Prime p₀= 4062976581790583687 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 52 2 34 2 40 2 28 2 10 2 (?)
a_n: 0 2 60 62 114 116 150 152 192 194 222 224 234 236
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: 236
Found by: [AF] Kalianthys
db: batch=84, k=14, 58 52 34 40 28 10

SPT(16)	4062975394706566981	0 30 42 96 112 142 156 166 186 196 210 240 256 310 322 352	-1187084016706
STPT(10)	4062975641016063449	0 2 18 20 30 32 42 44 60 62	-940774520238
SPT(16)	4062975673524983687	0 6 26 30 90 146 150 180 182 212 216 272 332 336 356 362	-908265600000
STPT(10)	4062976017392922731	0 2 6 8 48 50 90 92 96 98	-564397660956
SPT(16)	4062976323639544057	0 42 52 60 64 70 112 154 162 204 246 252 256 264 274 316	-258151039630
SPT(16)	4062976470258368137	0 12 46 52 96 126 186 210 226 250 310 340 384 390 424 436	-111532215550
STPT(10)	4062977181157817849	0 2 12 14 90 92 168 170 180 182	599367234162
SPT(16)	4062977907761907461	0 18 26 56 60 126 132 152 216 236 242 308 312 342 350 368	1325971323774
SPT(16)	4062978049599713009	0 20 30 80 98 132 164 168 194 198 230 264 282 332 342 362	1467809129322
SPT(16)	4062978176122501579	0 28 88 100 114 118 142 198 214 270 294 298 312 324 384 412	1594331917892
STPT(10)	4062979071625286999	0 2 42 44 90 92 138 140 180 182	2489834703312