Prime p₀= 1321093228099175549 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 88 2 94 2 22 2 16 2 (?)
a_n: 0 2 18 20 42 44 132 134 228 230 252 254 270 272
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: 272
Found by: Megacruncher
db: batch=77, k=14, 16 22 88 94 22 16

SPT(16)	1321091348566187333	0 66 80 84 104 116 146 156 158 168 198 210 230 234 248 314	-1879532988216
SPT(16)	1321091602543143857	0 2 20 44 72 132 144 150 164 170 182 242 270 294 312 314	-1625556031692
STPT(12)	1321092059499518879	0 2 18 20 60 62 138 140 180 182 198 200	-1168599656670
SPT(16)	1321092463829990321	0 18 26 56 72 86 138 152 156 170 222 236 252 282 290 308	-764269185228
SPT(16)	1321092784999605197	0 12 20 26 56 74 90 140 156 206 222 240 270 276 284 296	-443099570352
SPT(18)	1321093094581906637	0 24 50 66 80 90 104 134 150 176 192 222 236 246 260 276 302 326	-133517268912
SPT(16)	1321093460267073253	0 18 34 48 60 76 94 124 180 210 228 244 256 270 286 304	232167897704
STPT(12)	1321093471495408319	0 2 18 20 42 44 78 80 102 104 120 122	243396232770
SPT(16)	1321093610116761527	0 26 30 54 74 102 144 170 186 212 254 282 302 326 330 356	382017585978
TPT(14)	1321093612844538371	0 2 66 68 168 170 198 200 276 278 306 308 348 350	384745362822
STPT(10)	1321093739964135659	0 2 18 20 30 32 42 44 60 62	511864960110