Prime p₀= 1295710056532183931 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 10 2 16 2 40 2 88 2 46 2 (?)
a_n: 0 2 6 8 18 20 36 38 78 80 168 170 216 218
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: Cruncher Pete
db: batch=77, k=14, 4 10 16 40 88 46

SPT(16)	1295709401610090911	0 12 20 26 80 90 96 120 278 302 308 318 372 378 386 398	-654922093020
STPT(10)	1295709490811688761	0 2 6 8 48 50 90 92 96 98	-565720495170
TPT(14)	1295709643466727911	0 2 6 8 30 32 78 80 90 92 120 122 156 158	-413065456020
SPT(16)	1295709897890352467	0 20 74 80 162 164 194 204 290 300 330 332 414 420 474 494	-158641831464
SPT(16)	1295709948100160093	0 50 56 74 78 96 114 120 134 140 158 176 180 198 204 254	-108432023838
SPT(16)	1295709981021393529	0 12 40 78 88 114 124 172 180 228 238 264 274 312 340 352	-75510790402
STPT(10)	1295710211081822867	0 2 90 92 102 104 114 116 204 206	154549638936
STPT(10)	1295710579493430809	0 2 42 44 60 62 78 80 120 122	522961246878
STPT(10)	1295710741068481217	0 2 54 56 132 134 210 212 264 266	684536297286
SPT(16)	1295711024492407213	0 4 6 28 54 66 88 118 186 216 238 250 276 298 300 304	967960223282
SPT(16)	1295711032781829577	0 6 46 84 124 144 154 166 294 306 316 336 376 414 454 460	976249645646