125 11.793 6110 Done as 67-1378339216389
31 67 132931011017 37004 124 11.788 4628
32 59 354663797011 44321 126 11.777 8384
33 83 2931487359433 75195 132 11.756 8094
34 67 650072358489 27810 120 11.727 7482
35 53 1030943838005 43187 125 11.711 7562
36 83 5187739022961 28368 120 11.704 4951
37 59 44549431055 36787 123 11.700 7066
38 83 58721022127 31144 121 11.695 6179
39 67 1639585686921 32011 121 11.664 8626
40 59 581338538697 25170 118 11.645 9084
41 53 1782926020855 25833 118 11.615 7256
42 101 48568720015071 20000 115 11.612 7178
43 53 2632245983931 28434 119 11.604 8276
44 61 18450742305 37335 122 11.588 9462
45 61 5274320251 31434 120 11.588 9603
46 101 3196190228975 29110 119 11.577 8490
47 67 2882469181769 31919 120 11.571 7824
48 53 1394429459529 24646 117 11.570 8420
49 107 39508074262189 38527 122 11.554 8399
50 53 246580719613 27749 118 11.534 7136
51 53 223580243791 33314 120 11.523 7687
52 67 2232861808559 28242 118 11.514 7652
53 83 1215507650411 47628 124 11.512 7597
54 83 7245887932337 20000 114 11.511 8903
55 67 4195586470999 22000 115 11.501 7595
56 67 135980427451 20230 114 11.498 9257
57 83 157639428379 26587 117 11.484 6690
58 67 643697078775 20560 114 11.479 9351
59 107 216263008344019 32592 119 11.451 9897
60 53 1106093443175 42374 122 11.451 9387
61 59 838422520523 25578 116 11.429 6134
62 101 7822821559961 25615 116 11.428 9987
63 67 1102272321579 20000 113 11.410 6881
64 83 2986006925223 20017 113 11.409 8415
65 67 755584622563 21960 114 11.403 9797
66 101 86475926712443 26415 116 11.393 7535
67 53 1439338251 27569 116 11.345 6149
68 53 181681767761 33197 118 11.335 7062
69 53 2562457278273 21555 113 11.325 8668
70 67 3626325799905 30739 117 11.323 8316
71 61 126014792173 52310 123 11.321 7542
72 53 887074003901 20000 112 11.309 9434
75 83 721457110513 20000 112 11.309 9531
74 83 4787038083625 20000 112 11.309 8794
73 83 10200107805041 20000 112 11.309 8118
76 53 2367521100037 20029 112 11.307 9590
77 83 5105032597357 21975 113 11.303 7080
78 101 171652306377675 20317 112 11.291 7261
79 67 1111147210737 22200 113 11.291 8002
80 67 2807554854083 24525 114 11.279 8779
81 67 14227569099675 18910 111 11.272 9610
82 67 1166880299109 18910 111 11.272 7795
83 101 75903439364915 27353 115 11.256 9297
84 101 19743600960335 27362 115 11.256 9487
85 61 583625072025 30000 116 11.252 8464
86 101 190423530464325 32919 117 11.248 9127
87 101 109139135495845 21162 112 11.245 9070
88 61 216022607101 27655 115 11.244 9149
89 67 133290101259 21460 112 11.229 9993
90 53 1322845239177 26088 114 11.210 9940
91 53 2732995339057 20000 111 11.208 7743
92 59 546421435843 20000 111 11.208 9134
93 59 387304364559 20000 111 11.208 8974
94 67 2934187788435 20000 111 11.208 9885
95 83 3966811064579 20000 111 11.208 9784
98 83 11613098507093 20000 111 11.208 9387
97 83 11730030736641 20000 111 11.208 9244
96 83 1268045994659 20000 111 11.208 7251
99 83 4189509745483 17000 109 11.190 7487
100 67 3953819504565 22500 112 11.176 9460
101 67 2528619568769 29523 115 11.173 8172
102 53 2618147732705 20640 111 11.173 8620
103 53 2206204972241 14450 107 11.171 9577
104 53 215886220855 14450 107 11.171 8682
105 53 2516441148893 14450 107 11.171 8541
106 53 1662290560099 14450 107 11.171 8127
107 53 2229929826019 14450 107 11.171 8097
108 59 68102182393 16000 108 11.157 9920
109 59 323109341021 16000 108 11.157 7841
110 67 1370090826199 21000 111 11.153 7906
111 67 3801806524317 30101 115 11.152 8197
112 37 198314124283 20000 110 11.107 9184
113 53 2030780730455 18289 109 11.107 9931
114 53 2630773010587 14115 106 11.094 8353
115 67 1789583243673 113765 129 11.081 6261
116 37 176776697181 10000 102 11.075 8030
117 67 4041645718707 10000 102 11.075 7549
118 67 3846443304797 10000 102 11.075 6356
119 53 879944491239 14450 106 11.067 9131
120 53 2291356967435 14450 106 11.067 9039
121 53 1806872869235 14450 106 11.067 8746
122 53 1390617022279 14450 106 11.067 8311
123 29 547038013 17442 108 11.058 8129
125 59 512528281705 16000 107 11.053 9418
124 59 177646354161 16000 107 11.053 9136
126 59 514472660303 16000 107 11.053 7819
127 67 498179107913 21010 110 11.052 9935
128 53 70073251271 16073 107 11.048 9977
129 59 636331922397 21148 110 11.045 7117
130 67 3026077759051 13500 105 11.040 9007
131 67 3794179552947 13500 105 11.040 8892
132 67 4152485119483 13500 105 11.040 8270
133 67 3384136174759 13500 105 11.040 8006
134 67 2253302898127 13500 105 11.040 7743
135 107 3528240874503 19549 109 11.032 8662
136 37 255911170795 19630 109 11.027 9086
137 67 143567524087 19712 109 11.022 9893
138 67 1175624915339 19800 109 11.017 8719
139 53 2662257628835 23752 111 11.017 8353
140 61 197793964319 28717 113 11.008 7081
141 29 373703051 20000 109 11.006 8409
142 61 48622210669 28850 113 11.003 8016
143 101 37933879098593 24224 111 10.995 9060
144 61 38886476903 31866 114 10.994 9793
145 83 4241660982683 10767 102 10.986 8096
146 67 18914454038503 18910 108 10.967 8397
147 59 708240321809 18931 108 10.966 8524
148 67 1583098704779 10000 101 10.966 8615
149 61 406713450161 27685 112 10.950 8263
150 83 2508280254913 12300 103 10.937 8884
151 83 3100447231731 12300 103 10.937 8183
152 67 2248422362825 13500 104 10.935 9920
153 67 925777324893 13500 104 10.935 9549
154 67 3213814677791 13500 104 10.935 9493
155 67 22334461555 13500 104 10.935 9443
156 67 2374195442249 13500 104 10.935 9362
157 67 1026619279015 13500 104 10.935 8930
158 107 171176144825869 28101 112 10.934 8473
159 59 491580860277 15000 105 10.920 9936
160 59 657752151441 15000 105 10.920 9444
161 61 195989400097 20000 108 10.905 9439
162 67 2093234092849 20000 108 10.905 8573
163 83 5855022739083 20000 108 10.905 8483
164 83 1806361620889 26341 111 10.905 7464
165 37 133581656467 18300 107 10.902 8013
166 53 768440105325 20749 108 10.865 9454
167 53 696219338021 14450 104 10.858 9515
168 53 1843822052193 14450 104 10.858 9132
169 53 2919421195929 14450 104 10.858 8597
170 53 1568680504507 14450 104 10.858 8526
171 83 3111030987175 25112 110 10.858 7841
172 37 218268558295 10000 100 10.857 9825
173 53 863106968087 10000 100 10.857 9947
174 53 1931888563731 10000 100 10.857 9796
175 101 88475910866235 10000 100 10.857 9725
176 83 4942274044547 12300 102 10.831 9730
177 67 1206204060651 13500 103 10.830 8839
178 67 325914572859 13500 103 10.830 8817
179 67 3977890351863 13500 103 10.830 7253
180 101 34964416850395 17860 106 10.827 9528
181 37 147377655077 20000 107 10.804 8008
183 83 9079836090073 20000 107 10.804 9726
182 83 12228640605139 20000 107 10.804 9666
184 53 685900043171 20347 107 10.786 9951
185 61 933294678535 14097 103 10.781 9866
186 53 353454181481 19030 106 10.757 8636
187 53 2530657964501 14450 103 10.753 9815
188 67 2158846621199 13500 102 10.725 8697
189 59 316104583913 15000 103 10.712 9910
190 83 5780208112465 18100 105 10.710 8853
191 67 3982074999875 21100 106 10.646 8634
192 53 415571569029 16073 103 10.635 9483
193 83 568584531317 12300 100 10.619 9899
194 61 586780960367 20499 105 10.576 9581
195 37 236033583093 19204 104 10.545 9545

