Prime p₀= 1950491284117767821 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 28 2 70 2 76 2 28 2 46 2 (?)
a_n: 0 2 78 80 108 110 180 182 258 260 288 290 336 338
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: Landjunge
db: batch=80, k=14, 76 28 70 76 28 46

SPT(16)	1950489191611730017	0 6 70 72 96 132 154 196 210 252 274 310 334 336 400 406	-2092506037804
SPT(16)	1950489520974622627	0 6 30 54 90 132 136 150 226 240 244 286 322 346 370 376	-1763143145194
STPT(10)	1950490281923639549	0 2 30 32 60 62 90 92 120 122	-1002194128272
SPT(16)	1950490438680820667	0 2 134 140 144 176 182 210 236 264 270 302 306 312 444 446	-845436947154
SPT(16)	1950490672193374189	0 22 28 118 120 162 172 204 208 240 250 292 294 384 390 412	-611924393632
STPT(10)	1950491130902870117	0 2 42 44 72 74 102 104 144 146	-153214897704
SPT(16)	1950491331336083747	0 50 72 74 92 122 150 162 164 176 204 234 252 254 276 326	47218315926
TPT(14)	1950491443825037669	0 2 12 14 48 50 132 134 138 140 150 152 162 164	159707269848
SPT(16)	1950491483121358703	0 96 114 138 144 164 170 194 240 264 270 290 296 320 338 434	199003590882
STPT(10)	1950491526587779907	0 2 30 32 42 44 54 56 84 86	242470012086
STPT(10)	1950491768581231199	0 2 18 20 30 32 42 44 60 62	484463463378