Prime p₀= 2720803250279757437 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 40 2 40 2 34 2 28 2 22 2 (?)
a_n: 0 2 90 92 132 134 174 176 210 212 240 242 264 266
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: 266
Found by: JayPi
db: batch=82, k=14, 88 40 40 34 28 22

SPT(16)	2720802015692617943	0 8 50 56 98 114 126 140 144 158 170 186 228 234 276 284	-1234587139494
SPT(16)	2720802030601268179	0 24 34 60 70 102 144 154 258 268 310 342 352 378 388 412	-1219678489258
STPT(10)	2720802047182114967	0 2 30 32 42 44 54 56 84 86	-1203097642470
STPT(10)	2720802418076811527	0 2 84 86 132 134 180 182 264 266	-832202945910
STPT(10)	2720802853735397537	0 2 30 32 42 44 54 56 84 86	-396544359900
STPT(10)	2720803191985206827	0 2 42 44 72 74 102 104 144 146	-58294550610
STPT(10)	2720803286496945017	0 2 30 32 42 44 54 56 84 86	36217187580
SPT(16)	2720803381409653609	0 10 18 28 54 88 168 180 292 304 384 418 444 454 462 472	131129896172
SPT(16)	2720803566417465259	0 34 42 48 64 78 82 90 142 150 154 168 184 190 198 232	316137707822
STPT(10)	2720803572664949711	0 2 36 38 78 80 120 122 156 158	322385192274
STPT(10)	2720803866397811609	0 2 48 50 60 62 72 74 120 122	616118054172