[/CODE]

 robert44444uk 2009-09-29 07:09

And that for Riesels (sorry for any duplicates):

[CODE]
Rank E y n p=primes p/ln(n) 100p at n= Discoverer
1 60 638621868573 233805 162 13.104 8110 R. Chaglassian
2 58 196866927943 75000 145 12.917 6617 R. Chaglassian
3 100 38612012001591 70000 143 12.818 6306 R Smith
4 82 1634620998691 75000 142 12.650 7237 R. Chaglassian
5 82 1923109539243 75000 140 12.472 6261 R. Chaglassian
6 58 660288556697 76281 140 12.453 6167 R Smith
7 82 534443544481 75000 139 12.383 9749 R. Chaglassian
8 60 868800846205 75000 138 12.294 9686 R. Chaglassian
9 82 2903265685133 75000 138 12.294 8077 R. Chaglassian
10 82 3595866123809 75924 138 12.280 9210 R Smith
11 106 336458226173 74709 137 12.209 9642 R Smith
12 52 98213127897 75000 137 12.205 6863 R. Chaglassian
13 66 295804381687 50000 132 12.200 8984 R. Chaglassian
14 60 2342836014713 70629 136 12.181 6520 R Smith
15 52 72702941519 75000 136 12.116 6724 R. Chaglassian
16 58 782507407593 75000 136 12.116 7734 R. Chaglassian
17 60 4237605251199 48714 129 11.951 9042 R Smith
18 60 4832067885263 20000 118 11.915 6538 R Smith
19 82 7987188035689 36772 124 11.795 7043 R Smith
20 82 2173328761571 19656 115 11.632 9653 R Smith
21 58 543298716599 21723 116 11.616 5768 R Smith
22 52 169160174245 20000 115 11.612 8191 R Smith
23 58 810747927647 20000 115 11.612 7248 R Smith
24 60 3454244358239 20000 115 11.612 6100 R Smith
25 60 189018321331 58808 127 11.564 7788 R Smith
26 52 114230062971 20000 114 11.511 9945 R Smith
27 52 1029369515711 20000 114 11.511 8895 R Smith
28 58 736928023853 20000 114 11.511 8642 R Smith
29 58 736928023853 20000 114 11.511 8642 R Smith
30 60 4821660919323 20000 114 11.511 8444 R Smith
31 100 159929185703 20000 114 11.511 8646 R Smith
32 66 3614192791887 15284 110 11.417 8863 R Smith
33 58 98708132615 20000 113 11.410 8756 R Smith
34 60 303323448333 20000 113 11.410 7996 R Smith
35 106 506972504569 20120 113 11.403 8564 R Smith
36 106 408251547745613 10000 105 11.400 8230 R Smith
37 82 5938953888893 19907 112 11.314 9010 R Smith
38 82 7425115793209 19907 112 11.314 9042 R Smith
39 52 42509546845 20000 112 11.309 5748 R Smith
40 52 89843365969 20000 112 11.309 8758 R Smith
41 52 150889892985 20000 112 11.309 9968 R Smith
42 58 782507407593 20000 112 11.309 7734 R Smith
43 60 4484344243755 20000 112 11.309 9481 R Smith
44 100 82206833338609 20000 112 11.309 7531 R Smith
45 58 222325060763 10000 104 11.292 7832 R Smith
46 52 3680068181457 13301 107 11.268 7836 R Smith
47 66 2517038016555 14840 108 11.244 7397 R Smith
48 82 2295909940011 19656 111 11.228 7195 R Smith
49 58 795329018075 23591 113 11.223 9934 R Smith
50 82 6442859915349 19907 111 11.213 9281 R Smith
51 52 1636889512137 20000 111 11.208 7724 R Smith
52 58 635481469401 20000 111 11.208 9208 R Smith
53 58 211956740839 20000 111 11.208 9545 R Smith
54 60 90779697267 20000 111 11.208 7307 R Smith
55 60 2997280737989 20000 111 11.208 8210 R Smith
56 60 4321264026225 20000 111 11.208 9470 R Smith
57 60 4445595365641 20000 111 11.208 9822 R Smith
58 52 688812815683 10000 103 11.183 8559 R Smith
59 82 38367867040615 10000 103 11.183 6920 R Smith
60 106 5858856352434629 10000 103 11.183 9050 R Smith
61 52 1212241451853 20000 110 11.107 8256 R Smith
62 58 52839326407 20000 110 11.107 9218 R Smith
63 58 1633249508195 20000 110 11.107 9807 R Smith
64 58 776579546957 20000 110 11.107 8448 R Smith
65 60 2853368710009 20000 110 11.107 9310 R Smith
66 60 2958974750767 20000 110 11.107 9898 R Smith
67 60 3468108555441 20000 110 11.107 9882 R Smith
68 60 4470681532631 20000 110 11.107 8372 R Smith
69 60 5160537303507 20000 110 11.107 9855 R Smith
70 66 29979474409 28913 114 11.098 5968 R Smith
71 58 469387109359 10000 102 11.075 8147 R Smith
72 58 557419349873 10000 102 11.075 8916 R Smith
73 58 1313295408947 10000 102 11.075 8233 R Smith
74 58 1319596402677 10000 102 11.075 8786 R Smith
75 60 1746492605077 10000 102 11.075 8014 R Smith
76 60 2319747344799 10000 102 11.075 9595 R Smith
77 66 10941694057 10000 102 11.075 8831 R Smith
78 66 3385909902081 10000 102 11.075 8063 R Smith
79 82 61976585459877 10000 102 11.075 8600 R Smith
80 106 101532422035567 10000 102 11.075 9253 R Smith
81 52 3995993454669 13301 105 11.058 9870 R Smith
82 82 701334132961 19656 109 11.026 9968 R Smith
83 100 43468118077543 20000 109 11.006 8452 R Smith
84 58 678487262125 20000 109 11.006 9376 R Smith
85 58 395178526267 20000 109 11.006 9409 R Smith
86 58 182579377155 20000 109 11.006 9520 R Smith
87 60 2916740069451 20000 109 11.006 8981 R Smith
88 106 158227976455 20000 109 11.006 9886 R Smith
89 130 1060872021917 24537 111 10.981 9726 R Smith
90 37 93061801369 26905 112 10.980 7480 R Smith
91 52 276458718213 10000 101 10.966 9684 R Smith
92 58 151403071919 10000 101 10.966 7717 R Smith
93 58 211956740839 10000 101 10.966 9545 R Smith
94 58 950392115281 10000 101 10.966 9073 R Smith
95 60 502968170927 10000 101 10.966 8247 R Smith
96 66 167928198647 10000 101 10.966 9822 R Smith
97 66 1876131394595 10000 101 10.966 8443 R Smith
98 82 272478401987 10000 101 10.966 8515 R Smith
99 82 63404089076241 10000 101 10.966 8159 R Smith
100 106 5071829957884753 10000 101 10.966 8856 R Smith
101 66 2211264287175 14840 105 10.932 8856 R Smith
102 66 2364307317539 14840 105 10.932 9294 R Smith
103 82 3329128302189 19656 108 10.924 9216 R Smith
104 52 1043827764761 20000 108 10.905 8888 R Smith
105 60 3462599603041 20000 108 10.905 8954 R Smith
106 37 4111071389 10000 100 10.857 8813 R Smith
107 58 141016944033 10000 100 10.857 9936 R Smith
108 58 805479768391 10000 100 10.857 8477 R Smith
109 60 2502262772385 10000 100 10.857 9732 R Smith
110 60 2781948761147 10000 100 10.857 9271 R Smith
111 60 2256305169303 10000 100 10.857 9821 R Smith
112 60 2476995416951 10000 100 10.857 9951 R Smith
113 60 2421745267415 10000 100 10.857 9769 R Smith
114 66 6085263665 10000 100 10.857 9492 R Smith
115 66 1416492589021 10000 100 10.857 8013 R Smith
116 66 1533927640019 10000 100 10.857 9972 R Smith
117 66 1842913644031 10000 100 10.857 9937 R Smith
118 66 1970620879533 10000 100 10.857 9500 R Smith
119 82 1019383426867 19656 107 10.823 9527 R Smith
120 52 39954902847 20000 107 10.804 9846 R Smith
121 58 452026989743 20000 107 10.804 9528 R Smith
122 60 5365195396417 20000 107 10.804 9016 R Smith
123 52 68110929705 20000 106 10.703 7339 R Smith
124 58 1513926608167 20000 106 10.703 9879 R Smith
125 58 795329018075 20000 106 10.703 9934 R Smith
126 60 4031837397447 20000 106 10.703 8706 R Smith
127 82 2653731528155 19656 104 10.520 9599 R Smith
128 60 3441114290305 20000 104 10.501 9546 R Smith
129 58 640953612177 20000 102 10.299 9084 R Smith

