Prime p₀= 2081941625439203651 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 10 2 106 2 40 2 58 2 (?)
a_n: 0 2 30 32 48 50 60 62 168 170 210 212 270 272
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: 272
Found by: Landjunge
db: batch=80, k=14, 28 16 10 106 40 58

SPT(16)	2081940192359453623	0 46 60 66 96 120 148 156 178 186 214 238 268 274 288 334	-1433079750028
SPT(16)	2081940459251873723	0 24 26 48 84 90 96 116 138 158 164 170 206 228 230 254	-1166187329928
SPT(16)	2081940601416753809	0 30 42 44 54 120 132 138 254 260 272 338 348 350 362 392	-1024022449842
SPT(16)	2081940707234168047	0 40 82 100 112 124 142 150 196 204 222 234 246 264 306 346	-918205035604
STPT(10)	2081941006536356489	0 2 18 20 30 32 42 44 60 62	-618902847162
TPT(14)	2081941168394758469	0 2 12 14 42 44 192 194 600 602 630 632 660 662	-457044445182
SPT(16)	2081941718476280887	0 4 10 22 64 94 162 172 234 244 312 342 384 396 402 406	93037077236
SPT(16)	2081941754966944193	0 56 108 138 140 156 180 206 240 266 290 306 308 338 390 446	129527740542
STPT(10)	2081941904589109601	0 2 96 98 108 110 120 122 216 218	279149905950
TPT(14)	2081942163984221309	0 2 78 80 138 140 168 170 180 182 192 194 240 242	538545017658
SPT(16)	2081942432834012233	0 16 18 24 58 70 78 106 108 136 144 156 190 196 198 214	807394808582