Prime p₀= 2306689497119390429 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 34 2 22 2 28 2 28 2 34 2 (?)
a_n: 0 2 12 14 48 50 72 74 102 104 132 134 168 170
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: Landjunge
db: batch=81, k=14, 10 34 22 28 28 34

TPT(14)	2306686123523090471	0 2 30 32 120 122 336 338 420 422 450 452 456 458	-3373596299958
STPT(10)	2306686143301387829	0 2 18 20 60 62 102 104 120 122	-3353818002600
SPT(16)	2306687691644086241	0 50 78 98 128 138 152 168 170 186 200 210 240 260 288 338	-1805475304188
SPT(16)	2306687722620623891	0 2 90 146 150 170 198 248 300 350 378 398 402 458 546 548	-1774498766538
STPT(10)	2306687745521879117	0 2 30 32 72 74 114 116 144 146	-1751597511312
TPT(16)	2306688664582424429	0 2 30 32 108 110 138 140 150 152 168 170 348 350 378 380	-832536966000
STPT(10)	2306689510821027557	0 2 30 32 42 44 54 56 84 86	13701637128
TPT(14)	2306690003701748657	0 2 54 56 114 116 150 152 192 194 222 224 312 314	506582358228
STPT(10)	2306690244443364419	0 2 12 14 90 92 168 170 180 182	747323973990
SPT(16)	2306690322519439903	0 16 18 28 60 76 88 100 144 156 168 184 216 226 228 244	825400049474
STPT(10)	2306690773607242571	0 2 6 8 48 50 90 92 96 98	1276487852142