Prime p₀= 2326726970576174867 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 10 2 28 2 4 2 40 2 (?)
a_n: 0 2 30 32 72 74 84 86 114 116 120 122 162 164
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: 164
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 28 40 10 28 4 40

STPT(10)	2326726288873358969	0 2 18 20 60 62 102 104 120 122	-681702815898
STPT(10)	2326726379490932561	0 2 6 8 18 20 30 32 36 38	-591085242306
SPT(16)	2326726388076551233	0 10 36 48 58 84 94 108 166 180 190 216 226 238 264 274	-582499623634
SPT(16)	2326726498149517381	0 12 88 136 168 186 208 220 228 240 262 280 312 360 436 448	-472426657486
STPT(10)	2326726579244641961	0 2 30 32 78 80 126 128 156 158	-391331532906
SPT(16)	2326726917856388629	0 22 40 58 88 102 114 138 154 178 190 204 234 252 270 292	-52719786238
STPT(10)	2326727033539467017	0 2 30 32 42 44 54 56 84 86	62963292150
SPT(16)	2326727295909193561	0 10 70 76 96 108 112 118 150 156 160 172 192 198 258 268	325333018694
STPT(10)	2326727746620053207	0 2 30 32 72 74 114 116 144 146	776043878340
STPT(10)	2326727767818791801	0 2 36 38 78 80 120 122 156 158	797242616934
STPT(10)	2326727820274911017	0 2 30 32 42 44 54 56 84 86	849698736150