[/CODE]

 robert44444uk 2009-09-29 08:49

Robert

Your program seems to work quite well, it certainly did not fall down on my machine. I will have to play with the variables to see how to maximise the response, but certainly 11 VPS in a couple of days compares rather favourably to my 2-3 a week, which is the best I could manage recently.

None of your Sierpinski VPS coincide with my table which is curious, you might have thought that at least one might have been picked up as the overall approach is not totally different and the range checked looks the same.

Whjen you mention in your instructions that an iteration covers 3*10^12 K values, do you mean 3*10^12 payam numbers or 3*10^12 y values? as K is defined as y*E(x).

 robert44444uk 2009-09-29 11:15

I used the athlon exe file on a beat up old athlon and it is eating numbers!!!!

Reserving 82 Sierpinski and Riesel

 robert44444uk 2009-09-29 12:12

[QUOTE=R. Gerbicz;191351]

The in.txt file is a little more complicated, there are some obvious parameters. Note that I'm computing also the Nash weight for the sequence, because by this I can predict the number of remaining primes, I'm using a weaker form (not to lost a solution): #(total number of primes found so far)+c0*#(expected number of primes from Nash)+c1. [/QUOTE]

By this can I infer that a number that would be eliminated by "Smith check" because of insufficient prime count at a given n, will still be calculated at higher n if the Nash weight predicts it should reach a higher "Smith check" hurdle?

 R. Gerbicz 2009-09-29 15:43

[QUOTE=robert44444uk;191415]
None of your Sierpinski VPS coincide with my table which is curious, you might have thought that at least one might have been picked up as the overall approach is not totally different and the range checked looks the same.

Whjen you mention in your instructions that an iteration covers 3*10^12 K values, do you mean 3*10^12 payam numbers or 3*10^12 y values? as K is defined as y*E(x).[/QUOTE]

In fact I've deleted the known numbers when submitted my post (using this forum and the two excel tables on your site), I've rediscovered on both sides some vps numbers, altogether there were about 5-6 such values, which is not very bad, indicates that the nash check is not very bad.

I'm checking about 3*10^12 y values at once, as you write in your paper only a fraction of them are payam numbers, thanks to a clever sieve I quickly eliminate many of them. In fact as I've written this is not exactly 3*10^12, the correct value is 2869549272527.

ps. Now I see my original post writing 3*10^12 K values, that was a typo.

 R. Gerbicz 2009-09-29 15:48

[QUOTE=robert44444uk;191427]By this can I infer that a number that would be eliminated by "Smith check" because of insufficient prime count at a given n, will still be calculated at higher n if the Nash weight predicts it should reach a higher "Smith check" hurdle?[/QUOTE]

No, these checks are independent. So it means that if both of the checks are enabled and only one of them or both of them indicates that we will not reach 100 primes then the code immediately breaks the test on that payam number.

 robert44444uk 2009-09-29 16:08

[QUOTE=R. Gerbicz;191446]No, these checks are independent. So it means that if both of the checks are enabled and only one of them or both of them indicates that we will not reach 100 primes then the code immediately breaks the test on that payam number.[/QUOTE]

Intuitively it seems it would be better if one of them indicates that will reach 100/10000 then that prime continues. But intuition does not match up against pure logic, so I must accept your logic.

I also reserve 66 Riesel and 100 Riesel as I experiment.

I am so impressed with the performance of this software! This generates and checks payams faster by 500% than Axn1's software generated payams with no prime checking on the old machine I have. This may be due to the fact that it is also Athlon optimised. I am a happy puppy right now.

The software is so fast that I am generating 74/3000 as my target rather than 100/10000 because I can check those at my leisure.

 robert44444uk 2009-09-29 16:10

[QUOTE=R. Gerbicz;191445]In fact I've deleted the known numbers when submitted my post (using this forum and the two excel tables on your site), I've rediscovered on both sides some vps numbers, altogether there were about 5-6 such values, which is not very bad, indicates that the nash check is not very bad.

[/QUOTE]

Then your rate of discovery is even greater!!!!

 Dougal 2009-09-29 19:28

my pentium version keeps crashing.and i cant figure out what to put in the in.txt file.

 R. Gerbicz 2009-09-29 19:48

[QUOTE=Dougal;191464]my pentium version keeps crashing.and i cant figure out what to put in the in.txt file.[/QUOTE]

You need also progress.txt file, download that also. (The exe and the two text files should be in the same folder).

If you change nothing then the program should work (it will test E=52), if you want to test other E values then E+1 should be such a prime for that 2 is a primitive root modulo E+1, so for example the good E values up to 140 are: 52,58,60,66,82,100,106,130,138. (For E<52 the program not works.)
If you want to start the computation from the beginning then not change iteration and I, so only modify E in progress.txt. For more information see my post above or ask.

ps.
I can imagine that something is bad with the exe, now I am at an Athlon computer, tomorrow I will see the exe on a Pentium, and if that is still bad then compile the code on that (I've installed gmp on that computer also.).

 robert44444uk 2009-09-30 01:20

Athlon and Pentium programs ran all night successfully on three machines and four cores. No problems. I always worry about screensavers, but this did not appear to impact performance.

 robert44444uk 2009-10-03 06:47

Also reserving Sierpinski 60.

Stupendous progress, as of now I generated 26 new values and a further 14 duplicates, in the 4 areas I reserved. No record breakers though yet. Thats 40 in 6 days, compared to the 2-3 a week before. I will post at a convenient time. The software has not fallen down at all.

