Prime p₀= 1143488956783343321 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 34 2 10 2 16 2 22 2 (?)
a_n: 0 2 30 32 90 92 126 128 138 140 156 158 180 182
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: 182
Found by: Putin Has a Small Dick
db: batch=76, k=14, 28 58 34 10 16 22

SPT(16)	1143487680512175311	0 18 26 42 80 150 200 228 230 258 308 378 416 432 440 458	-1276271168010
SPT(16)	1143487813009474403	0 60 104 170 216 248 254 284 300 330 336 368 414 480 524 584	-1143773868918
STPT(10)	1143487872864342527	0 2 30 32 42 44 54 56 84 86	-1083919000794
SPT(16)	1143488388956276189	0 14 74 128 150 170 264 282 290 308 402 422 444 498 558 572	-567827067132
SPT(16)	1143488530394240047	0 40 84 90 96 114 142 154 162 174 202 220 226 232 276 316	-426389103274
SPT(16)	1143488766228555883	0 10 78 90 96 108 120 126 148 154 166 178 184 196 264 274	-190554787438
SPT(16)	1143489132499765661	0 12 18 42 56 98 152 200 318 366 420 462 476 500 506 518	175716422340
STPT(10)	1143489288506986409	0 2 18 20 30 32 42 44 60 62	331723643088
SPT(16)	1143489404822811017	0 90 102 132 186 230 242 270 272 300 312 356 410 440 452 542	448039467696
SPT(16)	1143489475471105927	0 6 42 66 126 132 162 196 216 250 280 286 346 370 406 412	518687762606
SPT(16)	1143489678925776529	0 12 22 40 42 78 100 124 228 252 274 310 312 330 340 352	722142433208