Prime p₀= 2396682843405185939 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 136 2 40 2 16 2 70 2 (?)
a_n: 0 2 42 44 102 104 240 242 282 284 300 302 372 374
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: 374
Found by: JohnMD
db: batch=81, k=14, 40 58 136 40 16 70

SPT(16)	2396681197567164407	0 12 30 54 92 110 162 170 186 194 246 264 302 326 344 356	-1645838021532
SPT(16)	2396681226070819291	0 16 30 42 70 108 112 120 148 156 160 198 226 238 252 268	-1617334366648
STPT(10)	2396681487255527081	0 2 30 32 78 80 126 128 156 158	-1356149658858
SPT(16)	2396681561476689169	0 48 88 102 172 198 298 300 310 312 412 438 508 522 562 610	-1281928496770
SPT(16)	2396682573103371977	0 36 42 62 72 86 110 132 134 156 180 194 204 224 230 266	-270301813962
SPT(16)	2396682618792395789	0 32 38 60 62 72 122 128 162 168 218 228 230 252 258 290	-224612790150
SPT(16)	2396683408309846009	0 4 12 40 54 58 60 70 132 142 144 148 162 190 198 202	564904660070
SPT(16)	2396683740946047127	0 22 40 54 66 94 106 126 220 240 252 280 292 306 324 346	897540861188
SPT(16)	2396684080671462467	0 14 20 36 74 96 116 186 260 330 350 372 410 426 432 446	1237266276528
STPT(10)	2396684141569026497	0 2 24 26 42 44 60 62 84 86	1298163840558
STPT(10)	2396684156528456747	0 2 30 32 42 44 54 56 84 86	1313123270808