Prime p₀= 2286237988258173557 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 58 2 28 2 34 2 88 2 10 2 (?)
a_n: 0 2 24 26 84 86 114 116 150 152 240 242 252 254
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: 254
Found by: Landjunge
db: batch=81, k=14, 22 58 28 34 88 10

STPT(10)	2286234672274637267	0 2 30 32 42 44 54 56 84 86	-3315983536290
SPT(16)	2286234900927191639	0 14 38 78 80 90 98 102 140 144 152 162 164 204 228 242	-3087330981918
SPT(16)	2286234935016883927	0 30 40 66 82 96 126 136 216 226 256 270 286 312 322 352	-3053241289630
STPT(10)	2286235649106287741	0 2 30 32 78 80 126 128 156 158	-2339151885816
STPT(10)	2286235758274212929	0 2 30 32 60 62 90 92 120 122	-2229983960628
STPT(10)	2286236614446636167	0 2 30 32 42 44 54 56 84 86	-1373811537390
STPT(10)	2286238305855804269	0 2 12 14 30 32 48 50 60 62	317597630712
SPT(16)	2286238465037364053	0 80 104 128 144 150 188 198 266 276 314 320 336 360 384 464	476779190496
STPT(10)	2286238943712134417	0 2 30 32 42 44 54 56 84 86	955453960860
SPT(16)	2286239135574787781	0 36 50 108 110 122 180 212 246 278 336 348 350 408 422 458	1147316614224
SPT(16)	2286239296457405869	0 24 34 40 72 82 142 154 198 210 270 280 312 318 328 352	1308199232312