Prime p₀= 2302034059557574499 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 70 2 76 2 70 2 130 2 46 2 (?)
a_n: 0 2 108 110 180 182 258 260 330 332 462 464 510 512
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: 512
Found by: FritzB
db: batch=81, k=14, 106 70 76 70 130 46

SPT(16)	2302032471574464799	0 4 18 22 52 70 78 114 148 184 192 210 240 244 258 262	-1587983109700
STPT(10)	2302032520977020471	0 2 6 8 48 50 90 92 96 98	-1538580554028
SPT(16)	2302032850909069549	0 10 34 82 90 102 138 162 220 244 280 292 300 348 372 382	-1208648504950
STPT(10)	2302033067674239899	0 2 18 20 30 32 42 44 60 62	-991883334600
SPT(16)	2302033104325401077	0 24 50 66 102 116 152 180 206 234 270 284 320 336 362 386	-955232173422
SPT(16)	2302033385277089911	0 42 46 52 72 118 150 160 168 178 210 256 276 282 286 328	-674280484588
TPT(14)	2302034074362065201	0 2 6 8 90 92 138 140 198 200 228 230 306 308	14804490702
SPT(16)	2302034118809986621	0 16 42 46 78 100 112 132 196 216 228 250 282 286 312 328	59252412122
SPT(16)	2302034180378049329	0 18 32 62 84 98 134 164 168 198 234 248 270 300 314 332	120820474830
STPT(10)	2302035135483392339	0 2 30 32 60 62 90 92 120 122	1075925817840
STPT(10)	2302035316293090347	0 2 30 32 72 74 114 116 144 146	1256735515848