Robert G: Is there a way you could capture a racing table as well, that shows fastest performers to each prime level, each time the software is run? If this would slow things down then please do not change a thing!

The softest target is the Riesel record to 100 primes which is only at n=5748. I have found 6 Sierpinskis with better records than that.

 robert44444uk 2009-10-03 07:47

I spoke too soon, the program fell over.

progress.txt

c 1
E 60
iteration 0
I 0

Error message:
E+1 should be prime.

But E+1=61 prime.

Until fixed will take Sierpinski 58

 R. Gerbicz 2009-10-03 18:47

[QUOTE=robert44444uk;191763]
Stupendous progress, as of now I generated 26 new values and a further 14 duplicates, in the 4 areas I reserved. No record breakers though yet. Thats 40 in 6 days, compared to the 2-3 a week before. I will post at a convenient time. The software has not fallen down at all.

Robert G: Is there a way you could capture a racing table as well, that shows fastest performers to each prime level, each time the software is run? If this would slow things down then please do not change a thing!
[/QUOTE]

Obviously the number of vps numbers depend on the E value, and on the side.
Done that modification it isn't slower, it is writing the record table to a txt file. Be careful, it won't use this txt file at the start of the program even if there is a recordtable.txt file on the folder. The format of the text file: level n y E as in your paper.

And now there is much less screen output of the status (there is at least 5 seconds between consecutive outputs).

"Error message:
E+1 should be prime.
But E+1=61 prime."

Corrected, it is a minor bug, doesn't effect your earlier computations.

 robert44444uk 2009-10-04 09:22

Robert G

The racing table works very well...perfect. The E60 problem is fixed. Please note that there are other E values that could be checked that are not p-1, as their profiles are slightly different.

What is the highest E that can be checked? It was not possible to go beyond E=255 with Axn1's program.

A couple of minor improvements that could be made to the output files:

recordtable.txt - add whether it is Sierpinski (S) or Riesel (R)
results.txt - (i) add a date and time stamp to the output (ii) add the iteration and I value of discovered candidates. This will help build a statistical model for the possible number of VPS at a given level

Regards

Robert S

 R. Gerbicz 2009-10-04 12:55

[QUOTE=robert44444uk;191835]Robert G

The racing table works very well...perfect. The E60 problem is fixed. Please note that there are other E values that could be checked that are not p-1, as their profiles are slightly different.

What is the highest E that can be checked? It was not possible to go beyond E=255 with Axn1's program.

A couple of minor improvements that could be made to the output files:

recordtable.txt - add whether it is Sierpinski (S) or Riesel (R)
results.txt - (i) add a date and time stamp to the output (ii) add the iteration and I value of discovered candidates. This will help build a statistical model for the possible number of VPS at a given level

Regards

Robert S[/QUOTE]

E<sievelimit (default=2^27) should be true. But note that choosing a large E it might cause that there is no payam/vps number up to y=2^60, (this is the limit for y value in the code). Probably for E>1000 it is true.

 robert44444uk 2009-10-04 16:43

Great

Will run on 3 machines 4 cores tonight.

 robert44444uk 2009-10-05 10:46

Software fixes all working well !!

 robert44444uk 2009-10-07 16:54

[QUOTE=robert44444uk;191763]Also reserving Sierpinski 60.

The softest target is the Riesel record to 100 primes which is only at n=5748. I have found 6 Sierpinskis with better records than that.[/QUOTE]

Oooh, near miss

R 1709333922219 60 100/5811 106/10000

Still finding plenty of VPS, will post at the weekend

 robert44444uk 2009-10-08 10:58

In 11 days I found 80 new VPS, to add to the 320 already known before Robert's program became available, so that is 411 including Robert's 11 finds.

In 6 weeks I can singlehandedly double the known VPS, which were found over a period of 6 years

None of the 80 have > 106/10000 though. The juicy ones are still to come.

 robert44444uk 2009-10-16 11:51

After 2 weeks still do not have one 110/10000 but several new drag racing records:

New absolute drag racing records:

S 391170716069 60 48/271
S 391170716069 60 49/288
S 391170716069 60 50/292
S 2121365747455 58 75/1252
S 2442649832339 58 77/1409
S 2442649832339 58 78/1418
S 2442649832339 58 79/1421
S 2442649832339 58 80/1557
S 2442649832339 58 81/1634

Best Riesel at a given n - at least 1 Sierpinski beats or equals these

R 90235721373 60 21/41
R 1654011147057 60 83/2080
R 1654011147057 60 84/2123
R 1654011147057 60 85/2132
R 1654011147057 60 86/2200
R 1654011147057 60 87/2201
R 1654011147057 60 92/3326
R 1654011147057 60 93/3765
R 1654011147057 60 94/3827
R 1654011147057 60 95/3967
R 1709333922219 60 98/5269
R 1709333922219 60 99/5321
R 1709333922219 60 104/7266

Best Sierpinski at a given n - at least one Riesel beats or equals these:

S 2618651601039 58 9/9
S 2618651601039 58 10/10
S 391170716069 60 38/142
S 391170716069 60 39/143
S 391170716069 60 40/166
S 391170716069 60 41/167
S 391170716069 60 42/173
S 391170716069 60 43/185
S 391170716069 60 44/199
S 391170716069 60 46/234
S 2604607723337 60 47/254
S 2604607723337 60 57/471
S 2442649832339 58 76/1397

The Riesel record to 100 primes remains unbeaten

 robert44444uk 2009-10-16 12:01

As of yesterday (2 weeks in) I have found 86 new Sierpinski VPS and 105 Riesel VPS. One is 108/10000, there are 3 at 107/10000 and 5 at 106/10000.

I have also reserved Riesel 52 from Iteration 2 - just found my first 109/10000 after only 12 hours of searching

The very best performer at 10000, with 116 primes, found 6 years ago, looks a tough one to beat, although it is only 7th best Sierpinski performer overall

S 2158430601663 66 100/5496 116/10000 153/174566

 R. Gerbicz 2009-10-16 13:30

[QUOTE=robert44444uk;193001]As of yesterday (2 weeks in) I have found 86 new Sierpinski VPS and 105 Riesel VPS. One is 108/10000, there are 3 at 107/10000 and 5 at 106/10000.[/QUOTE]

That's a nice progress!

 robert44444uk 2009-10-24 04:06

Been working on the Riesel side this week, mainly on E52's. Many new drag racing records, the most noticeable of which is

R 15145054826747 52 19/31 20/32

It is really tough to break all time drag racing records at lower n as maybe a trillion k have been checked to this level.

It is prime at n=1,2,3,8,9,10,13,14,15,16,17,20,21,22,26,27,29,30,31,32, so 14 CCs in there.

I still have not achieved a better VPS on the Riesel side than 100/5748 nor have I found any new at 110+/10000, so I will persist on the Riesel side, checking at all E levels. If others join the hunt, they should concentrate on the Sierpinski side.

A minor record broken, there is a k, approximately 3.1249*10^36, which has 102/10000. This is the largest k to date which is VPS. The smallest k is approx 4.416*10^14, on the Sierpinski side.

I also found the first E138 VPS this week,

R 25988421035 138 100/9986 100/10000

In all, using Robert Gerbicz's software, I have now discovered 206 new Riesel VPS: 1 is 109/10000, 5 are 107, 8 are 106, and 11 are 105/10000. 67 are E52, 10 E58, 39 E60, 19 E66, 49 E82, 13 E100, 5 E106, 3 E130 and 1 E138. 2 have their hundredth prime between n=5K-6K, 14 in the 6000's, 21 in the 7K range, 64 in the 8K and 105 in the 9K.

