Prime p₀= 2786241971587400099 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 28 2 124 2 22 2 4 2 40 2 (?)
a_n: 0 2 42 44 72 74 198 200 222 224 228 230 270 272
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: 272
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 40 28 124 22 4 40

STPT(10)	2786239569539238089	0 2 12 14 90 92 168 170 180 182	-2402048162010
STPT(10)	2786239740467569577	0 2 42 44 72 74 102 104 144 146	-2231119830522
STPT(10)	2786241222279906371	0 2 78 80 138 140 198 200 276 278	-749307493728
SPT(16)	2786241469062572783	0 38 44 78 80 110 194 204 224 234 318 348 350 384 390 428	-502524827316
SPT(16)	2786241866855862973	0 28 108 130 174 180 186 244 270 328 334 340 384 406 486 514	-104731537126
SPT(16)	2786241889624259113	0 10 24 66 84 124 160 186 238 264 300 340 358 400 414 424	-81963140986
STPT(10)	2786242202059111889	0 2 30 32 60 62 90 92 120 122	230471711790
STPT(12)	2786242568361909269	0 2 18 20 30 32 60 62 72 74 90 92	596774509170
STPT(10)	2786242742127296069	0 2 48 50 60 62 72 74 120 122	770539895970
SPT(16)	2786242764590238169	0 52 60 88 102 112 150 168 244 262 300 310 324 352 360 412	793002838070
SPT(16)	2786243774734215403	0 24 48 54 90 108 114 154 180 220 226 244 280 286 310 334	1803146815304