Prime p₀= 2066746126839692867 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 46 2 70 2 76 2 28 2 10 2 (?)
a_n: 0 2 84 86 132 134 204 206 282 284 312 314 324 326
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: 326
Found by: Cruncher Pete
db: batch=80, k=14, 82 46 70 76 28 10

SPT(16)	2066745213788106737	0 20 26 56 96 116 120 132 140 152 156 176 216 246 252 272	-913051586130
SPT(16)	2066745247887424651	0 10 28 42 60 70 78 82 126 130 138 148 166 180 198 208	-878952268216
SPT(16)	2066745809261046101	0 2 30 66 86 96 122 138 140 156 182 192 212 248 276 278	-317578646766
STPT(10)	2066745841101765869	0 2 12 14 90 92 168 170 180 182	-285737926998
STPT(10)	2066746029773566577	0 2 42 44 72 74 102 104 144 146	-97066126290
SPT(16)	2066746075473773977	0 112 114 162 174 210 222 262 264 304 316 352 364 412 414 526	-51365918890
SPT(16)	2066746253465785937	0 36 56 96 110 114 134 206 264 336 356 360 374 414 434 470	126626093070
SPT(16)	2066746286200462429	0 28 34 58 72 118 154 162 190 198 234 280 294 318 324 352	159360769562
STPT(10)	2066746423404803051	0 2 6 8 18 20 30 32 36 38	296565110184
SPT(16)	2066746426461958567	0 60 82 96 130 250 256 310 366 420 426 546 580 594 616 676	299622265700
STPT(10)	2066746566910911239	0 2 48 50 90 92 132 134 180 182	440071218372