Prime p₀= 878726014629604409 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 40 2 28 2 64 2 10 2 (?)
a_n: 0 2 30 32 90 92 132 134 162 164 228 230 240 242
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: 242
Found by: GLeeM
db: batch=73, k=14, 28 58 40 28 64 10

SPT(16)	878725236991679137	0 42 46 82 180 190 196 232 264 300 306 316 414 450 454 496	-777637925272
SPT(16)	878725259456819963	0 68 80 84 86 114 194 200 234 240 320 348 350 354 366 434	-755172784446
STPT(10)	878725413699187697	0 2 30 32 42 44 54 56 84 86	-600930416712
SPT(16)	878725451858964769	0 22 24 82 90 108 198 220 222 244 334 352 360 418 420 442	-562770639640
SPT(16)	878725911407780453	0 30 56 80 90 108 128 146 150 168 188 206 216 240 266 296	-103221823956
STPT(10)	878725948803030191	0 2 6 8 108 110 210 212 216 218	-65826574218
SPT(16)	878726610147225877	0 36 70 90 94 100 102 114 232 244 246 252 256 276 310 346	595517621468
TPT(14)	878726713071109079	0 2 72 74 78 80 90 92 102 104 132 134 168 170	698441504670
SPT(16)	878726765773789349	0 18 50 68 110 138 152 158 222 228 242 270 312 330 362 380	751144184940
SPT(16)	878727264407284381	0 12 36 42 52 66 78 108 250 280 292 306 316 322 346 358	1249777679972
STPT(10)	878727478003437911	0 2 36 38 78 80 120 122 156 158	1463373833502