Prime p₀= 2567091799976539727 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 64 2 88 2 22 2 4 2 88 2 (?)
a_n: 0 2 24 26 90 92 180 182 204 206 210 212 300 302
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, 22 64 88 22 4 88

SPT(16)	2567091095769367703	0 6 68 90 98 138 176 188 216 228 266 306 314 336 398 404	-704207172024
SPT(16)	2567091126317664371	0 42 50 60 66 96 102 110 132 140 146 176 182 192 200 242	-673658875356
SPT(16)	2567091179789153419	0 24 28 34 52 58 78 112 120 154 174 180 198 204 208 232	-620187386308
STPT(10)	2567091482997298247	0 2 90 92 132 134 174 176 264 266	-316979241480
STPT(10)	2567091499478676347	0 2 60 62 72 74 84 86 144 146	-300497863380
SPT(16)	2567091747475090109	0 18 24 30 60 68 134 138 224 228 294 302 332 338 344 362	-52501449618
SPT(16)	2567092096087794589	0 34 88 108 124 150 210 222 250 262 322 348 364 384 438 472	296111254862
STPT(10)	2567092172648519741	0 2 36 38 78 80 120 122 156 158	372671980014
STPT(10)	2567092479139462529	0 2 12 14 90 92 168 170 180 182	679162922802
SPT(16)	2567092527557665007	0 14 20 32 54 90 134 180 224 270 314 350 372 384 390 404	727581125280
STPT(10)	2567092531005109097	0 2 12 14 42 44 72 74 84 86	731028569370