Prime p₀= 2037737622637425659 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: Landjunge
db: batch=80, k=10, 2 16 2 10 2

SPT(16)	2037735877359149551	0 42 72 78 96 108 126 138 150 162 180 192 210 216 246 288	-1745278276108
STPT(10)	2037736170183277181	0 2 36 38 78 80 120 122 156 158	-1452454148478
STPT(10)	2037736769013317789	0 2 18 20 30 32 42 44 60 62	-853624107870
SPT(16)	2037736870523847781	0 18 60 88 112 136 150 172 186 208 222 246 270 298 340 358	-752113577878
STPT(10)	2037737105305604369	0 2 18 20 60 62 102 104 120 122	-517331821290
SPT(16)	2037737415418012181	0 20 26 32 42 60 66 102 230 266 272 290 300 306 312 332	-207219413478
STPT(10)	2037737646481999457	0 2 30 32 72 74 114 116 144 146	23844573798
STPT(10)	2037737670055665437	0 2 30 32 72 74 114 116 144 146	47418239778
STPT(10)	2037737691767403971	0 2 36 38 78 80 120 122 156 158	69129978312
STPT(10)	2037737794351047167	0 2 30 32 42 44 54 56 84 86	171713621508
SPT(16)	2037737872261089451	0 22 36 60 82 102 120 150 208 238 256 276 298 322 336 358	249623663792