Prime p₀= 1127457568160358959 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 40 2 136 2 10 2 16 2 (?)
a_n: 0 2 42 44 60 62 102 104 240 242 252 254 270 272
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: crashtech
db: batch=76, k=14, 40 16 40 136 10 16

SPT(16)	1127455633318377469	0 12 22 58 60 82 88 108 142 162 168 190 192 228 238 250	-1934841981490
STPT(10)	1127456341348308689	0 2 12 14 90 92 168 170 180 182	-1226812050270
SPT(16)	1127456466667554917	0 20 92 122 134 144 150 152 174 176 182 192 204 234 306 326	-1101492804042
SPT(16)	1127457070747318879	0 18 52 78 94 120 150 214 228 292 322 348 364 390 424 442	-497413040080
SPT(16)	1127457208280149753	0 10 28 66 76 84 90 100 144 154 160 168 178 216 234 244	-359880209206
STPT(10)	1127457397501909007	0 2 30 32 120 122 210 212 240 242	-170658449952
STPT(10)	1127458323227053001	0 2 30 32 60 62 90 92 120 122	755066694042
SPT(16)	1127458699731192043	0 24 54 66 96 120 190 196 288 294 364 388 418 430 460 484	1131570833084
SPT(16)	1127459336479553641	0 18 40 70 72 82 130 156 172 198 246 256 258 288 310 328	1768319194682
STPT(10)	1127459592019605539	0 2 30 32 60 62 90 92 120 122	2023859246580
SPT(16)	1127460348269855837	0 42 84 102 152 180 222 224 282 284 326 354 404 422 464 506	2780109496878