I still find it astonishing that I am the only person on the planet using this crafted software. I do encourage others to join the hunt.

 robert44444uk 2009-10-24 04:21

If others do take the Sierpinski side, I have checked the following

S 58 to Iteration=0, i=98849
S 60 to Iteration=0, i=24786
S 82 to Iteration=1, i=51248

Robert Gerbicz has checked an unspecified number of S 52.

Another interesting thing to find is the first S 268. The in.txt file should be manipulated to check all finds at that level to at least n=10000. So set vpscount to 1, and smith_check to 0

 robert44444uk 2009-10-24 05:26

Total VPS and their discoverers:

Sierpinski:
195 R Smith/ P Carmody
89 R Smith/ R Gerbicz
8 R Gerbicz

292 Total

Riesel:
203 R Smith/ R Gerbicz
114 R Smith/ P Carmody
11 R Chaglassian/ P Carmody
3 R Gerbicz

331 Total

623 Grand Total

 robert44444uk 2009-10-27 16:29

Finally broke the century Riesel record, a certain E(60) candidate is 100/5566 and 110/10000.

And another E(66) candidate found 10 minutes later is 100/6660 and 109/10000. Either of these could easily become the most prime k known to date.

 robert44444uk 2009-11-09 11:07

A week away and the project is purring away nicely, although I am still the only person working on it. This is hard to comprehend given the rewards for small prime hunters and the possibility to discover a nice juicy k that might have 200 primes before n=1,000,000

How can I be the only person in the World doing this? I haven't even got someone, even another geek, to tell me this is a geeky thing I am doing.

The week produced no absolute (best of Riesel and Sierpinski) racing records, but plenty of Reisel records. There are now 67 new Reisel racing records to the 113th prime, of which 17 are absolute racing records.

And this week also produced one k at 112/10000 and one at 113/10000. Altogether I have found 366 new Riesel VPS, of which 54 are equal to, or better than, 105/10000.

Overall, since the software was written, the number of VPS has grown from 320 (195 S and 125 R) to 783 (292 S and 491 R).

 kar_bon 2009-11-09 12:39

[QUOTE=robert44444uk;195252]This is hard to comprehend given the rewards for small prime hunters and the possibility to discover a nice juicy k that might have 200 primes before n=1,000,000

How can I be the only person in the World doing this? I haven't even got someone, even another geek, to tell me this is a geeky thing I am doing.
[/QUOTE]

i think there're some reasons why:

- there's much less fame for finding 'small' primes than big ones

- to test a 30- or 40-digit k with a nash-weight of 8000 or 9000 will last for years; only to test up to n=100k it's a great effort

- another aspect: such big k-values cannot sieved with srsieve, you have to use newpgen in primorial mode! so sieving will take more time.

- the most primes of one k today (as far as i know) is for k=37850187375 from T.Ritschel: 159 primes up to n~620000; the 100th prime is at n=13719. so with your records with 113 primes at n=10000 it's a very big step to find such special k with 200 primes to n=1000000!

i think i will continue 'my' k with 130 primes up to n=100k the next weeks.

i haven't done much work the last month on the related page [url=http://www.rieselprime.de/Related/RieselPayam.htm]here[/url]!

perhaps you can fill some values there.

 robert44444uk 2009-11-09 16:22

[QUOTE=kar_bon;195261]i think there're some reasons why:

- another aspect: such big k-values cannot sieved with srsieve, you have to use newpgen in primorial mode! so sieving will take more time.

- the most primes of one k today (as far as i know) is for k=37850187375 from T.Ritschel: 159 primes up to n~620000; the 100th prime is at n=13719. so with your records with 113 primes at n=10000 it's a very big step to find such special k with 200 primes to n=1000000!
[/QUOTE]

Small primes are cute if you have no processing power.

The best at n=10000 I have found has 116, from several years ago.

You can use newpgen efficiently without primorial mode using * symbol between primes in E, and it works well but with these numbers only 70% to 75% of n get eliminated. But that is why they are so prime.

Most primes is 169 found by me at n=360000. There is a big difference between 169 at 360000 and 159 at 620000. I think getting a super VPS will give a huge advantage and Robert Gerbicz's program gives us the edge.

I agree they are quite slow to check above n=160000

But 200 at n=1000000 is doable in my opinion

 axn 2009-11-09 17:03

[QUOTE=robert44444uk;195284]Most primes is 169 found by me at n=360000[/QUOTE]
Sounds like time for a new project -- 31 or bust :smile:

 robert44444uk 2009-11-10 06:12

This certainly would be a good objective - I have sieved deeply to n=500000 if anyone is interested. I have forecast that the 200th prime is at about n=2000000

Most primes found (169): 708477982733*M(59)*2^n+1, checked to n=353045, prime for n=

2,3,4,9,16,23,28,41,49,52,58,87,94,98,100,106,130,141,145,149,152,154,161,166,167,175,177,179,181,
183,188,202,216,227,239,272,324,352,371,399,419,434,461,466,478,513,524,565,573,600,618,643,668,
680,703,736,758,807,855,883,908,915,934,945,1044,1049,1054,1200,1224,1250,1463,1810,2234,2317,
2388,2740,2879,3054,3108,3680,3692,3796,3867,3893,3917,3941,4001,4050,4080,4137,5202,5230,5805,
6134,6343,6540,7277,7440,7534,7815,8100,9360,9473,9844,9909,10277,10790,10918,11459,12716,
13641,13824,15863,17072,18041,18601,19470,22777,23750,25140,25558,31512,36659,36833,37522,
37525,38876,39047,39949,40663,43294,44173,46708,49784,50432,51378,51660,55708,58034,58798,
74103,76856,78788,80913,88261,88674,104186,105283,107911,122428,123760,125392,126478,129152,
129850,137749,172113,174521,184521,202474,206409,214727,226714,231290,240057,243709,300332,
340795,352601

But I think there are probably better candidates from the 453 new VPS I have discovered over the last 6 weeks. I am thinking it would be good to develop about 1000 new VPS, and then take these up to n=20000 before slimming down to the best 200 or so. I reckon that there about 10 which would be 165 or better at n=350000, and a reasonable chance of finding a candidate that reaches 175-177 primes by n=350000 and 200 by n=1000000.

 Thomas11 2009-11-10 11:10

[QUOTE=kar_bon;195261]
- the most primes of one k today (as far as i know) is for k=37850187375 from T.Ritschel: 159 primes up to n~620000; the 100th prime is at n=13719. [/QUOTE]

I just discovered the 160th prime for this k: 37850187375*2^706150-1

[QUOTE=robert44444uk;195349]
But I think there are probably better candidates from the 453 new VPS I have discovered over the last 6 weeks. I am thinking it would be good to develop about 1000 new VPS, and then take these up to n=20000 before slimming down to the best 200 or so. I reckon that there about 10 which would be 165 or better at n=350000, and a reasonable chance of finding a candidate that reaches 175-177 primes by n=350000 and 200 by n=1000000.[/QUOTE]

This sounds quite interesting to me. So you may count on me for such an effort...

 kar_bon 2009-11-10 14:50

[QUOTE=robert44444uk;195284]Most primes is 169 found by me at n=360000.[/QUOTE]

oh, yes, you're right. i was only referring to the Riesel-side of my collection of primes and Payem-numbers!

it's time to make a collection like mine for the '+'-side! somebody here to do so? :grin:

 robert44444uk 2009-11-10 15:54

[QUOTE=Thomas11;195374]
This sounds quite interesting to me. So you may count on me for such an effort...[/QUOTE]

Thomas 11, it will take a little time to develop 1000 new VPS but if you join in on the Sierpinski side, then this should double the effort!! I suggest you download Robert G's software, available from 3 October post, and also look at Oct 24 post on progress to date on Sierpinski side, and go from there.

