Prime p₀= 1127450346014036897 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 4 2 40 2 70 2 94 2 (?)
a_n: 0 2 12 14 24 26 30 32 72 74 144 146 240 242
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: 242
Found by: crashtech
db: batch=76, k=14, 10 10 4 40 70 94

SPT(16)	1127449619251062881	0 92 102 116 120 140 156 270 362 476 492 512 516 530 540 632	-726762974016
SPT(16)	1127449888844500541	0 8 26 38 42 66 78 92 126 140 152 176 180 192 210 218	-457169536356
SPT(16)	1127449945314070403	0 6 54 78 98 104 116 146 168 198 210 216 236 260 308 314	-400699966494
STPT(10)	1127450086979247761	0 2 36 38 78 80 120 122 156 158	-259034789136
STPT(10)	1127450154001568357	0 2 72 74 102 104 132 134 204 206	-192012468540
SPT(16)	1127450260706192861	0 32 36 60 102 110 116 120 158 162 168 176 218 242 246 278	-85307844036
SPT(16)	1127450739398925983	0 44 66 86 96 144 210 228 236 254 320 368 378 398 420 464	393384889086
SPT(16)	1127450962556428033	0 28 40 46 60 90 96 108 196 208 214 244 258 264 276 304	616542391136
SPT(16)	1127451041708286221	0 36 62 86 110 138 180 188 240 248 290 318 342 366 392 428	695694249324
TPT(14)	1127451632463430319	0 2 48 50 78 80 132 134 138 140 180 182 222 224	1286449393422
STPT(10)	1127451695598671591	0 2 30 32 78 80 126 128 156 158	1349584634694