Prime p₀= 4092710928978030167 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 28 2 10 2 4 2 40 2 (?)
a_n: 0 2 30 32 42 44 72 74 84 86 90 92 132 134
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: 134
Found by: Vitalii Koshura
db: batch=84, k=14, 28 10 28 10 4 40

SPT(16)	4092708968517044423	0 44 48 60 86 98 146 260 294 408 456 468 494 506 510 554	-1960460985744
TPT(14)	4092709950354166709	0 2 78 80 138 140 150 152 282 284 348 350 450 452	-978623863458
STPT(10)	4092710274442956497	0 2 90 92 102 104 114 116 204 206	-654535073670
SPT(16)	4092710756003853287	0 2 24 44 54 132 134 156 230 252 254 332 342 362 384 386	-172974176880
SPT(16)	4092710907652227661	0 6 72 108 120 142 166 168 190 192 216 238 250 286 352 358	-21325802506
STPT(10)	4092710917645042037	0 2 42 44 72 74 102 104 144 146	-11332988130
SPT(16)	4092710957225765701	0 52 66 168 186 192 210 220 288 298 316 322 340 442 456 508	28247735534
SPT(16)	4092711036019232119	0 30 34 48 58 64 78 114 124 160 174 180 190 204 208 238	107041201952
SPT(16)	4092711096794447887	0 12 22 34 64 84 90 126 250 286 292 312 342 354 364 376	167816417720
STPT(10)	4092711383122854389	0 2 18 20 30 32 42 44 60 62	454144824222
STPT(10)	4092711569885036237	0 2 12 14 42 44 72 74 84 86	640907006070