Prime p₀= 1540014024435674111 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 16 2 106 2 28 2 10 2 28 2 (?)
a_n: 0 2 60 62 78 80 186 188 216 218 228 230 258 260
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: 260
Found by: crashtech
db: batch=78, k=14, 58 16 106 28 10 28

STPT(10)	1540012791712354649	0 2 18 20 30 32 42 44 60 62	-1232723319462
SPT(16)	1540012857422555953	0 48 78 90 118 120 150 154 204 208 238 240 268 280 310 358	-1167013118158
SPT(16)	1540012887285700327	0 42 120 132 142 174 184 196 210 222 232 264 274 286 364 406	-1137149973784
STPT(10)	1540013343219846797	0 2 30 32 42 44 54 56 84 86	-681215827314
TPT(14)	1540013764242779867	0 2 42 44 114 116 192 194 222 224 312 314 354 356	-260192894244
SPT(16)	1540013886334993679	0 8 24 68 74 78 102 150 152 200 224 228 234 278 294 302	-138100680432
SPT(16)	1540014189582558181	0 6 60 72 76 88 90 120 238 268 270 282 286 298 352 358	165146884070
SPT(16)	1540014255983466979	0 58 70 94 100 114 118 130 198 210 214 228 234 258 270 328	231547792868
SPT(16)	1540014599156626699	0 18 30 52 84 94 100 138 184 222 228 238 270 292 304 322	574720952588
STPT(10)	1540014843652879199	0 2 12 14 90 92 168 170 180 182	819217205088
SPT(16)	1540015013143082537	0 12 20 24 32 42 54 80 84 110 122 132 140 144 152 164	988707408426