Prime p₀= 2327786590699016561 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 28 2 10 2 238 2 46 2 58 2 (?)
a_n: 0 2 6 8 36 38 48 50 288 290 336 338 396 398
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: 398
Found by: eclipse99
db: batch=81, k=14, 4 28 10 238 46 58

STPT(10)	2327784907141072859	0 2 18 20 30 32 42 44 60 62	-1683557943702
SPT(16)	2327785203981326801	0 12 60 62 126 150 176 182 186 192 218 242 306 308 356 368	-1386717689760
SPT(16)	2327785705898876819	0 32 38 78 140 162 170 192 338 360 368 390 452 492 498 530	-884800139742
SPT(16)	2327786046096047351	0 8 20 110 126 138 146 152 156 162 170 182 198 288 300 308	-544602969210
STPT(10)	2327786372327916581	0 2 6 8 48 50 90 92 96 98	-218371099980
STPT(10)	2327786492983283699	0 2 12 14 90 92 168 170 180 182	-97715732862
STPT(10)	2327787239539335941	0 2 6 8 48 50 90 92 96 98	648840319380
STPT(10)	2327787239841642947	0 2 30 32 42 44 54 56 84 86	649142626386
SPT(16)	2327787296218001869	0 10 60 84 102 118 154 160 192 198 234 250 268 292 342 352	705518985308
STPT(10)	2327787405264549647	0 2 42 44 72 74 102 104 144 146	814565533086
SPT(16)	2327787418399820183	0 6 36 44 66 78 80 108 146 174 176 188 210 218 248 254	827700803622