Prime p₀= 1028040602816766191 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 22 2 46 2 76 2 130 2 10 2 (?)
a_n: 0 2 6 8 30 32 78 80 156 158 288 290 300 302
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: 302
Found by: Theadalus
db: batch=76, k=14, 4 22 46 76 130 10

SPT(16)	1028039499083337803	0 24 96 116 144 164 206 230 234 258 300 320 348 368 440 464	-1103733428388
STPT(10)	1028040148653064229	0 2 42 44 90 92 138 140 180 182	-454163701962
TPT(14)	1028040169128820271	0 2 6 8 30 32 48 50 186 188 216 218 378 380	-433687945920
STPT(10)	1028040376330271657	0 2 42 44 132 134 222 224 264 266	-226486494534
SPT(16)	1028040502403141243	0 8 30 38 44 60 78 128 156 206 224 240 246 254 276 284	-100413624948
STPT(10)	1028040562400187377	0 2 30 32 42 44 54 56 84 86	-40416578814
STPT(10)	1028040753116577647	0 2 42 44 72 74 102 104 144 146	150299811456
SPT(16)	1028041078433088347	0 42 56 80 90 104 134 146 180 192 222 236 246 270 284 326	475616322156
SPT(16)	1028041181820781267	0 34 40 96 102 130 210 256 300 346 426 454 460 516 522 556	579004015076
STPT(10)	1028041364734889159	0 2 48 50 90 92 132 134 180 182	761918122968
SPT(16)	1028041502229895609	0 10 22 40 52 60 102 108 124 130 172 180 192 210 222 232	899413129418