Prime p₀= 2079734300488159307 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 142 2 34 2 40 2 28 2 70 2 28 2 (?)
a_n: 0 2 144 146 180 182 222 224 252 254 324 326 354 356
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: 356
Found by: Landjunge
db: batch=80, k=14, 142 34 40 28 70 28

STPT(10)	2079733607968172867	0 2 60 62 72 74 84 86 144 146	-692519986440
SPT(16)	2079733611206924917	0 10 46 100 124 132 144 216 220 292 304 312 336 390 426 436	-689281234390
SPT(16)	2079733898795946763	0 24 34 144 154 160 184 216 238 270 294 300 310 420 430 454	-401692212544
SPT(16)	2079734062069067737	0 36 54 124 186 216 244 286 300 342 370 400 462 532 550 586	-238419091570
SPT(13)	2079734086915490749	0 24 42 72 120 150 162 174 204 252 282 300 324	-213572668558
TPT(14)	2079734286511674389	0 2 120 122 132 134 210 212 240 242 258 260 342 344	-13976484918
STPT(10)	2079734380075672259	0 2 18 20 30 32 42 44 60 62	79587512952
SPT(16)	2079734640301371577	0 6 10 16 30 54 72 102 124 154 172 196 210 216 220 226	339813212270
SPT(18)	2079734776493068757	0 20 72 84 86 96 140 150 194 252 296 306 350 360 362 374 426 446	476004909450
SPT(16)	2079734777612048311	0 42 60 88 108 150 186 222 256 292 328 370 390 418 436 478	477123889004
SPT(16)	2079735322681672517	0 30 56 72 86 114 156 210 266 320 362 390 404 420 446 476	1022193513210