mersenneforum.org - View Single Post - Prime gaps in residue classes

mart_r · 2020-08-05, 21:11

From day to day I anticipated another result where q and r would both be prime, but to no avail. These are some of the most frustratingly near misses:

Code:

   q      phi     k       p           CSG     k*q/phi/log²p'
 792886  396442  204   445124227  1.012127792  0.997549475   (q/2 & p mod q/2 prime, simple CSG criteria not met)
 994102  497050  255  2001318337  1.10553142   1.09958173    (q/2 prime, p mod q/2 = 191011 = 251 × 761)
1933454  966726  219   686778133  1.031408014  1.009688338   (q/2 prime, p mod q/2 = 401963 = 541 × 743)
1889254  942480  228   954854339  1.048783531  1.031510191   (p mod q/2 prime, q/2 = 944627 = 617 × 1531)
 780814  390406  204   201321937  1.079546597  1.050952883   (p mod q prime, p mod q/2 not (1 of 4 examples))

Over one thousand candidates with CSG>1 (sum Ri'-method) - it's not a question of if, it's a question of when. The search continues.

Anywho, I've attached the data for p'<2⁴². It seems I was even more lucky than I originally thought with that gap at q=152. It gets increasingly hard to find gaps even with CSG>0.9.