Prime p₀= 797135026564707107 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 112 2 28 2 118 2 154 2 28 2 40 2 (?)
a_n: 0 2 114 116 144 146 264 266 420 422 450 452 492 494
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: 494
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 112 28 118 154 28 40

STPT(10)	797133056022758027	0 2 24 26 42 44 60 62 84 86	-1970541949080
STPT(10)	797133943954214897	0 2 30 32 60 62 90 92 120 122	-1082610492210
SPT(16)	797133982299207737	0 20 44 84 134 192 204 224 240 260 272 330 380 420 444 464	-1044265499370
SPT(16)	797134292033997859	0 12 42 60 100 118 142 172 210 240 264 282 322 340 370 382	-734530709248
SPT(16)	797134658463884093	0 36 38 44 66 78 108 114 140 146 176 188 210 216 218 254	-368100823014
TPT(14)	797134793095882229	0 2 48 50 72 74 132 134 162 164 228 230 240 242	-233468824878
SPT(16)	797135158740661843	0 4 34 46 64 78 168 186 268 286 376 390 408 420 450 454	132175954736
SPT(16)	797135181039025781	0 2 18 30 56 60 78 96 182 200 218 222 248 260 276 278	154474318674
SPT(16)	797135297504236283	0 38 110 158 180 194 206 236 318 348 360 374 396 444 516 554	270939529176
STPT(10)	797136024096109667	0 2 54 56 72 74 90 92 144 146	997531402560
SPT(16)	797136128052193879	0 28 70 108 112 132 154 190 192 228 250 270 274 312 354 382	1101487486772