Prime p₀= 1253025409795716629 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 100 2 106 2 22 2 16 2 10 2 (?)
a_n: 0 2 18 20 120 122 228 230 252 254 270 272 282 284
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: 284
Found by: Megacruncher
db: batch=77, k=14, 16 100 106 22 16 10

STPT(10)	1253024645806822151	0 2 6 8 48 50 90 92 96 98	-763988894478
SPT(16)	1253024665376417861	0 20 32 48 56 78 92 120 158 186 200 222 230 246 258 278	-744419298768
SPT(16)	1253024866124920457	0 44 60 72 74 140 144 150 164 170 174 240 242 254 270 314	-543670796172
STPT(10)	1253025163762927019	0 2 48 50 90 92 132 134 180 182	-246032789610
STPT(10)	1253025234057390791	0 2 6 8 48 50 90 92 96 98	-175738325838
STPT(10)	1253025275858446169	0 2 48 50 60 62 72 74 120 122	-133937270460
SPT(16)	1253025558512146103	0 68 128 150 156 168 180 194 240 254 266 278 284 306 366 434	148716429474
STPT(10)	1253026113557678357	0 2 60 62 72 74 84 86 144 146	703761961728
TPT(14)	1253026370893715399	0 2 60 62 102 104 120 122 258 260 330 332 372 374	961097998770
SPT(16)	1253026376869841809	0 22 42 54 70 82 114 120 124 130 162 174 190 202 222 244	967074125180
SPT(16)	1253026698753095281	0 10 36 58 72 100 162 178 240 256 318 346 360 382 408 418	1288957378652