Prime p₀= 2377679243744103071 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 40 2 4 2 88 2 28 2 28 2 (?)
a_n: 0 2 78 80 120 122 126 128 216 218 246 248 276 278
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: 278
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 76 40 4 88 28 28

STPT(10)	2377677722257472249	0 2 18 20 30 32 42 44 60 62	-1521486630822
STPT(10)	2377677843307169189	0 2 48 50 90 92 132 134 180 182	-1400436933882
SPT(16)	2377677891175642163	0 54 80 108 150 168 170 194 294 318 320 338 380 408 434 488	-1352568460908
SPT(16)	2377678339042146373	0 10 16 70 88 90 160 168 178 186 256 258 276 330 336 346	-904701956698
SPT(16)	2377678919474510459	0 14 38 44 48 62 98 104 108 114 150 164 168 174 198 212	-324269592612
STPT(10)	2377678930493835641	0 2 30 32 78 80 126 128 156 158	-313250267430
SPT(16)	2377679329206038657	0 2 30 60 116 134 140 176 210 246 252 270 326 356 384 386	85461935586
SPT(16)	2377679449581026621	0 6 20 32 50 62 66 108 140 182 186 198 216 228 242 248	205836923550
TPT(14)	2377679725571537501	0 2 48 50 90 92 156 158 168 170 186 188 240 242	481827434430
SPT(16)	2377679731824481453	0 6 10 36 40 70 90 120 124 154 174 204 208 234 238 244	488080378382
STPT(10)	2377679758983974969	0 2 18 20 30 32 42 44 60 62	515239871898