Prime p₀= 726775891358015747 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 130 2 40 2 76 2 10 2 28 2 46 2 (?)
a_n: 0 2 132 134 174 176 252 254 264 266 294 296 342 344
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: 344
Found by: schoussi
db: batch=73, k=14, 130 40 76 10 28 46

SPT(16)	726775446791485411	0 6 12 22 36 40 42 46 126 130 132 136 150 160 166 172	-444566530336
SPT(16)	726775799746162799	0 42 54 78 90 120 132 164 318 350 362 392 404 428 440 482	-91611852948
SPT(16)	726775830880584773	0 30 78 96 98 110 114 120 134 140 144 156 158 176 224 254	-60477430974
SPT(16)	726775844872371169	0 30 52 94 108 120 124 144 148 168 172 184 198 240 262 292	-46485644578
STPT(10)	726775879823361419	0 2 18 20 30 32 42 44 60 62	-11534654328
STPT(10)	726775888579987859	0 2 18 20 30 32 42 44 60 62	-2778027888
SPT(16)	726776248674554719	0 12 34 70 84 120 132 138 154 160 172 208 222 258 280 292	357316538972
SPT(16)	726776360832698269	0 42 48 60 84 88 100 120 142 162 174 178 202 214 220 262	469474682522
SPT(16)	726776475972702989	0 30 44 72 92 108 150 204 248 302 344 360 380 408 422 452	584614687242
SPT(16)	726776480328133343	0 20 66 146 150 168 170 180 224 234 236 254 258 338 384 404	588970117596
SPT(16)	726776782463835863	0 6 8 36 68 84 86 110 114 138 140 156 188 216 218 224	891105820116