I am running 2.5 cores approx on this exercise.

 robert44444uk 2009-11-10 15:57

[QUOTE=kar_bon;195388]oh, yes, you're right. i was only referring to the Riesel-side of my collection of primes and Payem-numbers!

it's time to make a collection like mine for the '+'-side! somebody here to do so? :grin:[/QUOTE]

You will find Sierpinski VPS found before Robert's program in my post of 29 Sep

There is a superior Riesel - see post of 29 Sept (Reisel)

Regards

Robert

 Thomas11 2009-11-11 10:32

[QUOTE=robert44444uk;195397]... I suggest you download Robert G's software, available from 3 October post, and also look at Oct 24 post on progress to date on Sierpinski side, and go from there.[/QUOTE]

Okay, I've got the code and it compiled well on my 64 bit Linux machine.

For the beginning I will take (according to your 24 Oct 09 post):
S 58 from Iteration=0, i=98849

Will take more, once I got some feeling about the software (cpu and memory utilization, running times, ...) and the theory behind it.

 Thomas11 2009-11-11 12:14

After just two hours I already found some nice candidates:

S 201456540759 58 100/6929 105/10000 K=27547987231931215530195
S 581338538697 58 100/9084 105/10000 K=79494597599651554004685
S 2246005540369 58 100/8809 103/10000 K=307127937945434173384245
S 125445708657 58 100/9608 100/10000 K=17153956716241359070485

Now I caught fire...

Also taking:
S 60 from Iteration=0, i=24786

 robert44444uk 2009-11-11 14:54

[QUOTE=Thomas11;195471]Okay, I've got the code and it compiled well on my 64 bit Linux machine.

For the beginning I will take (according to your 24 Oct 09 post):
S 58 from Iteration=0, i=98849

Will take more, once I got some feeling about the software (cpu and memory utilization, running times, ...) and the theory behind it.[/QUOTE]

I did not find it necessary to adjust any of the settings for S 58, I think this and 60 are about optimal for quick finds. 52 is just too slow, because a lot of close candidates.

When you post, don't forget to check your candidates against the original Sierpinski list which contains the cumulative list of 194 finds before Robert's software. Of the 4 you posted the first two are known 20145... is 152/137581 and 58133...is 118/25170. The other two are new. And I will add these to the master list of new finds and credit you.

The duplication issue should cease once you are past the first 3 iterations for 58 and 60 given that the largest finds were 838422520523 for 58 and 933294678535 for 60.

4 in a couple of hours is awesome. My poor laptops and no electricity here in Bangladesh make for snail-like progress.

Don't forget to save the record tables either. You have to check these every time you stop the program, otherwise you lose that record for ever. You never know, you might find an 16/16 in there. I am keeping records for each E level.

 Thomas11 2009-11-12 14:18

Okay, after one day I've got 23 VPS candidates for S 58, out of which (only) 4 were duplicates. So here are just the new ones (including the two reported yesterday):

S 52930116711 58 100/7489 104/10000 K=7237879563729757669155
S 125445708657 58 100/9608 100/10000 K=17153956716241359070485
S 251671885031 58 100/9867 100/10000 K=34414637764300621582755
S 1045666111343 58 100/8726 100/10000 K=142988639513076872029515
S 1461196621251 58 100/6837 105/10000 K=199809972482937566175855
S 1526585622539 58 100/8345 101/10000 K=208751530626465272827095
S 1712013118665 58 100/9006 103/10000 K=234107641063399884677325
S 1729977121403 58 100/9969 100/10000 K=236564111904189367255815
S 1780903684577 58 100/8389 102/10000 K=243528017403598252982085
S 1880663844267 58 100/9973 100/10000 K=257169627624053528204535
S 2166054501341 58 100/8704 101/10000 K=296195107499597269840305
S 2246005540369 58 100/8809 103/10000 K=307127937945434173384245
S 2354360292597 58 100/8357 101/10000 K=321944807726132334214185
S 2562085263199 58 100/9853 100/10000 K=350349965564828800966395
S 3241817377221 58 100/9958 100/10000 K=443299301077406965467705
S 3787165959141 58 100/7042 103/10000 K=517872485522463490009305
S 4392705084017 58 100/9672 100/10000 K=600676369763058021003285
S 4679042300103 58 100/9973 100/10000 K=639831285970023930669315
S 5622377417391 58 100/8369 101/10000 K=768826768909295041500555

Meanwhile I'm running all E<=106 (58, 60, 66, 82, 100, and 106) and will probably extend this to even higher ones during the weekend.

Just one question about the in.txt file:
I noticed that you (Robert) posted also some "near misses". So should I change the "vpscount" to somewhat lower than 100 (perhaps 95)?

And another question:
Do I need to check whether, let's say, a "S 58" may be already listed as a "S 60" (or higher) candidate?

Will post more results (e.g. for S 60) soon...

 robert44444uk 2009-11-12 15:34

[QUOTE=Thomas11;195616]Okay, after one day I've got 23 VPS candidates for S 58 [/QUOTE]

I envy your processing power! Hail to thee!!! I will credit your results to the master list. We will get to 1000 new VPS quite quickly I think.

[QUOTE=Thomas11;195616]

Just one question about the in.txt file:
I noticed that you (Robert) posted also some "near misses". So should I change the "vpscount" to somewhat lower than 100 (perhaps 95)?
[/QUOTE]

No, we will have problems with running even 100/10000 up to higher numbers. We should let these 99/10000 lie. The discussion around 99/10000 was before Robert G's program.

[QUOTE=Thomas11;195616]
And another question:
Do I need to check whether, let's say, a "S 58" may be already listed as a "S 60" (or higher) candidate?
[/QUOTE]

Yes, you should factorise y and look to see if the factorisation contains the next prime or even 2 primes in M(x). If so, divide y by the prime factor(s) and check to make sure it is not duplicated. All y values posted should be efficient in this respect. Robert's program does not carry out this step.

It is not so important for the racing tables if a y is not perfectly stated. There are only so many racing records, and values can be adjusted by hand if necessary.

 robert44444uk 2009-11-12 15:41

By the way, when we take these numbers to higher n, we need to do at least prp-3 checking on the first 10000 n. Robert's program (I understand) gambles with prp-1. It is worth noting that I have not found any count discrepancies between prp-3 and prime, neither have I discovered any discrepancies between prp-1 and prp-3.

Also for lower n, we must recognise that k> 2^n and adjust tests accordingly for these low n.

 robert44444uk 2009-11-12 15:45

[QUOTE=Thomas11;195616]

S 52930116711 58 100/7489 104/10000 K=7237879563729757669155
[/QUOTE]

Can you also post date, iteration number, and i value and date found. Would like to get a full record for statistical purposes.

 Thomas11 2009-11-13 11:10

1 Attachment(s)
[QUOTE=robert44444uk;195625]Can you also post date, iteration number, and i value and date found. Would like to get a full record for statistical purposes.[/QUOTE]

Meanwhile the number of VPS sequences from my end has increased to 116, out of which 80 are new. They are attached to this post, sorted by E and y.
By factorizing the y values I've found that two of them are indeed candidates of the next higher E series (one 60 -> 66, and the other one 66 -> 82). They are indicated in the file (at the rightmost column).

I was quite excited when I hit a "116/10000", but unfortunately this one was already discovered earlier (S 2158430601663 66). So the highest unknown one is a still quite nice 110/10000 (S 5475497492533 58).

BTW.: I haven't found any VPS for E=130 and E=138 so far. I know that they become quite rare with increasing E. But I'm a bit concerned about the "smith_check" levels. Should I relax those constrains a bit? E.g. there is a Riesel 97/10000 candidate I found earlier, which would have been thrown out already at the "10 50" level but otherwise would have survived the "smith_check" at all other (higher) levels.

