Prime p₀= 2154302782587417227 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 118 2 28 2 58 2 28 2 208 2 (?)
a_n: 0 2 54 56 174 176 204 206 264 266 294 296 504 506
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: 506
Found by: Paul
db: batch=81, k=14, 52 118 28 58 28 208

STPT(12)	2154301836395279267	0 2 12 14 30 32 72 74 90 92 102 104	-946192137960
SPT(16)	2154302029069102333	0 58 88 106 120 136 166 168 208 210 240 256 270 288 318 376	-753518314894
SPT(16)	2154302239649698993	0 28 30 70 148 184 240 298 306 364 420 456 534 574 576 604	-542937718234
SPT(16)	2154302345918898803	0 18 24 38 80 104 110 150 218 258 264 288 330 344 350 368	-436668518424
STPT(10)	2154302441896288037	0 2 12 14 72 74 132 134 144 146	-340691129190
STPT(10)	2154302713156120529	0 2 30 32 60 62 90 92 120 122	-69431296698
TPT(14)	2154303365751936689	0 2 108 110 132 134 138 140 210 212 222 224 342 344	583164519462
STPT(10)	2154303508274073587	0 2 30 32 72 74 114 116 144 146	725686656360
SPT(16)	2154303611318335643	0 26 38 140 168 176 180 188 378 386 390 398 426 528 540 566	828730918416
SPT(16)	2154304245195954149	0 18 30 48 50 90 110 152 288 330 350 390 392 410 422 440	1462608536922
SPT(16)	2154304294940911613	0 48 78 90 110 134 140 168 230 258 264 288 308 320 350 398	1512353494386