# command: python3 band_check.py 175 60 # started: 2026-10-27 02:23:13 UTC # Python 3.13.17, python-flint 0.9.0, numpy 2.5.3, sympy 1.14.0 # machine: 2 cores, 7 GB RAM, Linux x86_64 # sha256 of the scripts in the directory: # 62ba14c054023c20a139428938aa4561365d93366172e919afde228d09b40d4e band_check.py # e3b29b32dee33a3771e46eee7fd3c7feb9d5281a0f880fb0ea2a9dc9bde9ea99 bergeron_certificate.py # a86969c6ce89c5a3aba23d4d30aa55d8fb9924613d794ab271728fe3f2035110 circle_check.py # 0ad5f6f485561df541b4e83a0e780275e5077b2e3a6baa864ca0419d01ef15af corner_check.py # 85f217ba1cc63c5421bb2df726223642e8289baab3f46dc55e026417f27cbb21 cww_certificate.py # 1b487046af3818f1b6e61f9903bb4dd3cbdb45e7d451c23cdce74faad8cf4eb0 pn_certificate.py # ea6a0e64e29ea4599808a3cb8023f9a18bfb4469f6b282d051f24034a5903108 pn_families.py # 33684b0c7134b1b7da3e1e5fd944fe28c067fcc4255b832d327d3aea4043f665 row_check.py # 0dd9195b2ba9a6ca36055c39fd90cd069ab530072d01786042400059e129e650 row_sweep.py # b077df5d9e0b9b7bf8be56cf2ab6763e5d8167a7408763c6ba54667837f077b3 rq_certificate.py # x= 3: 3 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 4: 5 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: fails at (N, gcd(x,N+1), degree) [(4, 1, 5), (5, 2, 5), (6, 1, 5)] x= 5: 7 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: fails at (N, gcd(x,N+1), degree) [(5, 1, 7), (6, 1, 11), (7, 1, 9), (8, 1, 13)] x= 6: 9 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: fails at (N, gcd(x,N+1), degree) [(6, 1, 7), (7, 2, 7), (8, 3, 7), (9, 2, 7)] x= 7: 11 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: fails at (N, gcd(x,N+1), degree) [(7, 1, 13), (8, 1, 19), (9, 1, 23), (10, 1, 29)] x= 8: 13 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: fails at (N, gcd(x,N+1), degree) [(8, 1, 25), (9, 2, 19), (10, 1, 31), (11, 4, 29)] x= 9: 15 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: fails at (N, gcd(x,N+1), degree) [(9, 1, 31), (10, 1, 37), (11, 3, 43), (12, 1, 47)] x= 10: 17 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: fails at (N, gcd(x,N+1), degree) [(10, 1, 43), (11, 2, 43), (12, 1, 53), (13, 2, 53)] x= 11: 19 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: fails at (N, gcd(x,N+1), degree) [(12, 1, 59)] x= 12: 21 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: fails at (N, gcd(x,N+1), degree) [(12, 1, 65), (13, 2, 67), (15, 4, 81), (17, 6, 91)] x= 13: 23 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 14: 25 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 15: 27 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 16: 29 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 17: 31 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 18: 33 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 19: 35 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 20: 37 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 21: 39 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 22: 41 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 23: 43 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 24: 45 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 25: 47 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 26: 49 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 27: 51 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 28: 53 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 29: 55 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 30: 57 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 31: 59 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 32: 61 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 33: 63 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 34: 65 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 35: 67 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 36: 69 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 37: 71 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 38: 73 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 39: 75 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 40: 77 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 41: 79 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 42: 81 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 43: 83 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 44: 85 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 45: 87 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 46: 89 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 47: 91 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 48: 93 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 49: 95 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 50: 97 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 51: 99 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 52: 101 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 53: 103 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 54: 105 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 55: 107 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 56: 109 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 57: 111 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 58: 113 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 59: 115 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 60: 117 breakpoints; identity and D_A >= 0 checked; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 61: 119 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 62: 121 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 63: 123 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 64: 125 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 65: 127 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 66: 129 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 67: 131 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 68: 133 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 69: 135 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 70: 137 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 71: 139 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 72: 141 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 73: 143 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 74: 145 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 75: 147 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 76: 149 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 77: 151 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 78: 153 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 79: 155 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 80: 157 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 81: 159 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 82: 161 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 83: 163 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 84: 165 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 85: 167 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 86: 169 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 87: 171 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 88: 173 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 89: 175 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 90: 177 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 91: 179 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 92: 181 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 93: 183 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 94: 185 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 95: 187 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 96: 189 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 97: 191 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 98: 193 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x= 99: 195 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=100: 197 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=101: 199 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=102: 201 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=103: 203 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=104: 205 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=105: 207 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=106: 209 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=107: 211 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=108: 213 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=109: 215 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=110: 217 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=111: 219 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=112: 221 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=113: 223 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=114: 225 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=115: 227 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=116: 229 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=117: 231 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=118: 233 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=119: 235 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=120: 237 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=121: 239 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=122: 241 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=123: 243 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=124: 245 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=125: 247 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=126: 249 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=127: 251 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=128: 253 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=129: 255 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=130: 257 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=131: 259 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=132: 261 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=133: 263 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=134: 265 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=135: 267 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=136: 269 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=137: 271 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=138: 273 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=139: 275 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=140: 277 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=141: 279 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=142: 281 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=143: 283 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=144: 285 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=145: 287 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=146: 289 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=147: 291 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=148: 293 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=149: 295 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=150: 297 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=151: 299 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=152: 301 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=153: 303 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=154: 305 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=155: 307 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=156: 309 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=157: 311 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=158: 313 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=159: 315 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=160: 317 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=161: 319 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=162: 321 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=163: 323 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=164: 325 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=165: 327 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=166: 329 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=167: 331 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=168: 333 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=169: 335 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=170: 337 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=171: 339 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=172: 341 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=173: 343 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=174: 345 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok x=175: 347 breakpoints; Y >= 0: ok; small-m: ok; (M) for x <= N <= 2x-2: ok done (2194s): identities, (II) and (III) hold; (M) holds for every 13 <= x <= 175 real 36m33.780s user 33m47.734s sys 0m0.489s # finished: 2026-10-27 02:59:47 UTC