Prime p₀= 2161138755372277787 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 148 2 46 2 22 2 28 2 76 2 (?)
a_n: 0 2 42 44 192 194 240 242 264 266 294 296 372 374
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: 374
Found by: Landjunge
db: batch=81, k=14, 40 148 46 22 28 76

SPT(16)	2161137244549454221	0 10 12 18 42 58 66 96 142 172 180 196 220 226 228 238	-1510822823566
SPT(16)	2161137265863350413	0 28 34 46 84 88 94 100 144 150 156 160 198 210 216 244	-1489508927374
STPT(10)	2161137647254845599	0 2 18 20 30 32 42 44 60 62	-1108117432188
SPT(16)	2161137784202929513	0 16 18 28 76 78 114 126 148 160 196 198 246 256 258 274	-971169348274
SPT(16)	2161138603201896139	0 24 40 52 54 78 82 100 162 180 184 208 210 222 238 262	-152170381648
SPT(16)	2161138624992839729	0 72 90 110 122 128 174 188 234 248 294 300 312 332 350 422	-130379438058
STPT(10)	2161138782982841507	0 2 24 26 42 44 60 62 84 86	27610563720
STPT(10)	2161139159198605679	0 2 42 44 60 62 78 80 120 122	403826327892
STPT(10)	2161139191970910059	0 2 18 20 30 32 42 44 60 62	436598632272
STPT(10)	2161139337889509977	0 2 24 26 42 44 60 62 84 86	582517232190
SPT(16)	2161139663302453279	0 4 28 42 64 88 108 112 270 274 294 318 340 354 378 382	907930175492