Prime p₀= 927567962441108477 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 88 2 46 2 40 2 70 2 28 2 (?)
a_n: 0 2 12 14 102 104 150 152 192 194 264 266 294 296
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: 296
Found by: crashtech
db: batch=76, k=14, 10 88 46 40 70 28

SPT(16)	927566850205308647	0 32 36 60 140 174 206 224 252 270 302 336 416 440 444 476	-1112235799830
TPT(14)	927567015642796367	0 2 12 14 24 26 102 104 114 116 144 146 210 212	-946798312110
SPT(16)	927567084426831047	0 12 50 84 90 96 134 140 216 222 260 266 272 306 344 356	-878014277430
SPT(16)	927567577968804659	0 14 20 38 54 78 80 110 132 162 164 188 204 222 228 242	-384472303818
STPT(10)	927567582712026857	0 2 12 14 42 44 72 74 84 86	-379729081620
SPT(16)	927567641892317719	0 30 34 72 88 112 144 154 228 238 270 294 310 348 352 382	-320548790758
STPT(10)	927568017423302711	0 2 30 32 78 80 126 128 156 158	54982194234
SPT(16)	927568090962731291	0 30 38 50 62 72 98 108 152 162 188 198 210 222 230 260	128521622814
SPT(16)	927568865998261363	0 10 18 64 106 108 120 130 174 184 196 198 240 286 294 304	903557152886
SPT(16)	927569022432726601	0 36 96 130 186 226 252 256 306 310 336 376 432 466 526 562	1059991618124
STPT(10)	927569211853046141	0 2 36 38 78 80 120 122 156 158	1249411937664