Prime p₀= 2120028789453117077 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 298 2 40 2 28 2 10 2 4 2 10 2 (?)
a_n: 0 2 300 302 342 344 372 374 384 386 390 392 402 404
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: 404
Found by: Ben
db: batch=80, k=14, 298 40 28 10 4 10

SPT(16)	2120028341588895631	0 6 10 102 108 112 130 132 166 168 186 190 196 288 292 298	-447864221446
SPT(16)	2120028384481496707	0 60 66 84 130 262 316 324 352 360 414 546 592 610 616 676	-404971620370
SPT(16)	2120028393763275169	0 12 54 58 124 150 208 252 280 324 382 408 474 478 520 532	-395689841908
STPT(10)	2120028395597394977	0 2 30 32 60 62 90 92 120 122	-393855722100
STPT(10)	2120028421441760309	0 2 18 20 30 32 42 44 60 62	-368011356768
STPT(10)	2120028504565115201	0 2 36 38 78 80 120 122 156 158	-284888001876
SPT(18)	2120028797738409157	0 4 52 90 112 120 150 160 204 220 264 274 304 312 334 372 420 424	8285292080
SPT(16)	2120028972997993357	0 24 66 72 84 114 132 180 256 304 322 352 364 370 412 436	183544876280
STPT(10)	2120029179617121887	0 2 90 92 102 104 114 116 204 206	390164004810
STPT(10)	2120029198255704191	0 2 30 32 78 80 126 128 156 158	408802587114
TPT(14)	2120029553774474261	0 2 6 8 36 38 78 80 138 140 150 152 216 218	764321357184