Prime p₀= 2079735350682772421 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 94 2 82 2 4 2 40 2 10 2 (?)
a_n: 0 2 60 62 156 158 240 242 246 248 288 290 300 302
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: 302
Found by: Landjunge
db: batch=80, k=14, 58 94 82 4 40 10

TPT(14)	2079734300488159307	0 2 144 146 180 182 222 224 252 254 324 326 354 356	-1050194613114
STPT(10)	2079734380075672259	0 2 18 20 30 32 42 44 60 62	-970607100162
SPT(16)	2079734640301371577	0 6 10 16 30 54 72 102 124 154 172 196 210 216 220 226	-710381400844
SPT(18)	2079734776493068757	0 20 72 84 86 96 140 150 194 252 296 306 350 360 362 374 426 446	-574189703664
SPT(16)	2079734777612048311	0 42 60 88 108 150 186 222 256 292 328 370 390 418 436 478	-573070724110
SPT(16)	2079735322681672517	0 30 56 72 86 114 156 210 266 320 362 390 404 420 446 476	-28001099904
SPT(16)	2079735537557270921	0 18 26 56 86 116 138 152 216 230 252 282 312 342 350 368	186874498500
SPT(16)	2079735567290231519	0 8 18 32 78 92 128 132 170 174 210 224 270 284 294 302	216607459098
SPT(16)	2079735685609308887	0 30 42 80 86 90 102 156 200 254 266 270 276 314 326 356	334926536466
SPT(16)	2079735972210050173	0 34 84 88 108 154 174 210 214 250 270 316 336 340 390 424	621527277752
STPT(10)	2079736012182283457	0 2 30 32 72 74 114 116 144 146	661499511036