Prime p₀= 3029386206656215331 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 40 2 106 2 58 2 70 2 4 2 (?)
a_n: 0 2 48 50 90 92 198 200 258 260 330 332 336 338
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: 338
Found by: Rantanplan
db: batch=82, k=14, 46 40 106 58 70 4

SPT(16)	3029385566220214763	0 6 8 30 56 78 84 108 146 170 176 198 224 246 248 254	-640436000568
SPT(20)	3029385622242609697	0 6 22 34 82 126 190 264 270 286 300 316 322 396 460 504 552 564 580 586	-584413605634
TPT(14)	3029385811739828339	0 2 12 14 78 80 138 140 162 164 192 194 402 404	-394916386992
SPT(16)	3029385941790641063	0 8 36 38 60 66 80 168 278 366 380 386 408 410 438 446	-264865574268
TPT(14)	3029386022948547257	0 2 30 32 84 86 114 116 282 284 414 416 480 482	-183707668074
SPT(16)	3029386110281475727	0 16 66 70 82 112 136 142 150 156 180 210 222 226 276 292	-96374739604
SPT(16)	3029386348525963831	0 6 18 28 40 66 108 132 136 160 202 228 240 250 262 268	141869748500
STPT(10)	3029386462693633841	0 2 108 110 138 140 168 170 276 278	256037418510
TPT(14)	3029386550790492419	0 2 72 74 90 92 198 200 300 302 330 332 378 380	344134277088
STPT(10)	3029386716786246449	0 2 42 44 90 92 138 140 180 182	510130031118
SPT(16)	3029387178409701259	0 22 40 42 124 132 204 208 534 538 610 618 700 702 720 742	971753485928