Prime p₀= 2949190533003595787 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 40 2 76 2 28 2 52 2 (?)
a_n: 0 2 60 62 90 92 132 134 210 212 240 242 294 296
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: 296
Found by: Landjunge
db: batch=82, k=14, 58 28 40 76 28 52

SPT(16)	2949188272236324509	0 62 108 122 132 140 152 174 188 210 222 230 240 254 300 362	-2260767271278
STPT(10)	2949188297214187331	0 2 30 32 120 122 210 212 240 242	-2235789408456
STPT(10)	2949189543848317109	0 2 18 20 30 32 42 44 60 62	-989155278678
SPT(16)	2949190142076888019	0 10 34 48 52 78 114 150 202 238 274 300 304 318 342 352	-390926707768
SPT(16)	2949190160692160857	0 16 40 42 72 106 124 156 190 222 240 274 304 306 330 346	-372311434930
SPT(16)	2949190189605968537	0 32 36 62 104 146 152 246 290 384 390 432 474 500 504 536	-343397627250
SPT(16)	2949190728237503039	0 2 24 38 50 54 68 140 162 234 248 252 264 278 300 302	195233907252
SPT(16)	2949190882017866903	0 14 18 36 86 128 140 156 158 174 186 228 278 296 300 314	349014271116
TPT(14)	2949191148309870251	0 2 30 32 138 140 168 170 216 218 270 272 300 302	615306274464
SPT(16)	2949191160382218319	0 12 18 22 40 60 78 102 130 154 172 192 210 214 220 232	627378622532
SPT(16)	2949191262709970923	0 28 30 144 198 274 276 298 456 478 480 556 610 724 726 754	729706375136