Prime p₀= 1368373618710752867 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 64 2 130 2 10 2 28 2 (?)
a_n: 0 2 12 14 24 26 90 92 222 224 234 236 264 266
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: 266
Found by: emoga
db: batch=77, k=14, 10 10 64 130 10 28

SPT(16)	1368372695949213893	0 38 50 54 78 138 158 164 180 186 206 266 290 294 306 344	-922761538974
STPT(10)	1368373097099225339	0 2 48 50 90 92 132 134 180 182	-521611527528
SPT(16)	1368373106586756139	0 4 18 22 28 30 94 100 162 168 232 234 240 244 258 262	-512123996728
SPT(16)	1368373189046172733	0 40 46 64 78 106 118 138 196 216 228 256 270 288 294 334	-429664580134
SPT(16)	1368373387344316081	0 22 60 78 106 108 138 180 238 280 310 312 340 358 396 418	-231366436786
SPT(16)	1368373491580639513	0 4 28 54 90 124 154 168 256 270 300 334 370 396 420 424	-127130113354
STPT(10)	1368374134195331687	0 2 12 14 72 74 132 134 144 146	515484578820
STPT(10)	1368374134524842111	0 2 6 8 18 20 30 32 36 38	515814089244
SPT(16)	1368374366037672743	0 24 110 114 116 126 144 150 170 176 194 204 206 210 296 320	747326919876
SPT(16)	1368375152337325537	0 12 60 72 100 132 160 184 240 264 292 324 352 364 412 424	1533626572670
SPT(16)	1368375256151288291	0 8 12 20 30 62 78 92 96 110 126 158 168 176 180 188	1637440535424