Prime p₀= 1368372349190948867 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 40 2 64 2 10 2 88 2 10 2 (?)
a_n: 0 2 42 44 84 86 150 152 162 164 252 254 264 266
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, 40 40 64 10 88 10

SPT(16)	1368371915057660783	0 44 50 54 86 96 140 156 158 174 218 228 260 264 270 314	-434133288084
STPT(10)	1368371952057835997	0 2 24 26 42 44 60 62 84 86	-397133112870
STPT(10)	1368371998324045457	0 2 30 32 42 44 54 56 84 86	-350866903410
SPT(16)	1368372070171855831	0 40 66 76 78 106 118 120 208 210 222 250 252 262 288 328	-279019093036
SPT(16)	1368372143909245061	0 12 56 66 68 80 96 110 168 182 198 210 212 222 266 278	-205281703806
STPT(10)	1368372306004814807	0 2 54 56 72 74 90 92 144 146	-43186134060
STPT(10)	1368372374583627221	0 2 6 8 48 50 90 92 96 98	25392678354
STPT(10)	1368372644917088771	0 2 36 38 78 80 120 122 156 158	295726139904
SPT(16)	1368372695949213893	0 38 50 54 78 138 158 164 180 186 206 266 290 294 306 344	346758265026
STPT(10)	1368373097099225339	0 2 48 50 90 92 132 134 180 182	747908276472
SPT(16)	1368373106586756139	0 4 18 22 28 30 94 100 162 168 232 234 240 244 258 262	757395807272