Prime p₀= 2766085105068688229 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 46 2 88 2 10 2 28 2 10 2 (?)
a_n: 0 2 30 32 78 80 168 170 180 182 210 212 222 224
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: 224
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 28 46 88 10 28 10

SPT(16)	2766084284157589973	0 14 18 36 44 134 144 224 240 320 330 420 428 446 450 464	-820911098256
STPT(10)	2766084601628499791	0 2 6 8 48 50 90 92 96 98	-503440188438
SPT(16)	2766084773868690427	0 46 54 96 112 114 174 180 256 262 322 324 340 382 390 436	-331199997802
SPT(16)	2766084962247624631	0 12 42 48 82 102 118 120 130 132 148 168 202 208 238 250	-142821063598
STPT(10)	2766085071846114827	0 2 54 56 72 74 90 92 144 146	-33222573402
STPT(12)	2766085073700602879	0 2 12 14 42 44 78 80 108 110 120 122	-31368085350
SPT(16)	2766085535638400827	0 4 54 76 90 150 196 210 220 234 280 340 354 376 426 430	430569712598
SPT(16)	2766085630583727719	0 12 14 68 98 102 120 134 168 182 200 204 234 288 290 302	525515039490
SPT(16)	2766085752218267807	0 14 42 72 84 110 116 146 180 210 216 242 254 284 312 326	647149579578
SPT(16)	2766085778818842343	0 24 36 48 58 100 108 136 138 166 174 216 226 238 250 274	673750154114
SPT(16)	2766086018785372189	0 4 30 60 148 168 180 202 210 232 244 264 352 382 408 412	913716683960