Prime p₀= 2338649586860973539 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 88 2 28 2 40 2 10 2 76 2 (?)
a_n: 0 2 18 20 108 110 138 140 180 182 192 194 270 272
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: Landjunge
db: batch=81, k=14, 16 88 28 40 10 76

SPT(16)	2338647758806151383	0 10 30 84 90 96 136 160 174 198 238 244 250 304 324 334	-1828054822156
SPT(16)	2338647791039984759	0 14 80 98 114 144 188 200 222 234 278 308 324 342 408 422	-1795820988780
SPT(16)	2338647795328103687	0 44 50 54 80 152 176 180 236 240 264 336 362 366 372 416	-1791532869852
SPT(16)	2338649075610583147	0 12 40 42 60 144 150 154 210 214 220 304 322 324 352 364	-511250390392
SPT(16)	2338649178427592077	0 40 42 76 130 132 172 192 280 300 340 342 396 430 432 472	-408433381462
STPT(10)	2338649337444398939	0 2 42 44 120 122 198 200 240 242	-249416574600
SPT(16)	2338649623899546847	0 42 106 156 162 172 180 184 192 196 204 214 220 270 334 376	37038573308
STPT(10)	2338649760288501629	0 2 12 14 30 32 48 50 60 62	173427528090
SPT(16)	2338649814109693093	0 16 58 64 66 84 106 196 228 318 340 358 360 366 408 424	227248719554
STPT(10)	2338650148849573367	0 2 30 32 42 44 54 56 84 86	561988599828
SPT(16)	2338650227929447373	0 50 54 56 74 96 120 146 168 194 218 240 258 260 264 314	641068473834