Prime p₀= 2350394958802263341 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 100 2 64 2 58 2 22 2 34 2 (?)
a_n: 0 2 48 50 150 152 216 218 276 278 300 302 336 338
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: Xenon
db: batch=81, k=14, 46 100 64 58 22 34

SPT(16)	2350394355707291977	0 24 30 72 94 100 114 132 202 220 234 240 262 304 310 334	-603094971364
SPT(16)	2350394372107985351	0 18 32 92 98 102 120 210 278 368 386 390 396 456 470 488	-586694277990
SPT(16)	2350394465474644627	0 34 54 64 82 90 112 120 124 132 154 162 180 190 210 244	-493327618714
STPT(10)	2350394751294728597	0 2 30 32 42 44 54 56 84 86	-207507534744
SPT(16)	2350394901676764751	0 12 42 76 78 90 118 120 208 210 238 250 252 286 316 328	-57125498590
STPT(10)	2350394933813360207	0 2 54 56 72 74 90 92 144 146	-24988903134
STPT(10)	2350395154621809857	0 2 42 44 72 74 102 104 144 146	195819546516
TPT(14)	2350395330583700549	0 2 30 32 42 44 210 212 270 272 288 290 378 380	371781437208
STPT(10)	2350395745288167947	0 2 30 32 42 44 54 56 84 86	786485904606
STPT(10)	2350395809201421809	0 2 42 44 60 62 78 80 120 122	850399158468
SPT(16)	2350396144976758057	0 12 22 40 70 90 102 114 130 142 154 174 204 222 232 244	1186174494716