Prime p₀= 813146100622473617 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: [SG]FX
db: batch=73, k=10, 2 22 2 16 2

SPT(16)	813145303228105051	0 18 46 58 72 88 96 102 166 172 180 196 210 222 250 268	-797394368566
STPT(10)	813145561997195699	0 2 18 20 30 32 42 44 60 62	-538625277918
STPT(10)	813145693924241267	0 2 42 44 72 74 102 104 144 146	-406698232350
SPT(16)	813145699478993729	0 30 38 78 98 122 132 140 150 158 168 192 212 252 260 290	-401143479888
STPT(10)	813145925549937149	0 2 18 20 30 32 42 44 60 62	-175072536468
SPT(16)	813146078202857149	0 22 28 60 72 88 130 148 192 210 252 268 280 312 318 340	-22419616468
STPT(10)	813146269569115367	0 2 12 14 42 44 72 74 84 86	168946641750
STPT(10)	813146321555098637	0 2 12 14 42 44 72 74 84 86	220932625020
TPT(14)	813146383019453237	0 2 30 32 42 44 54 56 72 74 144 146 210 212	282396979620
STPT(10)	813146420437808927	0 2 30 32 42 44 54 56 84 86	319815335310
STPT(10)	813146847250899989	0 2 18 20 60 62 102 104 120 122	746628426372