Prime p₀= 2367127321102586597 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 4 2 70 2 10 2 64 2 10 2 (?)
a_n: 0 2 84 86 90 92 162 164 174 176 240 242 252 254
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: Xenon
db: batch=81, k=14, 82 4 70 10 64 10

STPT(10)	2367125792135235881	0 2 36 38 78 80 120 122 156 158	-1528967350716
TPT(14)	2367126151689415757	0 2 54 56 60 62 102 104 114 116 240 242 312 314	-1169413170840
SPT(16)	2367126430683651401	0 48 56 86 90 108 140 156 182 198 230 248 252 282 290 338	-890418935196
STPT(10)	2367126538920342149	0 2 18 20 30 32 42 44 60 62	-782182244448
STPT(10)	2367126729125713169	0 2 18 20 30 32 42 44 60 62	-591976873428
STPT(10)	2367127116001942109	0 2 12 14 30 32 48 50 60 62	-205100644488
SPT(16)	2367127339501785433	0 6 60 108 114 144 160 180 214 234 250 280 286 334 388 394	18399198836
SPT(16)	2367127493539906777	0 4 10 30 40 70 114 120 130 136 180 210 220 240 246 250	172437320180
SPT(16)	2367127850046741107	0 2 6 30 32 36 44 72 104 132 140 144 146 170 174 176	528944154510
STPT(10)	2367127972189246709	0 2 18 20 60 62 102 104 120 122	651086660112
SPT(16)	2367128191955593531	0 6 48 70 72 78 100 106 132 138 160 166 168 190 232 238	870853006934