Prime p₀= 378609582203217017 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 28 2 28 2 10 2 28 2 (?)
a_n: 0 2 30 32 72 74 102 104 132 134 144 146 174 176
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: 176
Found by: Cruncher Pete
db: batch=70, k=14, 28 40 28 28 10 28

STPT(10)	378609482626162679	0 2 12 14 90 92 168 170 180 182	-99577054338
SPT(14)	378609503980848599	0 12 30 72 78 90 132 140 182 194 200 242 260 272	-78222368418
SPT(14)	378609530189026379	0 14 20 90 168 180 228 260 308 320 398 468 474 488	-52014190638
SPT(14)	378609544041319399	0 18 34 40 48 70 84 118 132 154 162 168 184 202	-38161897618
SPT(14)	378609553100963033	0 36 54 68 78 98 110 114 126 146 156 170 188 224	-29102253984
TPT(12)	378609579399092861	0 2 96 98 120 122 156 158 180 182 210 212	-2804124156
SPT(16)	378609585967797581	0 8 20 48 68 78 90 152 216 278 290 300 320 348 360 368	3764580564
SPT(14)	378609629656852651	0 10 28 52 70 78 100 120 142 150 168 192 210 220	47453635634
SPT(14)	378609633074390227	0 52 60 100 112 132 142 144 154 174 186 226 234 286	50871173210
TPT(12)	378609633581491649	0 2 150 152 348 350 360 362 372 374 390 392	51378274632
STPT(10)	378609640656571097	0 2 54 56 72 74 90 92 144 146	58453354080