Prime p₀= 2949200084513625749 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 118 2 28 2 22 2 88 2 76 2 (?)
a_n: 0 2 78 80 198 200 228 230 252 254 342 344 420 422
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: 422
Found by: Landjunge
db: batch=82, k=14, 76 118 28 22 88 76

SPT(16)	2949198488840043157	0 4 42 90 102 124 180 214 240 274 330 352 364 412 450 454	-1595673582592
SPT(16)	2949198526007008441	0 6 28 46 48 148 160 196 222 258 270 370 372 390 412 418	-1558506617308
STPT(10)	2949198565802746331	0 2 6 8 48 50 90 92 96 98	-1518710879418
STPT(10)	2949198661562869487	0 2 90 92 102 104 114 116 204 206	-1422950756262
SPT(16)	2949198990462664711	0 10 46 66 78 88 90 142 246 298 300 310 322 342 378 388	-1094050961038
SPT(16)	2949199186503559427	0 6 26 54 60 102 114 162 194 242 254 296 302 330 350 356	-898010066322
TPT(14)	2949200493213775679	0 2 48 50 168 170 180 182 258 260 270 272 420 422	408700149930
SPT(16)	2949200646586336673	0 6 24 108 126 174 180 186 188 194 200 248 266 350 368 374	562072710924
TPT(14)	2949200976336527279	0 2 12 14 48 50 78 80 108 110 120 122 162 164	891822901530
STPT(10)	2949201037357666367	0 2 42 44 132 134 222 224 264 266	952844040618
SPT(16)	2949201284707673053	0 6 28 34 60 70 76 100 174 198 204 214 240 246 268 274	1200194047304