Prime p₀= 2354896137123650147 starts a Symmetric tuple of 10 consecutive primes, which form 5 twin primes (STPT).
d_n: 0 2 22 2 16 2 16 2 22 2 (?)
a_n: 0 2 24 26 42 44 60 62 84 86
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: 86
Found by: fix
db: batch=81, k=10, 2 22 2 16 2

SPT(16)	2354894365135240547	0 6 26 66 80 86 120 126 176 182 216 222 236 276 296 302	-1771988409600
SPT(16)	2354894384516556287	0 44 54 56 66 72 84 86 210 212 224 230 240 242 252 296	-1752607093860
STPT(10)	2354895309107442797	0 2 90 92 150 152 210 212 300 302	-828016207350
STPT(10)	2354895573771916961	0 2 30 32 60 62 90 92 120 122	-563351733186
STPT(10)	2354895645668145467	0 2 30 32 42 44 54 56 84 86	-491455504680
SPT(16)	2354895871618261967	0 14 24 42 80 92 140 146 150 156 204 216 254 272 282 296	-265505388180
STPT(10)	2354896138903713407	0 2 30 32 72 74 114 116 144 146	1780063260
STPT(10)	2354896456473827051	0 2 30 32 60 62 90 92 120 122	319350176904
STPT(10)	2354896630016149871	0 2 36 38 78 80 120 122 156 158	492892499724
STPT(10)	2354896636226530577	0 2 30 32 42 44 54 56 84 86	499102880430
STPT(10)	2354896673647004477	0 2 42 44 72 74 102 104 144 146	536523354330