Prime p₀= 2356544263061777519 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 34 2 88 2 130 2 16 2 22 2 (?)
a_n: 0 2 42 44 78 80 168 170 300 302 318 320 342 344
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: 344
Found by: Landjunge
db: batch=81, k=14, 40 34 88 130 16 22

SPT(16)	2356542428925400403	0 56 98 108 128 150 206 240 254 288 344 366 386 396 438 494	-1834136377116
STPT(10)	2356542681166353851	0 2 78 80 108 110 138 140 216 218	-1581895423668
SPT(16)	2356542960589258387	0 34 64 90 100 102 112 154 192 234 244 246 256 282 312 346	-1302472519132
TPT(14)	2356543115761208201	0 2 36 38 78 80 90 92 156 158 240 242 246 248	-1147300569318
STPT(12)	2356543151577970799	0 2 12 14 42 44 90 92 120 122 132 134	-1111483806720
SPT(16)	2356543774645628773	0 10 24 28 154 174 184 190 204 210 220 240 366 370 384 394	-488416148746
SPT(16)	2356544323655370217	0 54 64 66 70 76 96 130 210 244 264 270 274 276 286 340	60593592698
STPT(10)	2356544394943412489	0 2 12 14 30 32 48 50 60 62	131881634970
SPT(16)	2356544698319181563	0 36 48 116 128 140 156 168 188 200 216 228 240 308 320 356	435257404044
STPT(10)	2356544712314522591	0 2 36 38 78 80 120 122 156 158	449252745072
SPT(16)	2356544738830631353	0 96 118 130 156 180 184 196 228 240 244 268 294 306 328 424	475768853834