Prime gaps in residue classes - where CSG > 1 is possible

[mart_r]

max. p searched:
       q <= 2690: 2.140e+13
2690 < q <= 4566: 9.076e+12
4566 < q <= 1e+5: 2.755e+11
1e+5 < q <= 2e+5: 1.764e+11
2e+5 < q <= 5e+5: 9.100e+10
5e+5 < q <= 1e+6: 2.800e+10
1e+6 < q <= 2e+6: 2.500e+10
2e+6 < q <= 6e+6: 4.000e+9
(only even q are examined;
 for q <= 4566, all first occurrence gaps are kept, for larger q only those with CSG > 1)

There are still some meters being made, but I'll be concentrating on some leftover work from the twin prime gap search and other stuff in the coming days (weeks, months...), so unless I find something unusual, I won't cause any more disturbance on this issue.

"TTFN - Ta Ta For Now"
-Tigger

P.S. in case anybody noticed it: there was a formal error in post # 27, it should be "...apply to prime gaps in AP with common difference q if the _square of the_ bounding prime p' is no larger than (p+n)² for very small n", more precisely I meant floor(p^0.5) = floor(p'^0.5). But nevermind.

[mart_r]

Well, these came in just today (I'm analyzing the data for 2692 <= q <= 4566 on a weekly basis):

q = 3796, gap = 1560156, p = 9585778010467.
Alas the gap is smaller than q², but it's only the second known example (beside q = 152) with CSG > 1 where sqrt(p+gap) - sqrt(p) < 1.

q = 3530, gap = 942510, p = 9135172488241.
This marks a CSG above 0.75, which means all q <= 4566 now have CSG_max > 3/4. Been waiting for this for a couple of weeks.

These have improved CSG_max:

   q  CSG_max          gap              p
2816  0.8390130829  957440  9275457669461
3238  0.8359371728 1204536  9128335558957
3274  0.8042210531 1175366  9560980356371
3346  0.8578641737 1090796  9106149236741
3350  0.8022416715  944700  9365794042873
3494  0.8024894174 1250852  9465405375911
3530  0.7516123241  942510  9135172488241
3796  1.0104960680 1560156  9585778010467
4342  0.8519201890 1511016  9101151235291
4398  0.7970757679 1042326  9544053094201
4418  0.8143152286 1568390  9171781378121

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