Prime p₀= 2486780217595212107 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 112 2 34 2 88 2 40 2 (?)
a_n: 0 2 60 62 90 92 204 206 240 242 330 332 372 374
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: SEARCHER
db: batch=82, k=14, 58 28 112 34 88 40

SPT(16)	2486778660027346739	0 20 38 42 54 110 138 164 168 194 222 278 290 294 312 332	-1557567865368
STPT(10)	2486778664997973551	0 2 6 8 18 20 30 32 36 38	-1552597238556
SPT(16)	2486779078079546447	0 2 26 42 66 80 84 126 140 182 186 200 224 240 264 266	-1139515665660
STPT(10)	2486779262689296227	0 2 72 74 102 104 132 134 204 206	-954905915880
SPT(16)	2486779687072205069	0 2 20 48 62 80 90 188 234 332 342 360 374 402 420 422	-530523007038
SPT(16)	2486779828527112841	0 2 32 50 60 66 92 108 140 156 182 188 198 216 246 248	-389068099266
STPT(10)	2486780292035722349	0 2 18 20 30 32 42 44 60 62	74440510242
STPT(10)	2486780665544592689	0 2 18 20 30 32 42 44 60 62	447949380582
SPT(16)	2486780685075856909	0 42 102 190 208 238 258 262 330 334 354 384 402 490 550 592	467480644802
SPT(16)	2486781260365637509	0 10 82 94 130 154 190 204 238 252 288 312 348 360 432 442	1042770425402
SPT(16)	2486781425988560153	0 26 38 66 74 96 104 116 258 270 278 300 308 336 348 374	1208393348046