Prime p₀= 1288996244231877191 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 124 2 40 2 10 2 124 2 22 2 16 2 (?)
a_n: 0 2 126 128 168 170 180 182 306 308 330 332 348 350
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: 350
Found by: Cruncher Pete
db: batch=77, k=14, 124 40 10 124 22 16

SPT(16)	1288994997473921053	0 60 114 196 198 238 250 264 310 324 336 376 378 460 514 574	-1246757956138
SPT(16)	1288995026242587887	0 14 20 62 72 80 104 110 186 192 216 224 234 276 282 296	-1217989289304
SPT(13)	1288995254203467781	0 12 42 48 60 78 90 102 120 132 138 168 180	-990028409410
SPT(16)	1288995801972151873	0 36 46 78 120 166 168 220 264 316 318 364 406 438 448 484	-442259725318
STPT(10)	1288995864195541919	0 2 18 20 30 32 42 44 60 62	-380036335272
STPT(10)	1288996142239409699	0 2 18 20 30 32 42 44 60 62	-101992467492
STPT(10)	1288996274433298967	0 2 30 32 42 44 54 56 84 86	30201421776
SPT(16)	1288996666497267001	0 10 18 28 36 52 70 88 120 138 156 172 180 190 198 208	422265389810
SPT(16)	1288997293507419521	0 6 18 36 48 56 68 110 288 330 342 350 362 380 392 398	1049275542330
SPT(16)	1288997422126585993	0 24 48 54 78 100 118 178 180 240 258 280 304 310 334 358	1177894708802
STPT(10)	1288997824207823069	0 2 18 20 30 32 42 44 60 62	1579975945878