Prime p₀= 1087254359186561327 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 4 2 52 2 28 2 64 2 112 2 (?)
a_n: 0 2 54 56 60 62 114 116 144 146 210 212 324 326
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: 326
Found by: crashtech
db: batch=76, k=14, 52 4 52 28 64 112

SPT(16)	1087253140931101847	0 44 92 132 150 164 236 264 332 360 432 446 464 504 552 596	-1218255459480
STPT(10)	1087253292503549837	0 2 30 32 42 44 54 56 84 86	-1066683011490
SPT(16)	1087253332691227921	0 6 16 18 22 36 48 76 102 130 142 156 160 162 172 178	-1026495333406
SPT(16)	1087253386517680817	0 2 30 44 84 86 92 96 200 204 210 212 252 266 294 296	-972668880510
SPT(16)	1087253754339374533	0 10 46 136 184 190 196 198 316 318 324 330 378 468 504 514	-604847186794
SPT(16)	1087254052633932913	0 36 48 64 66 94 144 178 186 220 270 298 300 316 328 364	-306552628414
SPT(16)	1087254506339520461	0 38 42 78 92 96 150 182 216 248 302 306 320 356 360 398	147152959134
STPT(10)	1087254546049131137	0 2 12 14 42 44 72 74 84 86	186862569810
STPT(10)	1087254676285077071	0 2 30 32 78 80 126 128 156 158	317098515744
TPT(14)	1087255097471377871	0 2 150 152 156 158 210 212 240 242 366 368 450 452	738284816544
SPT(16)	1087255205871561511	0 10 22 30 42 46 78 88 120 130 162 166 178 186 198 208	846685000184