Prime p₀= 2361624264128003339 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 244 2 28 2 58 2 22 2 124 2 (?)
a_n: 0 2 12 14 258 260 288 290 348 350 372 374 498 500
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: 500
Found by: Landjunge
db: batch=81, k=14, 10 244 28 58 22 124

STPT(10)	2361621915550573769	0 2 30 32 60 62 90 92 120 122	-2348577429570
STPT(10)	2361622719813942887	0 2 30 32 42 44 54 56 84 86	-1544314060452
SPT(13)	2361623068708676711	0 12 30 60 72 78 120 162 168 180 210 228 240	-1195419326628
SPT(16)	2361623165187258799	0 4 12 54 88 94 138 142 150 154 198 204 238 280 288 292	-1098940744540
SPT(16)	2361623544061960397	0 24 36 42 44 60 72 90 116 134 146 162 164 170 182 206	-720066042942
STPT(10)	2361624093163617257	0 2 84 86 132 134 180 182 264 266	-170964386082
STPT(10)	2361624278929344731	0 2 30 32 78 80 126 128 156 158	14801341392
STPT(10)	2361624494704802651	0 2 36 38 78 80 120 122 156 158	230576799312
SPT(16)	2361624651969015263	0 20 24 80 98 146 150 158 216 224 228 276 294 350 354 374	387841011924
SPT(16)	2361624782513791027	0 6 46 72 90 126 150 226 246 322 346 382 400 426 466 472	518385787688
STPT(10)	2361625017652380119	0 2 48 50 90 92 132 134 180 182	753524376780