Prime p₀= 2441409820799813597 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 22 2 136 2 40 2 28 2 58 2 (?)
a_n: 0 2 60 62 84 86 222 224 264 266 294 296 354 356
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: 356
Found by: JayPi
db: batch=82, k=14, 58 22 136 40 28 58

SPT(16)	2441408982907266167	0 42 50 54 66 80 90 176 180 266 276 290 302 306 314 356	-837892547430
STPT(10)	2441409033086737499	0 2 42 44 60 62 78 80 120 122	-787713076098
STPT(10)	2441409420843193637	0 2 12 14 72 74 132 134 144 146	-399956619960
SPT(16)	2441409555461357183	0 20 30 54 84 86 96 126 134 164 174 176 206 230 240 260	-265338456414
STPT(10)	2441409617879495687	0 2 54 56 72 74 90 92 144 146	-202920317910
SPT(16)	2441409774825117823	0 58 90 108 138 166 168 178 216 226 228 256 286 304 336 394	-45974695774
SPT(16)	2441409837332371307	0 26 42 84 140 146 152 174 182 204 210 216 272 314 330 356	16532557710
SPT(16)	2441410092238792421	0 32 36 66 80 90 140 146 246 252 302 312 326 356 360 392	271438978824
SPT(16)	2441410395041127547	0 36 52 126 196 234 280 286 330 336 382 420 490 564 580 616	574241313950
SPT(16)	2441410493381673487	0 22 24 72 76 114 120 142 204 226 232 270 274 322 324 346	672581859890
SPT(16)	2441410529206766167	0 4 24 36 42 46 64 72 94 102 120 124 130 142 162 166	708406952570