Prime p₀= 726878370673360097 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 58 2 46 2 40 2 58 2 16 2 (?)
a_n: 0 2 24 26 84 86 132 134 174 176 234 236 252 254
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: 254
Found by: crashtech
db: batch=73, k=14, 22 58 46 40 58 16

SPT(16)	726877276936665521	0 6 42 66 78 80 86 102 146 162 168 170 182 206 242 248	-1093736694576
SPT(16)	726877398954170039	0 2 14 30 60 78 120 144 188 212 254 272 302 318 330 332	-971719190058
SPT(16)	726877844815322587	0 4 24 46 70 126 154 160 210 216 244 300 324 346 366 370	-525858037510
STPT(10)	726878016969052547	0 2 30 32 42 44 54 56 84 86	-353704307550
SPT(16)	726878267776615483	0 28 64 78 84 124 138 166 168 196 210 250 256 270 306 334	-102896744614
SPT(16)	726878289738098921	0 80 108 120 146 150 176 206 222 252 278 282 308 320 348 428	-80935261176
SPT(16)	726878532600955531	0 16 18 40 42 58 66 82 156 172 180 196 198 220 222 238	161927595434
SPT(16)	726878602163342437	0 30 46 72 90 120 130 144 382 396 406 436 454 480 496 526	231489982340
STPT(10)	726878677627232717	0 2 30 32 72 74 114 116 144 146	306953872620
TPT(14)	726878680947649127	0 2 42 44 102 104 120 122 210 212 282 284 342 344	310274289030
SPT(16)	726878809784199899	0 14 24 30 50 60 102 168 194 260 302 312 332 338 348 362	439110839802