Prime p₀= 4305558438098980091 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 34 2 28 2 10 2 16 2 40 2 (?)
a_n: 0 2 30 32 66 68 96 98 108 110 126 128 168 170
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: 170
Found by: Chooka
db: batch=85, k=14, 28 34 28 10 16 40

SPT(16)	4305557541450969227	0 2 20 86 110 182 344 366 410 432 594 666 690 756 774 776	-896648010864
SPT(16)	4305557551379372117	0 44 74 84 90 92 104 156 200 252 264 266 272 282 312 356	-886719607974
SPT(16)	4305557704756104523	0 24 34 48 60 130 156 184 210 238 264 334 346 360 370 394	-733342875568
STPT(10)	4305558233668813151	0 2 30 32 60 62 90 92 120 122	-204430166940
SPT(16)	4305558299978973451	0 12 16 52 60 66 88 100 108 120 142 148 156 192 196 208	-138120006640
STPT(10)	4305558330781613027	0 2 90 92 132 134 174 176 264 266	-107317367064
STPT(10)	4305558633347305091	0 2 6 8 18 20 30 32 36 38	195248325000
SPT(16)	4305559303260319801	0 22 78 82 120 138 190 222 256 288 340 358 396 400 456 478	865161339710
TPT(14)	4305559340065746197	0 2 54 56 84 86 180 182 264 266 282 284 360 362	901966766106
SPT(16)	4305559453006186489	0 10 24 112 160 178 184 318 364 498 504 522 570 658 672 682	1014907206398
STPT(10)	4305559976365383599	0 2 42 44 90 92 138 140 180 182	1538266403508