Prime p₀= 1523373976595770919 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 28 2 16 2 10 2 34 2 28 2 (?)
a_n: 0 2 42 44 72 74 90 92 102 104 138 140 168 170
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: 170
Found by: Theadalus
db: batch=78, k=14, 40 28 16 10 34 28

SPT(16)	1523373143154110377	0 42 70 72 84 90 106 112 114 120 136 142 154 156 184 226	-833441660542
SPT(20)	1523373186213503519	0 24 30 90 98 102 144 164 234 312 320 398 468 488 530 534 542 602 608 632	-790382267400
STPT(10)	1523373331313370137	0 2 42 44 72 74 102 104 144 146	-645282400782
SPT(16)	1523373629286349769	0 8 78 102 110 122 134 140 162 168 180 192 200 224 294 302	-347309421150
SPT(16)	1523373898569347287	0 22 42 84 102 114 124 162 172 210 220 232 250 292 312 334	-78026423632
SPT(16)	1523373943312251181	0 46 72 78 112 126 142 172 186 216 232 246 280 286 312 358	-33283519738
STPT(10)	1523373978634585547	0 2 30 32 42 44 54 56 84 86	2038814628
SPT(16)	1523374029620204941	0 40 138 208 222 246 286 300 358 372 412 436 450 520 618 658	53024434022
STPT(10)	1523374146495311879	0 2 18 20 30 32 42 44 60 62	169899540960
STPT(10)	1523374645929131921	0 2 30 32 78 80 126 128 156 158	669333361002
SPT(16)	1523374773019353193	0 30 36 64 90 120 130 150 154 174 184 214 240 268 274 304	796423582274