Prime p₀= 1008467009210310161 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 34 2 88 2 28 2 28 2 22 2 (?)
a_n: 0 2 120 122 156 158 246 248 276 278 306 308 330 332
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 332
Found by: Theadalus
db: batch=76, k=14, 118 34 88 28 28 22

SPT(16)	1008465637241349569	0 8 18 32 72 84 102 122 210 230 248 260 300 314 324 332	-1371968960592
STPT(10)	1008465780204624347	0 2 60 62 72 74 84 86 144 146	-1229005685814
SPT(16)	1008466075909647997	0 6 12 36 52 64 76 82 204 210 222 234 250 274 280 286	-933300662164
SPT(16)	1008466309591522109	0 98 102 108 128 150 168 188 234 254 272 294 314 320 324 422	-699618788052
SPT(16)	1008466355714914933	0 18 64 78 84 156 174 196 258 280 298 370 376 390 436 454	-653495395228
TPT(14)	1008466728341527727	0 2 72 74 192 194 240 242 294 296 312 314 354 356	-280868782434
TPT(14)	1008467124906982751	0 2 36 38 48 50 138 140 216 218 288 290 360 362	115696672590
SPT(16)	1008467162870911231	0 82 112 120 148 166 222 232 306 316 372 390 418 426 456 538	153660601070
SPT(16)	1008467509107228061	0 28 40 58 78 100 138 162 238 262 300 322 342 360 372 400	499896917900
STPT(10)	1008467694205670117	0 2 12 14 42 44 72 74 84 86	684995359956
SPT(16)	1008467758488614087	0 20 72 110 152 170 174 182 222 230 234 252 294 332 384 404	749278303926