Prime p₀= 816349537430613941 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 64 2 28 2 22 2 34 2 40 2 (?)
a_n: 0 2 30 32 96 98 126 128 150 152 186 188 228 230
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: 230
Found by: Paul
db: batch=73, k=14, 28 64 28 22 34 40

TPT(14)	816348130744742537	0 2 30 32 54 56 60 62 102 104 144 146 210 212	-1406685871404
STPT(10)	816348265303651061	0 2 36 38 78 80 120 122 156 158	-1272126962880
TPT(14)	816348415458300449	0 2 60 62 90 92 132 134 138 140 168 170 258 260	-1121972313492
STPT(10)	816348499560612047	0 2 12 14 42 44 72 74 84 86	-1037870001894
SPT(16)	816349181015617069	0 34 88 90 94 100 112 130 132 150 162 168 172 174 228 262	-356414996872
SPT(16)	816349240608369001	0 10 28 36 48 52 66 108 130 172 186 190 202 210 228 238	-296822244940
TPT(14)	816350193279193709	0 2 12 14 78 80 120 122 132 134 138 140 168 170	655848579768
SPT(16)	816350586373908931	0 22 28 46 78 88 90 190 198 298 300 310 342 360 366 388	1048943294990
SPT(16)	816350673201432179	0 30 32 38 42 68 72 74 108 110 114 140 144 150 152 182	1135770818238
STPT(10)	816350991283929767	0 2 12 14 42 44 72 74 84 86	1453853315826
SPT(16)	816351312185787431	0 18 36 42 56 60 98 126 212 240 278 282 296 302 320 338	1774755173490