Prime p₀= 2923245898939056851 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 64 2 10 2 28 2 100 2 34 2 (?)
a_n: 0 2 30 32 96 98 108 110 138 140 240 242 276 278
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: 278
Found by: Landjunge
db: batch=82, k=14, 28 64 10 28 100 34

SPT(16)	2923243645044970103	0 6 8 20 38 86 108 164 180 236 258 306 324 336 338 344	-2253894086748
STPT(10)	2923243754715540161	0 2 6 8 48 50 90 92 96 98	-2144223516690
SPT(16)	2923243853755823467	0 30 42 64 84 90 126 204 322 400 436 442 462 484 496 526	-2045183233384
STPT(10)	2923244222975546681	0 2 30 32 78 80 126 128 156 158	-1675963510170
SPT(16)	2923245588761031403	0 28 94 108 150 174 178 216 238 276 280 304 346 360 426 454	-310178025448
SPT(16)	2923245684153470749	0 12 28 64 82 94 100 108 124 132 138 150 168 204 220 232	-214785586102
SPT(16)	2923245911854176379	0 4 22 28 42 154 174 232 240 298 318 430 444 450 468 472	12915119528
SPT(16)	2923246008257281631	0 8 36 42 96 126 140 240 308 408 422 452 506 512 540 548	109318224780
STPT(10)	2923246171770075059	0 2 18 20 30 32 42 44 60 62	272831018208
SPT(16)	2923246689657236783	0 26 36 38 60 84 98 144 200 246 260 284 306 308 318 344	790718179932
TPT(14)	2923247147358164351	0 2 60 62 96 98 138 140 168 170 180 182 228 230	1248419107500