Prime p₀= 2531272125450973691 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 10 2 28 2 28 2 28 2 34 2 (?)
a_n: 0 2 78 80 90 92 120 122 150 152 180 182 216 218
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: 218
Found by: Roadranner
db: batch=82, k=14, 76 10 28 28 28 34

SPT(16)	2531270971301113001	0 2 20 36 86 126 132 140 192 200 206 246 296 312 330 332	-1154149860690
SPT(16)	2531271060587286911	0 20 32 110 116 230 242 266 306 330 342 456 462 540 552 572	-1064863686780
SPT(16)	2531271288168460769	0 8 50 54 68 122 152 162 200 210 240 294 308 312 354 362	-837282512922
TPT(14)	2531271391186583189	0 2 18 20 60 62 72 74 138 140 258 260 282 284	-734264390502
SPT(13)	2531271757399427807	0 42 66 72 120 156 246 336 372 420 426 450 492	-368051545884
SPT(16)	2531271805554251887	0 4 54 72 102 130 154 156 220 222 246 274 304 322 372 376	-319896721804
STPT(12)	2531273294436269441	0 2 36 38 60 62 186 188 210 212 246 248	1168985295750
TPT(14)	2531274903167390447	0 2 72 74 144 146 210 212 240 242 264 266 300 302	2777716416756
STPT(10)	2531275512231939017	0 2 30 32 42 44 54 56 84 86	3386780965326
SPT(16)	2531275741056042581	0 2 20 72 80 90 96 128 150 182 188 198 206 258 276 278	3615605068890
STPT(10)	2531275827363034649	0 2 42 44 60 62 78 80 120 122	3701912060958