Prime p₀= 2688142719311460911 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 52 2 28 2 94 2 58 2 22 2 (?)
a_n: 0 2 36 38 90 92 120 122 216 218 276 278 300 302
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: 302
Found by: JayPi
db: batch=82, k=14, 34 52 28 94 58 22

SPT(16)	2688141799340614207	0 10 24 30 54 66 70 76 90 96 100 112 136 142 156 166	-919970846704
STPT(10)	2688141997044093209	0 2 12 14 90 92 168 170 180 182	-722267367702
SPT(16)	2688142028210631679	0 4 18 30 52 60 64 84 88 108 112 120 142 154 168 172	-691100829232
SPT(16)	2688142427169260203	0 10 16 18 48 90 136 150 154 168 214 256 286 288 294 304	-292142200708
SPT(16)	2688142550693888657	0 24 26 50 90 110 146 150 206 210 246 266 306 330 332 356	-168617572254
TPT(14)	2688142683865673051	0 2 66 68 108 110 216 218 276 278 288 290 330 332	-35445787860
SPT(16)	2688142940661932431	0 10 12 28 46 72 88 108 130 150 166 192 210 226 228 238	221350471520
SPT(16)	2688143280721945621	0 12 22 40 130 150 180 220 222 262 292 312 402 420 430 442	561410484710
SPT(16)	2688143362124184589	0 4 88 114 130 132 150 198 274 322 340 342 358 384 468 472	642812723678
SPT(16)	2688143662463017399	0 28 40 70 82 84 190 238 264 312 418 420 432 462 474 502	943151556488
STPT(10)	2688144183022129859	0 2 18 20 30 32 42 44 60 62	1463710668948