Prime p₀= 2123353259945899739 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 16 2 28 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 60 62 90 92 102 104 132 134
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: 134
Found by: [SG-2W]Kurzer
db: batch=80, k=14, 28 10 16 28 10 28

SPT(16)	2123351489355452771	0 8 42 78 140 182 260 282 296 318 396 438 500 536 570 578	-1770590446968
TPT(14)	2123351656820650829	0 2 18 20 102 104 108 110 138 140 210 212 240 242	-1603125248910
TPT(14)	2123351659833264167	0 2 114 116 234 236 264 266 390 392 420 422 444 446	-1600112635572
SPT(18)	2123352216757076303	0 8 14 26 48 56 60 176 188 216 228 344 348 356 378 390 396 404	-1043188823436
SPT(16)	2123352769408116461	0 8 36 42 68 96 168 210 218 260 332 360 386 392 420 428	-490537783278
SPT(16)	2123352879172681661	0 18 32 36 72 96 126 138 140 152 182 206 242 246 260 278	-380773218078
SPT(16)	2123353315306843421	0 2 8 90 110 126 138 146 162 170 182 198 218 300 306 308	55360943682
STPT(12)	2123353477850420741	0 2 48 50 90 92 168 170 210 212 258 260	217904521002
STPT(10)	2123353555646125469	0 2 42 44 60 62 78 80 120 122	295700225730
STPT(10)	2123353960866729947	0 2 30 32 72 74 114 116 144 146	700920830208
SPT(16)	2123354118094855369	0 28 34 48 52 78 100 114 118 132 154 180 184 198 204 232	858148955630