Prime p₀= 2777715077176844867 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 22 2 94 2 40 2 40 2 34 2 (?)
a_n: 0 2 30 32 54 56 150 152 192 194 234 236 270 272
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: 272
Found by: [SG-FC] hl
db: batch=82, k=14, 28 22 94 40 40 34

SPT(16)	2777713467688203973	0 90 106 168 178 196 208 246 250 288 300 318 328 390 406 496	-1609488640894
STPT(10)	2777713740160809419	0 2 12 14 30 32 48 50 60 62	-1337016035448
SPT(16)	2777713893409234133	0 68 128 134 144 158 210 258 266 314 366 380 390 396 456 524	-1183767610734
TPT(14)	2777714537091049571	0 2 30 32 36 38 120 122 240 242 276 278 306 308	-540085795296
STPT(10)	2777714867951552687	0 2 30 32 72 74 114 116 144 146	-209225292180
SPT(16)	2777714912418274489	0 12 24 34 48 72 90 118 174 202 220 244 258 268 280 292	-164758570378
STPT(10)	2777715398339184179	0 2 30 32 60 62 90 92 120 122	321162339312
SPT(16)	2777715550534658413	0 30 36 58 66 70 138 150 154 166 234 238 246 268 274 304	473357813546
TPT(14)	2777715859192823597	0 2 12 14 42 44 72 74 144 146 180 182 222 224	782015978730
SPT(16)	2777715943087055461	0 36 52 60 96 130 178 196 222 240 288 322 358 366 382 418	865910210594
STPT(10)	2777716274144430077	0 2 30 32 42 44 54 56 84 86	1196967585210