Prime p₀= 1297254153951416231 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 16 2 10 2 64 2 10 2 76 2 (?)
a_n: 0 2 30 32 48 50 60 62 126 128 138 140 216 218
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: 218
Found by: Cruncher Pete
db: batch=77, k=14, 28 16 10 64 10 76

TPT(14)	1297253292040645271	0 2 36 38 48 50 78 80 96 98 168 170 180 182	-861910770960
STPT(10)	1297253323428495281	0 2 30 32 60 62 90 92 120 122	-830522920950
SPT(16)	1297253487606530539	0 24 30 40 54 70 112 114 148 150 192 208 222 232 238 262	-666344885692
SPT(16)	1297253815291459999	0 22 54 70 102 124 130 154 288 312 318 340 372 388 420 442	-338659956232
TPT(14)	1297253887711617917	0 2 42 44 144 146 180 182 210 212 252 254 264 266	-266239798314
SPT(16)	1297253929132362197	0 72 90 96 146 156 176 182 294 300 320 330 380 386 404 476	-224819054034
STPT(10)	1297254409640950991	0 2 66 68 168 170 270 272 336 338	255689534760
SPT(16)	1297254703809461297	0 20 24 26 32 36 50 54 62 66 80 84 90 92 96 116	549858045066
SPT(16)	1297255081668449669	0 20 50 72 110 120 128 140 162 174 182 192 230 252 282 302	927717033438
SPT(16)	1297255193437295461	0 6 28 40 66 88 118 168 220 270 300 322 348 360 382 388	1039485879230
STPT(10)	1297255651099854221	0 2 156 158 198 200 240 242 396 398	1497148437990