Prime p₀= 3030394902476887949 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 4 2 28 2 10 2 40 2 76 2 (?)
a_n: 0 2 42 44 48 50 78 80 90 92 132 134 210 212
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: 212
Found by: Conan
db: batch=82, k=14, 40 4 28 10 40 76

SPT(16)	3030392871360719699	0 8 32 102 128 134 162 164 168 170 198 204 230 300 324 332	-2031116168250
STPT(10)	3030393099775785347	0 2 42 44 102 104 162 164 204 206	-1802701102602
STPT(10)	3030393450041351627	0 2 72 74 102 104 132 134 204 206	-1452435536322
SPT(16)	3030393789060095449	0 10 12 70 78 82 102 120 280 298 318 322 330 388 390 400	-1113416792500
SPT(16)	3030394157520370409	0 18 38 140 192 230 234 270 272 308 312 350 402 504 524 542	-744956517540
SPT(16)	3030394370316082151	0 30 42 50 68 120 140 170 210 240 260 312 330 338 350 380	-532160805798
STPT(10)	3030395015218580921	0 2 6 8 18 20 30 32 36 38	112741692972
SPT(16)	3030395032950897461	0 12 26 72 108 150 168 180 278 290 308 350 386 432 446 458	130474009512
SPT(16)	3030395766319648127	0 20 24 36 66 90 104 120 146 162 176 200 230 242 246 266	863842760178
STPT(10)	3030396226329595559	0 2 18 20 60 62 102 104 120 122	1323852707610
SPT(16)	3030396226462794529	0 22 58 82 112 142 174 190 222 238 270 300 330 354 390 412	1323985906580