Prime p₀= 1458804997727312513 starts a Symmetric tuple of 16 consecutive primes (SPT).
d_n: 0 50 6 60 42 16 30 6 14 6 30 16 42 60 6 50 (?)
a_n: 0 50 56 116 158 174 204 210 224 230 260 276 318 378 384 434
All 16 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 434
Found by: JonS
db: batch=78, k=16, 50 6 60 42 16 30 6 14

SPT(16)	1458804403564501717	0 10 36 40 54 94 96 100 120 124 126 166 180 184 210 220	-594162810796
STPT(12)	1458804495854420087	0 2 60 62 72 74 90 92 102 104 162 164	-501872892426
STPT(10)	1458804507638590661	0 2 6 8 48 50 90 92 96 98	-490088721852
SPT(18)	1458804517045772551	0 6 18 48 58 88 156 160 162 196 198 202 270 300 310 340 352 358	-480681539962
STPT(10)	1458804757667673497	0 2 54 56 72 74 90 92 144 146	-240059639016
TPT(14)	1458804827840599607	0 2 12 14 42 44 84 86 144 146 210 212 222 224	-169886712906
SPT(16)	1458805708263347099	0 38 42 54 84 108 120 132 140 152 164 188 218 230 234 272	710536034586
STPT(10)	1458805864595753459	0 2 30 32 60 62 90 92 120 122	866868440946
SPT(16)	1458805868801926261	0 18 28 40 58 126 166 180 268 282 322 390 408 420 430 448	871074613748
STPT(10)	1458805985015925911	0 2 30 32 78 80 126 128 156 158	987288613398
STPT(10)	1458806142474369509	0 2 42 44 60 62 78 80 120 122	1144747056996