 Thomas11 2009-11-13 13:13

I've just hit my first VPS for E=130:
S 179782224211057 130 100/7663 104/10000
K=11806316649721727826033357267756435645
iteration=62 I=82756 Fri Nov 13 12:30:36 2009

 R. Gerbicz 2009-11-13 14:54

[QUOTE=Thomas11;195691]
BTW.: I haven't found any VPS for E=130 and E=138 so far. I know that they become quite rare with increasing E. But I'm a bit concerned about the "smith_check" levels. Should I relax those constrains a bit? E.g. there is a Riesel 97/10000 candidate I found earlier, which would have been thrown out already at the "10 50" level but otherwise would have survived the "smith_check" at all other (higher) levels.[/QUOTE]

You can also disable the whole "smith check" if you change the in.txt file line's to "smith_check 0". It will be slower but produce more solutions, the problem here is to maximize the number of found solutions/day, and this is far from trivial.

The other option is to edit the table by changing say "10 50" to for example "8 50". (By this the code will be also slower but produce a little more solutions.)

 robert44444uk 2009-11-14 01:41

[QUOTE=Thomas11;195691]

BTW.: I haven't found any VPS for E=130 and E=138 so far. I know that they become quite rare with increasing E. But I'm a bit concerned about the "smith_check" levels. Should I relax those constrains a bit? E.g. there is a Riesel 97/10000 candidate I found earlier, which would have been thrown out already at the "10 50" level but otherwise would have survived the "smith_check" at all other (higher) levels.[/QUOTE]

You should definitely lower the smith_check levels for 130 onwards if you want to find VPS. Here the series have fewer primes at low n and more at higher n.

For 130 my smith_check table looked as follows:

7 50
13 100
21 200
32 500
53 1000
65 2000
73 3000
89 6000

Look at my paper for prime frequencies at varying levels, this should help guide you on selecting the most appropriate levels.

 robert44444uk 2009-11-14 01:46

[QUOTE=Thomas11;195691]

I was quite excited when I hit a "116/10000", but unfortunately this one was already discovered earlier (S 2158430601663 66). So the highest unknown one is a still quite nice 110/10000 (S 5475497492533 58).

[/QUOTE]

This the record holder! You can get excited if you find another or 116+ because that will be new

 robert44444uk 2009-11-14 02:31

[QUOTE=Thomas11;195691]Meanwhile the number of VPS sequences from my end has increased to 116, out of which 80 are new. They are attached to this post, sorted by E and y.
By factorizing the y values I've found that two of them are indeed candidates of the next higher E series (one 60 -> 66, and the other one 66 -> 82). They are indicated in the file (at the rightmost column).

[/QUOTE]

OK one of these was a duplicate, after restating.

I have posted all of your new values, except the 130, so can you include this in your next file you send, which should exclude the values in the posted file.

The results to date (combined R & S)

[CODE]
primes total 52 58 60 66 82 100 106 130 138
100 181 43 39 35 30 22 7 3 0 1
101 127 22 25 28 28 19 3 1 1 0
102 83 11 16 15 22 12 4 1 1 0
103 70 11 15 20 14 7 0 1 2 0
104 52 10 8 13 14 4 2 1 0 0
105 34 6 7 7 6 6 1 1 0 0
106 21 2 3 4 8 3 1 0 0 0
107 15 2 4 4 4 1 0 0 0 0
108 4 0 0 2 1 0 0 0 0 0
109 4 1 0 0 3 0 0 0 0 0
110 2 0 1 1 0 0 0 0 0 0
111 0 0 0 0 0 0 0 0 0 0
112 1 0 0 0 1 0 0 0 0 0
113 1 0 0 1 0 0 0 0 0 0
tot 595 108 118 130 131 74 18 8 4 1

[/CODE]

 robert44444uk 2009-11-14 06:05

Thinking ahead a bit, can anyone write a dos code for cllr.exe and cnewpgen.exe or its pfgw equivalent to work together without intervention, so that we can automate >10000 checking.

An input file will look like:

S 179782224211057 130 K=11806316649721727826033357267756435645

And the automated file will allow checking from n min to n max, with appropriate upper limit for p in cnewpgen.exe, output of prp-3 will go into a results file for each candidate. The output file name might be S_179782_130_[nmin]_n[max]_[# of primes found].txt and the file contents the value of prime n.

Or perhaps a c code, in a dos shell, that does the same trick.

 robert44444uk 2009-11-16 08:13

Definitive Racing Records

Below is a definitive list of payam racing records, which combines the old lists above with the new findings since Robert's program was written. It is short any information from Thomas 11 or R Gerbicz's finds on the Sierpinski side

[CODE]
Overall S R
1 1 1 1
2 2 2 2
3 3 3 3
4 4 4 4
5 5 5 5
6 6 6 6
7 7 7 7
8 8 8 8
9 9 9 9
10 10 10 10
11 11 12 11
12 13 13 13
13 15 16 15
14 17 17 17
15 18 20 18
16 19 23 19
17 23 28 23
18 28 29 28
19 31 32 31
20 32 37 32
21 41 41 41
22 45 45 45
23 47 48 47
24 53 55 53
25 55 56 55
26 59 63 59
27 63 68 63
28 67 77 67
29 79 81 79
30 83 83 87
31 85 85 88
32 92 94 92
33 94 96 94
34 98 108 98
35 101 117 101
36 120 120 128
37 135 135 135
38 137 142 137
39 142 143 142
40 151 166 151
41 160 167 160
42 167 173 167
43 180 185 180
44 182 199 182
45 188 210 188
46 204 234 204
47 247 254 247
48 260 271 260
49 270 288 270
50 292 292 326
51 323 323 327
52 338 338 360
53 368 368 370
54 378 383 378
55 392 427 392
56 424 457 424
57 438 471 438
58 439 521 439
59 466 522 466
60 513 550 513
61 565 565 565
62 577 577 622
63 583 583 631
64 589 589 673
65 605 605 698
66 612 612 718
67 682 682 764
68 735 735 799
69 841 841 892
70 847 847 954
71 1001 1001 1102
72 1003 1003 1137
73 1044 1044 1171
74 1079 1079 1180
75 1244 1252 1244
76 1327 1327 1378
77 1399 1409 1399
78 1414 1418 1414
79 1421 1421 1495
80 1557 1557 1647
81 1634 1634 1693
82 1663 1663 1706
83 1684 1684 2014
84 1818 1818 2026
85 1844 1844 2028
86 1861 1861 2112
87 1880 1880 2190
88 1892 1892 2340
89 1946 1946 2398
90 1951 1951 2448
91 1971 1971 2589
92 2044 2044 2693
93 2130 2130 2826
94 2150 2150 3360
95 2227 2227 3500
96 2328 2328 3909
97 2393 2393 4420
98 3215 3215 4924
99 3224 3224 4926
100 3258 3258 5566
101 3289 3289 5871
102 3405 3405 5941
103 3436 3436 6537
104 3450 3450 6855
105 3722 3722 6974
106 3833 3833 7560
107 4172 4172 7826
108 4227 4227 8127
109 4337 4337 8486
110 4495 4495 9071
111 7544 7544 9282
112 8221 8221 9543
113 8720 8720 9903
114 9023 9023 12716
115 9277 9277 12856
116 9971 9971 14007

[/CODE]

 Thomas11 2009-11-16 11:10

1 Attachment(s)
Here are some new VPS for E=52, 58, 60, 130, and 138.
All but one duplicates are removed from the list.
Just for your statistics I kept S 2965954850809 58 in the list,
which is already known as S 48622210669 60.

