Prime p₀= 1025783527756580687 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 40 2 208 2 94 2 22 2 28 2 (?)
a_n: 0 2 12 14 54 56 264 266 360 362 384 386 414 416
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: 416
Found by: HenkM
db: batch=76, k=14, 10 40 208 94 22 28

SPT(16)	1025782414686796121	0 12 68 80 90 108 180 182 186 188 260 278 288 300 356 368	-1113069784566
SPT(16)	1025782548873532691	0 42 92 98 120 146 180 192 206 218 252 278 300 306 356 398	-978883047996
STPT(10)	1025782587904870931	0 2 36 38 78 80 120 122 156 158	-939851709756
SPT(16)	1025782695041122279	0 34 48 60 78 154 202 214 228 240 288 364 382 394 408 442	-832715458408
SPT(16)	1025782807738866637	0 64 76 106 124 154 174 196 270 292 312 342 360 390 402 466	-720017714050
SPT(16)	1025783234425980389	0 50 60 62 78 90 134 164 168 198 242 254 270 272 282 332	-293330600298
SPT(16)	1025783593425428269	0 24 70 138 168 180 190 204 238 252 262 274 304 372 418 442	65668847582
STPT(10)	1025783759081289797	0 2 30 32 120 122 210 212 240 242	231324709110
STPT(10)	1025783810751276287	0 2 60 62 72 74 84 86 144 146	282994695600
SPT(16)	1025784082894658089	0 4 28 60 70 100 112 142 270 300 312 342 352 384 408 412	555138077402
SPT(16)	1025784152770681417	0 42 54 70 84 136 150 156 220 226 240 292 306 322 334 376	625014100730