Prime p₀= 1266525369974012609 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 58 2 52 2 136 2 76 2 52 2 (?)
a_n: 0 2 108 110 168 170 222 224 360 362 438 440 492 494
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: 494
Found by: Megacruncher
db: batch=77, k=14, 106 58 52 136 76 52

SPT(16)	1266524865366339751	0 22 28 30 42 130 156 160 168 172 198 286 298 300 306 328	-504607672858
TPT(14)	1266524865415092431	0 2 30 32 66 68 78 80 120 122 126 128 156 158	-504558920178
SPT(16)	1266524954021974861	0 12 18 42 60 78 82 162 166 246 250 268 286 310 316 328	-415952037748
SPT(16)	1266525031783392559	0 52 78 118 124 148 154 220 222 288 294 318 324 364 390 442	-338190620050
SPT(16)	1266525117978641537	0 14 56 66 90 104 150 156 200 206 252 266 290 300 342 356	-251995371072
STPT(10)	1266525340475312189	0 2 18 20 30 32 42 44 60 62	-29498700420
STPT(10)	1266525809721666491	0 2 6 8 48 50 90 92 96 98	439747653882
STPT(10)	1266526241758419581	0 2 30 32 60 62 90 92 120 122	871784406972
SPT(16)	1266526799723046107	0 26 36 50 96 116 120 140 162 182 186 206 252 266 276 302	1429749033498
STPT(10)	1266526916330296067	0 2 42 44 72 74 102 104 144 146	1546356283458
SPT(16)	1266526979358941873	0 6 30 68 86 96 104 138 146 180 188 198 216 254 278 284	1609384929264