Prime p₀= 729068044415797517 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 160 2 40 2 118 2 88 2 (?)
a_n: 0 2 30 32 60 62 222 224 264 266 384 386 474 476
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: 476
Found by: MarkRBright
db: batch=73, k=14, 28 28 160 40 118 88

STPT(10)	729067032114509651	0 2 96 98 138 140 180 182 276 278	-1012301287866
STPT(10)	729067118340924029	0 2 18 20 30 32 42 44 60 62	-926074873488
STPT(10)	729067197175993139	0 2 48 50 60 62 72 74 120 122	-847239804378
SPT(16)	729067257529453669	0 24 40 58 112 114 144 150 172 178 208 210 264 282 298 322	-786886343848
STPT(10)	729067618349693219	0 2 42 44 60 62 78 80 120 122	-426066104298
STPT(12)	729067952493951197	0 2 12 14 30 32 54 56 72 74 84 86	-91921846320
SPT(16)	729068099656438063	0 18 40 54 78 114 156 184 210 238 280 316 340 354 376 394	55240640546
SPT(16)	729068644117066753	0 36 40 58 64 78 90 126 148 184 196 210 216 234 238 274	599701269236
STPT(10)	729068882282328491	0 2 36 38 78 80 120 122 156 158	837866530974
STPT(10)	729068970940483037	0 2 42 44 72 74 102 104 144 146	926524685520
SPT(16)	729069073085295473	0 18 24 128 164 194 216 264 410 458 480 510 546 650 656 674	1028669497956