Prime p₀= 728706857853235169 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 40 2 46 2 130 2 76 2 70 2 (?)
a_n: 0 2 18 20 60 62 108 110 240 242 318 320 390 392
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: 392
Found by: MarkRBright
db: batch=73, k=14, 16 40 46 130 76 70

SPT(16)	728705443924208339	0 2 50 92 102 108 120 158 162 200 212 218 228 270 318 320	-1413929026830
STPT(12)	728705591143647209	0 2 42 44 72 74 108 110 138 140 180 182	-1266709587960
STPT(10)	728705897643855947	0 2 12 14 132 134 252 254 264 266	-960209379222
SPT(16)	728706251484870233	0 44 56 98 128 138 198 210 254 266 326 336 366 408 420 464	-606368364936
STPT(10)	728706490735322129	0 2 30 32 60 62 90 92 120 122	-367117913040
SPT(16)	728706662966929733	0 14 74 80 98 104 114 146 228 260 270 276 294 300 360 374	-194886305436
SPT(16)	728707291219693273	0 54 88 120 148 154 190 208 210 228 264 270 298 330 364 418	433366458104
SPT(16)	728707657006963903	0 16 96 114 154 156 210 250 294 334 388 390 430 448 528 544	799153728734
SPT(16)	728708622486757361	0 8 56 60 66 78 98 116 120 138 158 170 176 180 228 236	1764633522192
SPT(18)	728708641653315269	0 20 44 62 122 144 200 234 240 242 248 282 338 360 420 438 462 482	1783800080100
SPT(16)	728709196926635539	0 30 42 88 90 102 118 150 160 192 208 220 222 268 280 310	2339073400370