Prime p₀= 2356308531668855381 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 58 2 4 2 28 2 52 2 16 2 (?)
a_n: 0 2 60 62 120 122 126 128 156 158 210 212 228 230
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: 230
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 58 58 4 28 52 16

STPT(10)	2356308045141386459	0 2 12 14 30 32 48 50 60 62	-486527468922
STPT(10)	2356308156099287639	0 2 18 20 30 32 42 44 60 62	-375569567742
STPT(10)	2356308328172621087	0 2 42 44 72 74 102 104 144 146	-203496234294
STPT(10)	2356308437784382979	0 2 42 44 60 62 78 80 120 122	-93884472402
SPT(16)	2356308447717504347	0 44 84 110 116 174 194 200 420 426 446 504 510 536 576 620	-83951351034
STPT(10)	2356308468581545727	0 2 12 14 72 74 132 134 144 146	-63087309654
SPT(16)	2356309414135502801	0 6 50 72 98 120 132 150 188 206 218 240 266 288 332 338	882466647420
STPT(10)	2356309568440128359	0 2 42 44 60 62 78 80 120 122	1036771272978
SPT(16)	2356309582991761841	0 12 36 56 78 90 132 140 168 176 218 230 252 272 296 308	1051322906460
STPT(10)	2356309999444795787	0 2 30 32 42 44 54 56 84 86	1467775940406
SPT(16)	2356310040809080933	0 16 24 76 78 96 100 126 148 174 178 196 198 250 258 274	1509140225552