Prime p₀= 1120081822830667181 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 64 2 58 2 52 2 16 2 46 2 (?)
a_n: 0 2 90 92 156 158 216 218 270 272 288 290 336 338
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: 338
Found by: Daniel
db: batch=76, k=14, 88 64 58 52 16 46

SPT(16)	1120080792196595927	0 32 92 96 102 104 120 146 180 206 222 224 230 234 294 326	-1030634071254
SPT(16)	1120080797384242579	0 12 28 42 48 88 90 118 264 292 294 334 340 354 370 382	-1025446424602
STPT(10)	1120080866340423341	0 2 6 8 48 50 90 92 96 98	-956490243840
SPT(16)	1120081422621452111	0 62 80 98 108 150 212 228 272 288 350 392 402 420 438 500	-400209215070
TPT(14)	1120081630464474479	0 2 18 20 42 44 60 62 90 92 138 140 180 182	-192366192702
SPT(16)	1120081713377425091	0 18 38 62 140 156 182 192 206 216 242 258 336 360 380 398	-109453242090
STPT(12)	1120082135768435027	0 2 24 26 42 44 222 224 240 242 264 266	312937767846
STPT(10)	1120082188707506597	0 2 24 26 42 44 60 62 84 86	365876839416
SPT(16)	1120082479913906783	0 14 18 24 60 66 108 128 156 176 218 224 260 266 270 284	657083239602
STPT(10)	1120082534747624351	0 2 36 38 78 80 120 122 156 158	711916957170
SPT(16)	1120082649587024111	0 20 30 42 62 80 146 150 182 186 252 270 290 302 312 332	826756356930