Prime p₀= 2327709563792061221 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 4 2 160 2 10 2 88 2 28 2 (?)
a_n: 0 2 120 122 126 128 288 290 300 302 390 392 420 422
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: 422
Found by: Landjunge
db: batch=81, k=14, 118 4 160 10 88 28

SPT(16)	2327708940624798439	0 52 88 90 102 132 154 168 244 258 280 310 322 324 360 412	-623167262782
STPT(10)	2327709257505311039	0 2 42 44 90 92 138 140 180 182	-306286750182
STPT(10)	2327709338758432127	0 2 30 32 72 74 114 116 144 146	-225033629094
STPT(10)	2327709348130890011	0 2 36 38 78 80 120 122 156 158	-215661171210
SPT(16)	2327709414459942911	0 2 30 56 62 72 116 140 198 222 266 276 282 308 336 338	-149332118310
SPT(16)	2327709418604161987	0 6 52 64 72 96 124 156 160 192 220 244 252 264 310 316	-145187899234
STPT(10)	2327709598512844751	0 2 6 8 18 20 30 32 36 38	34720783530
STPT(10)	2327709983056222859	0 2 48 50 90 92 132 134 180 182	419264161638
SPT(16)	2327710149588192781	0 10 52 58 90 118 156 202 216 262 300 328 360 366 408 418	585796131560
SPT(16)	2327710487489328751	0 40 90 112 150 160 168 208 222 262 270 280 318 340 390 430	923697267530
STPT(10)	2327711481614949629	0 2 42 44 90 92 138 140 180 182	1917822888408