Riesel Primes k*2^n-1, k<300 [Part II]

[VBCurtis]

Originally Posted by pinhodecarlos

RPS is working on k<300 except a few k's. I was wondering how much CPU power has been used so far for actual progress and how that would reflect if we only tested one k, meaning how much further in comparison with Gimps we would stand now, example k=5.

For a first approximation, we can look at the top-5000 score for primes found. RPS' current total is ~2500. Even if we double that to account for all the primes that have fallen off the list, we are still 20% below the single prime at 20M for mersennes.

So, I'd say we are equivalent to a number between 15M and 19M for mersennes.

A second approximation: Work done scales with the cube of exponent tested. You could sum the cubes of the test limits multiplied by the weight of each k. Divide by weight of k=1 and take the cube root, and you'd have a better equivalence.

[Thomas11]

Based on Curtis' second approximation I created a spreadsheet (see attachment) using the Nash weights and current test limits.

Here are just the first few lines:

k   Nash weight    square free    n_max [M]    w * n^3    equiv. n_max (single k)
---------------------------------------------------------------------------------
1        925          925           --                        17.028
3       2976         2976           --	                      11.535
5       2180         2180          4.34       178207.4        12.796
7        912          912          4.23        69026.5        17.109
9       1674         1447          5.22       205816.4        14.669

The Nash weights are given in the second column, followed by the corrected (square free) Nash weights in the third column. The fourth column contains the current test limits (n_max). Column 5 is Curtis' formula: weight times n_max cubed. We could take this as a measure of how much effort was spent into which k.
And finally column 6 is an "equivalent n_max" if we would have spent all our effort into just a single k.

The "equivalent n_max" are ranging between n_max = 10.36M for k=195 (highest weight) and n_max = 29.12M for k=253 (lowest weight).

[sjtjung]

k=31 is at 2.1M
k=207 is at 1.73M

[VBCurtis]

Thomas-
Thanks for the analysis!

Note that column 6 for k=3 is 11.5M. Primegrid is near 11.5M on this k, suggesting that there has been nearly as much effort put into k=3 as all of k=5 to 299 combined! Amazing.

[pinhodecarlos]

Thank you both. When I get back from my trip I will take a look on that file.

[lalera]

k=119
n=2100000

[pinhodecarlos]

Originally Posted by lalera

k=119
n=2100000

Could you post here your results? Thank you in advance.

PS( Let me know if you need the file up to n=6M)

[lalera]

Originally Posted by lalera

k=119
n=2100000

here are the results

continuing

to pinhodecarlos: no thanks - I do the presieveing by myself.

[Thomas11]

Originally Posted by lalera

to pinhodecarlos: no thanks - I do the presieveing by myself.

I would highly suggest to use the sieve file from PrimeGrid as provided by pinhodecarlos in his earlier post.

This one is already perfectly sieved up to p=100P - much more than one could do by individual sieving.
Just complare it to your sieve file and count the number of candidates...

[lalera]

Originally Posted by Thomas11

I would highly suggest to use the sieve file from PrimeGrid as provided by pinhodecarlos in his earlier post.

This one is already perfectly sieved up to p=100P - much more than one could do by individual sieving.
Just complare it to your sieve file and count the number of candidates...

I looked at the presieved file and in the first line is standing that it is presieved to 500 mio p (that is not much)
and there are not much candidates in it.

[VBCurtis]

Originally Posted by lalera

I looked at the presieved file and in the first line is standing that it is presieved to 500 mio p (that is not much)
and there are not much candidates in it.

The header line is not updated by the sieve program they use; it is just a marker to tell LLR what type of file it is. Trust us that it's sieved to 100P = 100000T. Or, test it for yourself- try sieving the good file on any region below 100P. There really isn't any reason to repeat even a fraction of this factoring work.