Prime p₀= 797158242229453217 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 16 2 40 2 28 2 64 2 (?)
a_n: 0 2 12 14 24 26 42 44 84 86 114 116 180 182
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: 182
Found by: [SG-2W]Kurzer
db: batch=73, k=14, 10 10 16 40 28 64

SPT(16)	797157736881723157	0 6 10 40 42 70 94 136 240 282 306 334 336 366 370 376	-505347730060
SPT(16)	797157741475858979	0 14 30 68 108 140 152 170 192 210 222 254 294 332 348 362	-500753594238
TPT(14)	797157932433779027	0 2 24 26 114 116 144 146 150 152 192 194 210 212	-309795674190
STPT(10)	797157990544372739	0 2 42 44 60 62 78 80 120 122	-251685080478
SPT(16)	797158034606831407	0 70 132 156 210 240 250 376 396 522 532 562 616 640 702 772	-207622621810
SPT(16)	797158239263002597	0 12 22 142 162 192 204 222 322 340 352 382 402 522 532 544	-2966450620
SPT(16)	797158394286781997	0 42 44 60 72 86 92 96 200 204 210 224 236 252 254 296	152057328780
SPT(16)	797158454751870349	0 22 48 84 90 102 118 132 190 204 220 232 238 274 300 322	212522417132
STPT(10)	797158519354287071	0 2 36 38 78 80 120 122 156 158	277124833854
SPT(16)	797158626860168273	0 24 30 44 54 60 84 126 194 236 260 266 276 290 296 320	384630715056
SPT(16)	797159049919961083	0 10 28 60 70 88 130 160 246 276 318 336 346 378 396 406	807690507866