Prime p₀= 3715509999663956969 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 28 2 34 2 40 2 28 2 16 2 (?)
a_n: 0 2 72 74 102 104 138 140 180 182 210 212 228 230
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: 230
Found by: [AF] Kalianthys
db: batch=84, k=14, 70 28 34 40 28 16

SPT(16)	3715508550064119899	0 48 62 68 114 132 150 188 234 272 290 308 354 360 374 422	-1449599837070
STPT(10)	3715508716741384007	0 2 12 14 132 134 252 254 264 266	-1282922572962
STPT(10)	3715509034843197419	0 2 42 44 60 62 78 80 120 122	-964820759550
SPT(16)	3715509573581772451	0 6 18 36 58 102 168 190 198 220 286 330 352 370 382 388	-426082184518
STPT(10)	3715509676679961701	0 2 30 32 78 80 126 128 156 158	-322983995268
SPT(16)	3715509794737735861	0 18 28 42 48 96 102 118 180 196 202 250 256 270 280 298	-204926221108
SPT(16)	3715510067042870029	0 70 114 124 150 160 168 208 234 274 282 292 318 328 372 442	67378913060
STPT(10)	3715510076313142181	0 2 6 8 48 50 90 92 96 98	76649185212
SPT(16)	3715510219076953471	0 10 48 72 82 130 150 220 258 328 348 396 406 430 468 478	219412996502
TPT(14)	3715510509247513517	0 2 30 32 60 62 72 74 114 116 132 134 162 164	509583556548
SPT(16)	3715511827036336637	0 14 30 50 92 126 134 162 164 192 200 234 276 296 312 326	1827372379668