Prime p₀= 2154828833815432667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 40 2 10 2 28 2 34 2 130 2 (?)
a_n: 0 2 60 62 102 104 114 116 144 146 180 182 312 314
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: 314
Found by: Landjunge
db: batch=81, k=14, 58 40 10 28 34 130

SPT(16)	2154826963302788573	0 36 74 78 120 126 156 170 234 248 278 284 326 330 368 404	-1870512644094
SPT(16)	2154827079217259429	0 24 30 78 92 110 120 140 192 212 222 240 254 302 308 332	-1754598173238
STPT(10)	2154827169425944829	0 2 12 14 30 32 48 50 60 62	-1664389487838
STPT(10)	2154827190762463739	0 2 18 20 30 32 42 44 60 62	-1643052968928
SPT(16)	2154827652260110969	0 72 78 148 150 168 204 234 238 268 304 322 324 394 400 472	-1181555321698
STPT(10)	2154828677140459319	0 2 18 20 30 32 42 44 60 62	-156674973348
STPT(10)	2154829348576920017	0 2 30 32 60 62 90 92 120 122	514761487350
STPT(10)	2154829420837319297	0 2 30 32 42 44 54 56 84 86	587021886630
STPT(10)	2154829665950330231	0 2 30 32 78 80 126 128 156 158	832134897564
SPT(16)	2154830083230416297	0 24 44 84 96 140 144 206 270 332 336 380 392 432 452 476	1249414983630
SPT(16)	2154830680444835623	0 40 48 88 90 118 154 174 250 270 306 334 336 376 384 424	1846629402956