Prime p₀= 726878680947649127 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 16 2 88 2 70 2 58 2 (?)
a_n: 0 2 42 44 102 104 120 122 210 212 282 284 342 344
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: crashtech
db: batch=73, k=14, 40 58 16 88 70 58

SPT(16)	726878267776615483	0 28 64 78 84 124 138 166 168 196 210 250 256 270 306 334	-413171033644
SPT(16)	726878289738098921	0 80 108 120 146 150 176 206 222 252 278 282 308 320 348 428	-391209550206
TPT(14)	726878370673360097	0 2 24 26 84 86 132 134 174 176 234 236 252 254	-310274289030
SPT(16)	726878532600955531	0 16 18 40 42 58 66 82 156 172 180 196 198 220 222 238	-148346693596
SPT(16)	726878602163342437	0 30 46 72 90 120 130 144 382 396 406 436 454 480 496 526	-78784306690
STPT(10)	726878677627232717	0 2 30 32 72 74 114 116 144 146	-3320416410
SPT(16)	726878809784199899	0 14 24 30 50 60 102 168 194 260 302 312 332 338 348 362	128836550772
STPT(10)	726878832265305701	0 2 36 38 78 80 120 122 156 158	151317656574
STPT(10)	726879025274623937	0 2 60 62 72 74 84 86 144 146	344326974810
SPT(16)	726879449887420279	0 30 64 84 90 120 154 160 198 204 238 268 274 294 328 358	768939771152
SPT(16)	726879651409484297	0 6 36 44 54 72 90 92 174 176 194 212 222 230 260 266	970461835170