Prime p₀= 2796244728485813021 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 196 2 16 2 40 2 46 2 70 2 16 2 (?)
a_n: 0 2 198 200 216 218 258 260 306 308 378 380 396 398
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: 398
Found by: JayPi
db: batch=82, k=14, 196 16 40 46 70 16

SPT(18)	2796243050755491223	0 28 40 90 96 118 130 258 288 298 328 456 468 490 496 546 558 586	-1677730321798
SPT(16)	2796243336007326923	0 6 50 56 78 116 120 146 168 194 198 236 258 264 308 314	-1392478486098
SPT(16)	2796243844715875867	0 36 112 132 136 162 174 234 262 322 334 360 364 384 460 496	-883769937154
STPT(10)	2796244219698537071	0 2 36 38 78 80 120 122 156 158	-508787275950
SPT(16)	2796244324199511733	0 10 88 94 108 214 228 298 300 370 384 490 504 510 588 598	-404286301288
STPT(10)	2796244587339364331	0 2 30 32 78 80 126 128 156 158	-141146448690
SPT(16)	2796244771736264983	0 28 36 40 94 96 114 120 184 190 208 210 264 268 276 304	43250451962
SPT(16)	2796245682794603047	0 22 40 84 130 172 180 184 210 214 222 264 310 354 372 394	954308790026
STPT(10)	2796246078751855757	0 2 24 26 42 44 60 62 84 86	1350266042736
SPT(16)	2796246098293447013	0 14 44 48 60 114 146 156 188 198 230 284 296 300 330 344	1369807633992
SPT(16)	2796246246666750887	0 20 42 44 62 86 122 146 150 174 210 234 252 254 276 296	1518180937866