Prime p₀= 2117777654723094107 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 46 2 22 2 28 2 34 2 (?)
a_n: 0 2 30 32 72 74 120 122 144 146 174 176 210 212
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: 212
Found by: gemini8
db: batch=80, k=14, 28 40 46 22 28 34

SPT(18)	2117776016572038751	0 10 42 48 52 60 78 82 102 196 216 220 238 246 250 256 288 298	-1638151055356
STPT(10)	2117776132003207757	0 2 12 14 72 74 132 134 144 146	-1522719886350
SPT(16)	2117776829900968751	0 56 110 116 140 146 152 186 302 336 342 348 372 378 432 488	-824822125356
SPT(18)	2117777060787317899	0 12 40 58 72 84 100 142 160 162 180 222 238 250 264 282 310 322	-593935776208
STPT(10)	2117777144114101409	0 2 30 32 60 62 90 92 120 122	-510608992698
SPT(16)	2117777410750360963	0 24 58 60 90 114 130 160 168 198 214 238 268 270 304 328	-243972733144
SPT(16)	2117777690492834057	0 20 36 42 84 122 156 174 242 260 294 332 374 380 396 416	35769739950
STPT(10)	2117777912259388409	0 2 18 20 30 32 42 44 60 62	257536294302
STPT(10)	2117778421403774159	0 2 18 20 30 32 42 44 60 62	766680680052
SPT(16)	2117778639987628309	0 4 42 48 54 58 70 102 280 312 324 328 334 340 378 382	985264534202
STPT(10)	2117778742045726337	0 2 30 32 42 44 54 56 84 86	1087322632230