Prime p₀= 2396215702558199657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 112 2 16 2 40 2 124 2 10 2 16 2 (?)
a_n: 0 2 114 116 132 134 174 176 300 302 312 314 330 332
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: 332
Found by: Boliver
db: batch=81, k=14, 112 16 40 124 10 16

SPT(16)	2396214246735647999	0 8 24 44 104 108 110 122 180 192 194 198 258 278 294 302	-1455822551658
STPT(10)	2396214486773146181	0 2 6 8 18 20 30 32 36 38	-1215785053476
SPT(16)	2396214525596581357	0 6 40 52 72 84 94 132 184 222 232 244 264 276 310 316	-1176961618300
SPT(13)	2396214761103101377	0 24 60 90 96 126 180 234 264 270 300 336 360	-941455098280
SPT(16)	2396214813227836033	0 6 24 54 66 124 136 166 264 294 306 364 376 406 424 430	-889330363624
SPT(16)	2396215363384693423	0 30 66 94 226 238 256 286 378 408 426 438 570 598 634 664	-339173506234
STPT(10)	2396216450631603371	0 2 36 38 78 80 120 122 156 158	748073403714
TPT(14)	2396217190263844877	0 2 24 26 42 44 72 74 114 116 150 152 210 212	1487705645220
SPT(16)	2396217232682785651	0 16 42 46 88 130 132 142 156 166 168 210 252 256 282 298	1530124585994
SPT(16)	2396217937273152221	0 6 8 20 26 42 60 78 80 98 116 132 138 150 152 158	2234714952564
STPT(10)	2396218053502730057	0 2 12 14 42 44 72 74 84 86	2350944530400