Currently I'm looking at a relationship between k mod 30 and k mod 7 relating to found passed primes for Riesel Sieve. It's a little more complicated than that but it's my start. I wanted to see how that matched up against n weight. It seems as though for me it went smoothly. Atleast what I calculated as the ending digit for n was one of the few remaining choices. Below is a list of SoB k's and the bust out for ending digits of n. We know that k's ending in 1 and 9 are even n's and those ending in 1, 3 and 7 will have odd n's. The sieve takes care of this in the first few passes. The sieve also should have quickly taken out all k/n pairs that didn't produce a number that ended in 7 for SoB and ending in 3 for Riesel Sieve. I've yet to check for SoB but for Riesel Sieve every k/n pair produces a number that ends in 3...so we know that all our primes will end in 3...just as all Primes found for SoB will end in 7. This is for k's that are kmod 30= 1,17,19 and 23. Other kmod 30 values follow different rules and prime out much sooner. Take a look at the chart.
Code:
K #Ns 0 1 2 3 4 5 6 7 8 9
4847 71346 0 24044 0 20927 0 0 0 26375 0 0
5359 88505 25164 0 33079 0 0 0 30262 0 0 0
10223 82150 0 21760 0 0 0 17928 0 22307 0 20155
19249 29988 0 0 10467 0 0 0 8755 0 10766 0
21181 70322 17209 0 19162 0 17076 0 0 0 16875 0
22699 28842 7089 0 6999 0 7121 0 0 0 7633 0
24737 74099 0 27442 0 25892 0 0 0 20765 0 0
27653 41348 0 6534 0 8597 0 8351 0 8575 0 9291
28433 39941 0 0 0 12857 0 14459 0 12625 0 0
33661 69838 13542 0 15293 0 7297 0 17295 0 16411 0
55459 98383 11888 0 0 0 28608 0 29262 0 28625 0
67607 24938 0 19110 0 0 0 0 0 5827 0 0
These numbers were pulled from the Sob.txt file and are not current. I'll pull the lowresults.txt and the nodubewhatever.txt files from the Sob.txt later and then look at the numbers once again.
For Riesel Sieve I predicted, more like guessed since I don't have enough historical data to go on, each k for what n will end in to hit prime. It's just a guess since I can't prove that the ending digit for n has any predictability for finding a prime....yet. I'm still working on a few ideas. Viewing the above chart with the new one that I'll produce after pulling all factors from the Sob.txt should give me a better understanding of how the n's are being pulled. Historical data from the 5 previous k's would be a help. If we could derive a way to look at the ending digit for n and PRP test those values first, then maybe a shortcut could be found to skip nonprobable n values.
It is late for me and I'm sure I left out some stuff and maybe even sounded confused. I will pull the factors out tomorrow and relook at the data. This was mostly a post to display data for n's.