Prime p₀= 1296953316021257579 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 40 2 76 2 10 2 4 2 22 2 (?)
a_n: 0 2 60 62 102 104 180 182 192 194 198 200 222 224
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: 224
Found by: Cruncher Pete
db: batch=77, k=14, 58 40 76 10 4 22

STPT(10)	1296952295931380981	0 2 6 8 48 50 90 92 96 98	-1020089876598
STPT(10)	1296952328591879987	0 2 24 26 42 44 60 62 84 86	-987429377592
SPT(16)	1296952382339079769	0 24 42 72 78 114 120 150 232 262 268 304 310 340 358 382	-933682177810
STPT(10)	1296952427366823551	0 2 36 38 78 80 120 122 156 158	-888654434028
STPT(10)	1296952826349671987	0 2 12 14 42 44 72 74 84 86	-489671585592
SPT(16)	1296952945998603581	0 42 62 98 108 140 146 150 158 162 168 200 210 246 266 308	-370022653998
STPT(10)	1296954022425553109	0 2 48 50 60 62 72 74 120 122	706404295530
STPT(10)	1296954152343429401	0 2 6 8 48 50 90 92 96 98	836322171822
SPT(16)	1296954273390980257	0 6 34 76 84 100 114 130 210 226 240 256 264 306 334 340	957369722678
SPT(16)	1296954453422639119	0 28 70 84 94 108 114 120 148 154 160 174 184 198 240 268	1137401381540
STPT(10)	1296954501066117041	0 2 36 38 78 80 120 122 156 158	1185044859462