Prime p₀= 2987418162396638681 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 40 2 28 2 88 2 10 2 76 2 (?)
a_n: 0 2 96 98 138 140 168 170 258 260 270 272 348 350
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: 350
Found by: JonS
db: batch=82, k=14, 94 40 28 88 10 76

SPT(16)	2987416251108947941	0 12 30 66 72 126 132 136 156 160 166 220 226 262 280 292	-1911287690740
SPT(16)	2987416713481825439	0 2 8 20 24 62 68 128 174 234 240 278 282 294 300 302	-1448914813242
STPT(10)	2987416806941132639	0 2 132 134 150 152 168 170 300 302	-1355455506042
SPT(16)	2987416876128388777	0 6 22 36 76 84 120 132 184 196 232 240 280 294 310 316	-1286268249904
SPT(16)	2987417184453771143	0 6 26 78 104 116 140 144 170 174 198 210 236 288 308 314	-977942867538
SPT(16)	2987417273054979097	0 4 6 16 22 90 130 142 144 156 196 264 270 280 282 286	-889341659584
SPT(16)	2987418847851408989	0 2 44 120 134 140 170 188 204 222 252 258 272 348 390 392	685454770308
SPT(16)	2987418879865782151	0 66 82 96 142 150 160 166 186 192 202 210 256 270 286 352	717469143470
STPT(10)	2987418938822831267	0 2 30 32 42 44 54 56 84 86	776426192586
TPT(14)	2987419112239063991	0 2 150 152 186 188 240 242 348 350 420 422 450 452	949842425310
STPT(10)	2987419506666094457	0 2 24 26 42 44 60 62 84 86	1344269455776