Prime p₀= 816350193279193709 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 64 2 40 2 10 2 4 2 28 2 (?)
a_n: 0 2 12 14 78 80 120 122 132 134 138 140 168 170
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: Paul
db: batch=73, k=14, 10 64 40 10 4 28

STPT(10)	816348265303651061	0 2 36 38 78 80 120 122 156 158	-1927975542648
TPT(14)	816348415458300449	0 2 60 62 90 92 132 134 138 140 168 170 258 260	-1777820893260
STPT(10)	816348499560612047	0 2 12 14 42 44 72 74 84 86	-1693718581662
SPT(16)	816349181015617069	0 34 88 90 94 100 112 130 132 150 162 168 172 174 228 262	-1012263576640
SPT(16)	816349240608369001	0 10 28 36 48 52 66 108 130 172 186 190 202 210 228 238	-952670824708
TPT(14)	816349537430613941	0 2 30 32 96 98 126 128 150 152 186 188 228 230	-655848579768
SPT(16)	816350586373908931	0 22 28 46 78 88 90 190 198 298 300 310 342 360 366 388	393094715222
SPT(16)	816350673201432179	0 30 32 38 42 68 72 74 108 110 114 140 144 150 152 182	479922238470
STPT(10)	816350991283929767	0 2 12 14 42 44 72 74 84 86	798004736058
SPT(16)	816351312185787431	0 18 36 42 56 60 98 126 212 240 278 282 296 302 320 338	1118906593722
SPT(16)	816351651948725797	0 6 36 76 90 132 136 160 186 210 214 256 270 310 340 346	1458669532088