Still no 116+ candidates, but I found a very nice 115/10000!

Will post more results (e.g. for E=66, 82, 100, 106) tomorrow...

 robert44444uk 2009-11-16 15:05

[QUOTE=Thomas11;196027]Here are some new VPS for E=52, 58, 60, 130, and 138.
All but one duplicates are removed from the list.
Just for your statistics I kept S 2965954850809 58 in the list,
which is already known as S 48622210669 60.

Still no 116+ candidates, but I found a very nice 115/10000!

Will post more results (e.g. for E=66, 82, 100, 106) tomorrow...[/QUOTE]

Luvverly jubby, as I would say in London, if I was there...but I am not.

115/10000..star!

Will update the master file. Heading towards 1000 new VPS

 robert44444uk 2009-11-16 15:14

I notice there have been several views of Thomas11's file. If anyone is working on these numbers please reserve the number in this thread and post the results. No-one can get to 200 primes without this being a team effort. A little co-ordination will go a long way. And yes, we need people to take these numbers forward. Don't be shy.

We are now over 1000 known VPS (1027, R 577, S 450), of which 707 (452 Riesel, and 255 Sierpinski) are due to Robert G's program.

We have a juicy 115, a 114, 1 113, 1 112, 1 111, 3 110, 4 109, 4 108, 19 107, 28 106, and 43 105. The most prime series might be one of these.

Of great interest, as well as the obvious monsters we have 1 106 at 108/10000, 2 130's at 105/10000 and 3 138's at 100/10000. These have huge Nash weights.

 em99010pepe 2009-11-16 18:51

[quote=robert44444uk;196043] And yes, we need people to take these numbers forward. Don't be shy.

[/quote]

Please explain step by step how to set up the client. Thank you.

 Dougal 2009-11-16 19:26

program still crashing on me.anyone else have any problems?

 robert44444uk 2009-11-17 02:20

[QUOTE=em99010pepe;196054]Please explain step by step how to set up the client. Thank you.[/QUOTE]
There are only 2 users of the program at present and we are not having problems. The way I am using this is as follows:

version - Robert G has 3 at his site [url]http://sites.google.com/site/robertgerbicz/payam[/url], I have tried both athlon and pentium. I have not tried to compile the c.

Robert also gives samples of the other two "must have" files, in.txt and progress.txt.

Put all three files, .exe and 2 .txt files into the same subdirectory. Just start.
[QUOTE=Dougal;196057]program still crashing on me.anyone else have any problems?[/QUOTE]

It has not crashed on me once. Maybe if you are a serious prime hunter you have overclocked.

If you are using this program, check here for available ranges. Right now I am working on 58,60 and 66 Riesel and will soon free up 52 when I finish one of the iterations.

The following are available on Riesel:

R 52 Iteration 0,1 - not sure what work done by Robert G
R 52 Iteration 2 - reserved by me
R 52 Iteration 3, from i=41868
R 52 Iteration 4 from i=41919
R 52 Iteration 5 from i=39111
R 52 Iteration 6 from i=9849
R 82 from Iteration 7, i=89094
R 100 from Iteration 23, i=27211, see notes on smith_check for this and values above
R 106 from Iteration 31, i=75969
R 130 from Iteration 65, i=31537
> R 130 unchecked, except
R 268 done to Iteration 7, i=444

We will need checkers to take the stars forward from n>10000, see request about automation of this routine

 robert44444uk 2009-11-17 07:52

[QUOTE=em99010pepe;196054]Please explain step by step how to set up the client. Thank you.[/QUOTE]

You need to get newpgen.exe and pfgw.exe

Say you have a candidate 12345*E(52)

For taking beyond n=10,000, run newpgen. Select Type as k.b^n+1 with k fixed, or -1 equivalent. Type in 2 for the base. For n type in 12345*3*5*11*13*19*29*37*53 (or similar according to the E-value), type in kmin 10001, kmax 20000, choose an appropriate output file name, say 12345svdfrom10to20K.txt. Hit start, continue this file until p's up to about 400 million have been checked as factors. Then stop.

Start pfgw.

Command line: pfgw 12345svdfrom10to20K.txt -l12345res10to20K.txt

Do the next value.

Automation of this process is essential if we are to get through 1000 new VPS.

 robert44444uk 2009-11-17 08:55

[I][B]Some basic frequency analysis for Riesel E66:[/B][/I]

VPS finds per iteration: Iteration 1 = 42, Iteration 2 = 39
Payam E66 per iteration: Approx 84,682,000
Frequency of VPS: approx 1 in 2,100,000 E66 Payam Numbers

Finds will slowly decrease for higher iteration count, but there are clearly a lot to be found, the question is, how many.

[I]
[B]Gross Estimations of VPS:[/B][/I]

Assume that 10^36 is the largest k that will be VPS - largest found to date is approx 3*10^36 and that E<52 VPS and E>66 are rare. Clearly there are many at all levels, but these will be discounted.

There are 10^36/(2*1.89*10^19) E66's in there = 2.6*10^16 Payam E66 values, spread over 312,000,000 iterations (84.7 million E66 per iteration). If the average frequency is 50% of the 1 in 2.1 million found for small iterations, then we should see 6*10^9 VPS.

There will be many more E61, possibly as many as 40 times this number. Similarly there should be at least 700 times this number of E58, and 20,000 times this number of E52. Add on those at E36and smaller, and E82 and plus, and there is a surmise that there could be [B]10^14 VPS[/B] in the first 10^36 k, or 1 in every 10^22 k. And that is just Riesel. So multiply that by 2.

That's a lot.... but they are rare.
[I]
[B]What is the maximum number of primes likely up to k=10^36[/B][/I]

If there are 1 in 2000 of VPS that are 115+/10000, that means that there are probably 10^11 that are 115+/10000, 5*10^7 that are 130/10000, 2.5*10^4 that are 145/10000 and [B]a handful that are 160/10000. [/B]

Comments welcome, but we have only scratched at the surface!!

 Thomas11 2009-11-17 09:59

1 Attachment(s)
Here are another 159 Proth VPS for E=52, 58, 66, 82, 100, and 106.
One of them (S 4873844836541 66) is already known as S 58721022127 82.

Currently I'm working on all E<=138 (on the Proth side). But feel free to ask for any of them, as there are many iterations left...

 robert44444uk 2009-11-17 12:19

A real bumper crop. We already have 865 new, of which 132 are 105/10000 or better and 12 that are 110/10000 or better. Should get to the 1000 mark by weekend.

There is quite a mismatch between best to 100 primes. Thomas11 has already found 5 Sierpinskis at better than the Riesel record, in addition to the old finds.

 Dougal 2009-11-17 18:01

i cant get the program to run,but not to worry,il start testing one of the riesel k's from 10k onwards,let me know which ones have been taken past 10k and/or are reserved by someone so i can take another free one.

 Dougal 2009-11-17 21:24

im taking this up to 20k,i dont think anyone has done any work on it.

R 10941694057 E66

 Dougal 2009-11-17 21:54

1 Attachment(s)
done,il take it further over the next couple of days. found 13 3-prp's

[ATTACH]4313[/ATTACH]

 robert44444uk 2009-11-18 01:18

[QUOTE=Dougal;196222]done,il take it further over the next couple of days. found 13 3-prp's

[ATTACH]4313[/ATTACH][/QUOTE]

Thank you Dougal - absolutely no need to send the file otherwise site might run out of space, just the n that are prime. Maybe a good format would be

R 10941694057 E66 102/10000 115/20000
10729
10819
...

To be honest, the absolute values of n at these low levels is not critical. The 115/20000 information is.

We think we will not have the resources to check those with less than 105/10000 and you should therefore concentrate on those posted by Thomas11.

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