Very Prime Riesel and Sierpinski k

[Thomas11]

Originally Posted by robert44444uk

I wonder what the Nash weight is?

The Nash weight for S 100 1323953181459703 is 8741.
Seems to be about the average for the E100 sequences, as I get similar values for the other candidates.

The second best sequence S 106 1061615018040269 (165/150000) yields a Nash weight of 9041.

Actually the computation of Nash weights using my tool fails for larger candidates (E>106) by getting a segmentation fault. Could be a problem with GMP, but I need to check this.
However, Jack Brennen's Java applet still works and can cope with this kind of candidates. Note that his weights are scaled by a factor of 1/1751.542.

A quick check yields a weight of 9241 for S 148 3763782581288275.

Edit: You can even use the Java applet for Riesel sequences by entering the k as -k (k*2^n-1 --> -k*2^n+1).

[Thomas11]

Highest Nash weight so far is: 9399 for S 148 594730917690329.

Note, that this is the weight for n=100001-110000 (the usual range for the Nash weight). For n=1-10000 the weight is 9396.

[henryzz]

Since I last posted in this thread i have found the following prps:

3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^49225+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^54900+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^55501+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^57804+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^58600+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^64534+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^66017+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^70389+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^71742+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^72375+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^72574+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^76435+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^77693+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^81433+1

This takes it to 150/81433

[robert44444uk]

Originally Posted by henryzz

Since I last posted in this thread i have found the following prps:

3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^81433+1

This takes it to 150/81433

Not to bad a candidate, as not far off the best.

I finally got my second batch to 30K, there were 2 at 136/30000, one already reported. Will post the batch when I get the chance. One new Riesel record:

R 40210975621077 82 135/27644

[henryzz]

I can now add 3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^83365+1 to the list
151/83365

[robert44444uk]

Ok: here is the second batch of Reisels taken to 30K. The top 2 I have already taken higher.

