Prime p₀= 1276578598512097649 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 16 2 10 2 10 2 16 2 (?)
a_n: 0 2 18 20 30 32 42 44 60 62
All 10 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 62
Found by: HenkM
db: batch=77, k=10, 2 16 2 10 2

SPT(16)	1276577722273583029	0 4 34 70 94 114 124 130 138 144 154 174 198 234 264 268	-876238514620
SPT(16)	1276577738959250647	0 22 36 76 90 96 132 150 166 184 220 226 240 280 294 316	-859552847002
SPT(16)	1276578057598389079	0 22 30 42 48 88 102 114 118 130 144 184 190 202 210 232	-540913708570
STPT(10)	1276578225238107521	0 2 36 38 78 80 120 122 156 158	-373273990128
STPT(10)	1276578336402893429	0 2 12 14 90 92 168 170 180 182	-262109204220
STPT(10)	1276578515651798477	0 2 24 26 42 44 60 62 84 86	-82860299172
SPT(16)	1276578601870801507	0 40 70 84 94 130 154 160 180 186 210 246 256 270 300 340	3358703858
STPT(10)	1276578745631702657	0 2 42 44 72 74 102 104 144 146	147119605008
STPT(10)	1276578818781944441	0 2 30 32 78 80 126 128 156 158	220269846792
SPT(16)	1276578966658222729	0 10 12 34 54 64 82 130 294 342 360 370 390 412 414 424	368146125080
SPT(16)	1276579469947444001	0 56 66 78 86 96 98 120 128 150 152 162 170 182 192 248	871435346352