Prime p₀= 1233867035216176157 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 148 2 40 2 16 2 10 2 (?)
a_n: 0 2 30 32 42 44 192 194 234 236 252 254 264 266
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: 266
Found by: Megacruncher
db: batch=77, k=14, 28 10 148 40 16 10

STPT(10)	1233866576674171409	0 2 48 50 90 92 132 134 180 182	-458542004748
SPT(16)	1233866639855681731	0 28 60 78 120 196 246 258 268 280 330 406 448 466 498 526	-395360494426
TPT(14)	1233866652711008759	0 2 18 20 60 62 240 242 252 254 282 284 300 302	-382505167398
SPT(16)	1233866685652624451	0 18 26 72 80 96 150 152 156 158 212 228 236 282 290 308	-349563551706
STPT(10)	1233866828612786651	0 2 6 8 48 50 90 92 96 98	-206603389506
SPT(16)	1233867018863363407	0 4 6 34 84 102 154 174 202 222 274 292 342 370 372 376	-16352812750
TPT(14)	1233867072315431249	0 2 78 80 90 92 150 152 168 170 180 182 222 224	37099255092
SPT(16)	1233867179726097211	0 12 36 58 78 96 100 166 252 318 322 340 360 382 406 418	144509921054
STPT(10)	1233867358862221841	0 2 6 8 18 20 30 32 36 38	323646045684
STPT(10)	1233867383735792327	0 2 30 32 42 44 54 56 84 86	348519616170
STPT(12)	1233867875649877199	0 2 30 32 42 44 198 200 210 212 240 242	840433701042