Prime p₀= 997776743309846657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 64 2 52 2 58 2 64 2 40 2 (?)
a_n: 0 2 54 56 120 122 174 176 234 236 300 302 342 344
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: 344
Found by: HenkM
db: batch=76, k=14, 52 64 52 58 64 40

SPT(16)	997775517114827323	0 66 70 126 138 148 174 196 228 250 276 286 298 354 358 424	-1226195019334
STPT(10)	997775975770815251	0 2 6 8 48 50 90 92 96 98	-767539031406
SPT(16)	997776040063882811	0 2 18 86 132 158 180 182 216 218 240 266 312 380 396 398	-703245963846
STPT(12)	997776421658071787	0 2 30 32 54 56 90 92 114 116 144 146	-321651774870
STPT(10)	997776497128138697	0 2 54 56 72 74 90 92 144 146	-246181707960
STPT(10)	997776596569146731	0 2 78 80 138 140 198 200 276 278	-146740699926
STPT(10)	997776846153695759	0 2 48 50 90 92 132 134 180 182	102843849102
STPT(10)	997776856498415837	0 2 30 32 42 44 54 56 84 86	113188569180
STPT(10)	997776900025947707	0 2 30 32 42 44 54 56 84 86	156716101050
STPT(10)	997776929881535129	0 2 18 20 30 32 42 44 60 62	186571688472
SPT(16)	997776996374625013	0 10 16 24 40 46 54 60 94 100 108 114 130 138 144 154	253064778356