Prime p₀= 1247268426918423737 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 118 2 178 2 28 2 118 2 28 2 22 2 (?)
a_n: 0 2 120 122 300 302 330 332 450 452 480 482 504 506
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: 506
Found by: Cruncher Pete
db: batch=77, k=14, 118 178 28 118 28 22

TPT(14)	1247267481283562927	0 2 24 26 60 62 84 86 102 104 114 116 144 146	-945634860810
SPT(16)	1247267540943225667	0 10 94 126 196 210 232 270 406 444 466 480 550 582 666 676	-885975198070
SPT(16)	1247267857950368203	0 10 24 60 66 78 88 136 138 186 196 208 214 250 264 274	-568968055534
STPT(10)	1247268109048167917	0 2 42 44 72 74 102 104 144 146	-317870255820
SPT(16)	1247268258784872293	0 60 68 78 84 116 120 144 170 194 198 230 236 246 254 314	-168133551444
TPT(14)	1247268411035910761	0 2 36 38 180 182 246 248 276 278 390 392 408 410	-15882512976
SPT(16)	1247268680228573153	0 6 30 50 60 78 86 90 224 228 236 254 264 284 308 314	253310149416
STPT(10)	1247268731341060397	0 2 12 14 72 74 132 134 144 146	304422636660
SPT(16)	1247268960902065219	0 24 48 60 70 84 88 154 174 240 244 258 268 280 304 328	533983641482
SPT(16)	1247268968561287613	0 18 50 74 134 156 186 198 266 278 308 330 390 414 446 464	541642863876
SPT(16)	1247269074015458723	0 8 54 78 138 144 150 180 188 218 224 230 290 314 360 368	647097034986