Prime p₀= 2300349628709297309 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 94 2 58 2 142 2 46 2 (?)
a_n: 0 2 18 20 42 44 138 140 198 200 342 344 390 392
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: 392
Found by: Landjunge
db: batch=81, k=14, 16 22 94 58 142 46

SPT(16)	2300348181172986023	0 18 30 56 74 114 144 146 198 200 230 270 288 314 326 344	-1447536311286
STPT(10)	2300348205941651681	0 2 6 8 48 50 90 92 96 98	-1422767645628
SPT(16)	2300348271938619349	0 10 58 90 130 150 172 184 228 240 262 282 322 354 402 412	-1356770677960
SPT(16)	2300348296416155341	0 46 70 82 88 118 130 166 222 258 270 300 306 318 342 388	-1332293141968
SPT(16)	2300348679379283207	0 56 72 86 132 174 204 240 266 302 332 374 420 434 450 506	-949330014102
SPT(16)	2300349624966617639	0 8 32 42 50 74 132 164 228 260 318 342 350 360 384 392	-3742679670
STPT(10)	2300349661185984407	0 2 24 26 42 44 60 62 84 86	32476687098
SPT(16)	2300350197712193453	0 30 38 66 80 84 168 170 204 206 290 294 308 336 344 374	569002896144
SPT(16)	2300350477995922553	0 6 26 38 68 80 84 146 168 230 234 246 276 288 308 314	849286625244
STPT(10)	2300350639609424627	0 2 30 32 42 44 54 56 84 86	1010900127318
STPT(10)	2300352202523447921	0 2 30 32 60 62 90 92 120 122	2573814150612