R 40210975621077 82 112/10000 127/20000 136/30000
R 211199705992169 100 107/10000 126/20000 136/30000
R 24341838170275 60 110/10000 126/20000 134/30000
R 677709313826537 100 109/10000 122/20000 132/30000
R 21013492486553 66 110/10000 128/20000 130/30000
R 13005167738751 60 114/10000 121/20000 129/30000
R 32988843959463 82 113/10000 125/20000 128/30000
R 15969842357567 66 105/10000 122/20000 128/30000
R 11018713289309 52 105/10000 119/20000 128/30000
R 14766422397261 60 106/10000 119/20000 128/30000
R 19818893573029 60 105/10000 119/20000 127/30000
R 13236231921937 52 108/10000 121/20000 126/30000
R 19997060196903 66 110/10000 121/20000 126/30000
R 247695811021067 100 110/10000 120/20000 126/30000
R 24313528509499 60 107/10000 119/20000 126/30000
R 4233661803915 52 108/10000 120/20000 125/30000
R 32963529753887 66 105/10000 120/20000 125/30000
R 625332802763205 100 108/10000 120/20000 125/30000
R 14310819302787 52 109/10000 119/20000 125/30000
R 21170922770311 60 106/10000 119/20000 125/30000
R 20293799312829 66 105/10000 118/20000 125/30000
R 32677157886245 66 109/10000 118/20000 125/30000
R 30147566607277 66 108/10000 117/20000 125/30000
R 746213583678857 100 108/10000 119/20000 124/30000
R 450100835531975 100 108/10000 117/20000 124/30000
R 18980043643925 60 108/10000 120/20000 123/30000
R 29081024837439 82 105/10000 117/20000 123/30000
R 19564390653629 66 106/10000 118/20000 122/30000
R 18752149885763 52 110/10000 117/20000 122/30000
R 22471637911749 60 105/10000 116/20000 122/30000
R 18712472868691 60 105/10000 116/20000 122/30000
R 13372186524821 60 107/10000 116/20000 122/30000
R 14779390632999 60 108/10000 116/20000 122/30000
R 25348021517451 66 107/10000 116/20000 122/30000
R 396462390582321 100 107/10000 116/20000 122/30000
R 41302528042741 82 105/10000 119/20000 121/30000
R 313074939004761 100 107/10000 116/20000 121/30000
R 114676822048221 138 106/10000 114/20000 121/30000
R 35152463092877 82 105/10000 117/20000 120/30000
R 413929177323339 100 105/10000 117/20000 120/30000
R 25187435317679 66 105/10000 116/20000 120/30000
R 29204048501535 66 106/10000 116/20000 120/30000
R 35749520383347 82 107/10000 116/20000 120/30000
R 4885228063439 52 106/10000 118/20000 119/30000
R 15079033672065 66 106/10000 117/20000 119/30000
R 20399845607867 66 105/10000 116/20000 119/30000
R 34380230512807 82 107/10000 116/20000 119/30000
R 35313118006985 82 105/10000 117/20000 118/30000
R 3169158804789 52 106/10000 115/20000 
R 12772416671967 58 106/10000 115/20000 
R 24215256845247 66 107/10000 115/20000 
R 29642976384349 66 110/10000 115/20000 
R 30255662968667 66 105/10000 115/20000 
R 26297895597317 82 107/10000 115/20000 
R 30231629501777 82 107/10000 115/20000 
R 545978647484149 100 105/10000 115/20000 
R 2360847311065 52 107/10000 114/20000 
R 11514157750327 58 105/10000 114/20000 
R 26427297677781 82 109/10000 114/20000 
R 26500112417955 82 105/10000 114/20000 
R 657288953812025 100 105/10000 114/20000 
R 721317333290741 100 105/10000 114/20000 
R 3801182264487 52 107/10000 113/20000 
R 24827475219459 60 106/10000 113/20000 
R 36206599162393 82 105/10000 113/20000 
R 410541436597817 100 105/10000 113/20000 
R 540023319094971 100 105/10000 113/20000 
R 591333766759391 100 105/10000 113/20000 
R 648583527976713 100 105/10000 113/20000 
R 23130411737727 66 106/10000 112/20000 
R 32432663105775 82 106/10000 112/20000 
R 34136308132621 82 105/10000 112/20000 
R 324529467640433 100 106/10000 112/20000 
R 30482183883869 82 105/10000 111/20000 
R 26335894174537 66 106/10000 110/20000 
R 30596659284231 66 105/10000 110/20000

[henryzz]

Originally Posted by henryzz

I can now add 3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^83365+1 to the list
151/83365

and 3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^86273+1
152/86273

[Thomas11]

Sorry, Robert, but I had to kick your S 708477982733 58 from the record table:

S 1323953181459703 100 168/158967
S 1323953181459703 100 169/172886

This is now the fastest sequence to 169 primes!

[robert44444uk]

Originally Posted by Thomas11

Sorry, Robert, but I had to kick your S 708477982733 58 from the record table:

S 1323953181459703 100 168/158967
S 1323953181459703 100 169/172886

This is now the fastest sequence to 169 primes!

Congratulations, Thomas11, you well deserve it, after 6 months of effort.

I think you should let yahoo primenumbers know about the k when you reach 170. Also at primepuzzles.

http://www.primepuzzles.net/puzzles/puzz_006.htm

This will be an important record I think for prime hunters. This will be the first of the initial targets to be achieved when you find 170. The other obvious targets are:

180/any n
190/any n
200/any n;
200/<1000000
100/<3000 and
120/<10000

I'm still taking the better candidates from the 2nd Riesel bunch to 50K and in some cases beyond. Annoyingly I have 3 at 139/40000. Good, but no real breakthroughs. And 2 of these fail to advance meaningfully.

[robert44444uk]

Originally Posted by henryzz

and 3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^86273+1
152/86273

Well done Henryzz. One of the best.

[henryzz]

Originally Posted by robert44444uk

Well done Henryzz. One of the best.

3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^94941+1
3019*3986252057*3*5*11*13*19*29*37*53*59*61*67*2^96706+1
154/96706