Prime p₀= 728701704414968489 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 52 2 124 2 22 2 58 2 28 2 (?)
a_n: 0 2 78 80 132 134 258 260 282 284 342 344 372 374
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: 374
Found by: Theadalus
db: batch=73, k=14, 76 52 124 22 58 28

SPT(16)	728700389615936611	0 16 76 102 150 156 228 252 286 310 382 388 436 462 522 538	-1314799031878
SPT(16)	728700473885049929	0 8 54 90 110 132 168 180 212 224 260 282 302 338 384 392	-1230529918560
SPT(16)	728700618597901021	0 10 22 28 36 46 48 66 112 130 132 142 150 156 168 178	-1085817067468
STPT(10)	728701110566732657	0 2 54 56 72 74 90 92 144 146	-593848235832
STPT(10)	728701649250256439	0 2 18 20 30 32 42 44 60 62	-55164712050
STPT(10)	728701690211684009	0 2 18 20 30 32 42 44 60 62	-14203284480
SPT(18)	728701921820576807	0 24 26 54 56 90 126 164 204 206 246 284 320 354 356 384 386 410	217405608318
STPT(10)	728702317444659671	0 2 36 38 78 80 120 122 156 158	613029691182
SPT(16)	728702518963509703	0 34 48 64 70 100 114 126 148 160 174 204 210 226 240 274	814548541214
STPT(10)	728702603715576167	0 2 12 14 42 44 72 74 84 86	899300607678
SPT(16)	728703012002344861	0 28 82 108 118 132 136 138 250 252 256 270 280 306 360 388	1307587376372