Prime p₀= 1365005120501883569 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 16 2 40 2 16 2 76 2 52 2 (?)
a_n: 0 2 42 44 60 62 102 104 120 122 198 200 252 254
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: 254
Found by: stoneageman
db: batch=77, k=14, 40 16 40 16 76 52

SPT(16)	1365003081992379211	0 42 48 82 120 130 142 148 180 186 198 208 246 280 286 328	-2038509504358
STPT(10)	1365003796704921557	0 2 30 32 60 62 90 92 120 122	-1323796962012
STPT(10)	1365003840899236607	0 2 24 26 42 44 60 62 84 86	-1279602646962
SPT(16)	1365003856589258929	0 42 72 108 124 130 150 154 168 172 192 198 214 250 280 322	-1263912624640
SPT(16)	1365004314625812097	0 40 96 102 142 186 196 216 220 240 250 294 334 340 396 436	-805876071472
SPT(16)	1365004767418468643	0 20 24 56 60 98 104 108 176 180 186 224 228 260 264 284	-353083414926
STPT(10)	1365005146234161317	0 2 12 14 72 74 132 134 144 146	25732277748
SPT(16)	1365005308063203473	0 38 78 80 120 140 146 174 200 228 234 254 294 296 336 374	187561319904
STPT(10)	1365005503329065597	0 2 24 26 42 44 60 62 84 86	382827182028
SPT(16)	1365005725245438901	0 16 28 52 66 76 118 126 202 210 252 262 276 300 312 328	604743555332
SPT(16)	1365005955748945171	0 16 30 60 78 88 102 112 156 166 180 190 208 238 252 268	835247061602