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unprimeable n.  and  weird n.

First numbers that belong to both sets:

4030, 10570, 13370, 15890, 16730, 17272, 17990, 19670, 20510, 24290, 24710, 25130, 28070, 30170, 30730, 31430, 32270, 34090, 34370, 35210, 35630, 36610, 40390, 41090, 41930, 42910, 43190, 45356, 45710, 47390, 49070, 51310, 51730, 52010, 54110, 55090, 57470, 57610, 59710, 61390, 65870, 69790, 76790, 77630, 78610, 80570, 81410, 82670, 83510, 84070, 86030, 88130, 91210, 95690, 96110, 99890, 100030, 102970, 103670, 104090, 105770, 108710, 109690, 109970, 112070, 112490, 112630, 113072, 113330, 113470, 115990, 116690, 118510, 121870, 123130, 124390, 126770, 127610, 131390, 131530, 136430, 138530, 139790, 140210, 141890, 149590, 150710, 154910, 158830, 160510, 160790, 163310, 164570, 165970, 166810, 167230, 167510, 167930, 168770, 169610, 170590, 172130, 172690, 173110, 173390, 176470, 178010, 178990, 181370, 184310, 186130, 186970, 187810, 188090, 188230, 189770, 191870, 192710, 193690, 194390, 195230, 195370, 196210, 199010, 199570, 201530, 203630, 204190, 204890, 205730, 206710, 207410, 213430, 214270, 215810, 217630, 218330, 221690, 223370, 224210, 225190, 226030, 227570, 228970, 232610, 233030, 234010, 235130, 241430, 242690, 242830, 243892, 247310, 248990, 252490, 253190, 254012, 256970, 257110, 258790, 259070, 261310, 263690, 263830, 264530, 265790, 266210, 268310, 269290, 270410, 271670, 273490, 274610, 275170, 279230, 280070, 281470, 283430, 283990, 286370, 286930, 287770, 288890, 291130, 294070, 296030, 296170, 296870, 298130, 298270, 298970, 299810, 304990, 306110, 307370, 307790, 309610, 310870, 311570, 311990, 313810, 315910, 316610, 320810, 326410, 327110, 327530, 329210, 330470, 334810, 335090, 335230, 335930, 337190, 340270, 341390, 343876, 344330, 345170, 346570, 346990, 347690, 347830, 348110, 350630, 351610, 353570, 355390, 357490, 360710, 361690, 362530, 363230, 364630, 365890, 373310, 374570, 377930, 385210, 388076, 389410, 395570, 395990, 396130, 398230, 398510, 399770, 401870, 402010, 402430, 406910, 408730, 409010, 410690, 411530, 413210, 415730, 418670, 419090, 422030, 422590, 425110, 426370, 429170, 429310, 431410, 432110, 433790, 434210, 434770, 435470, 436030, 437990, 439390, 441770, 444010, 445130, 449890, 456470, 457030.

Some larger examples :