Prime p₀= 2577436255284332009 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 76 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 120 122 150 152 162 164
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 164
Found by: JayPi
db: batch=82, k=12, 2 10 2 28 2 76

SPT(16)	2577435104804226091	0 10 12 42 88 120 148 162 178 192 220 252 298 328 330 340	-1150480105918
STPT(10)	2577435171638985941	0 2 6 8 48 50 90 92 96 98	-1083645346068
SPT(16)	2577435280633282219	0 12 40 52 54 72 78 108 154 184 190 208 210 222 250 262	-974651049790
TPT(14)	2577435296141216207	0 2 30 32 72 74 90 92 222 224 264 266 294 296	-959143115802
STPT(10)	2577435933731348717	0 2 24 26 42 44 60 62 84 86	-321552983292
SPT(16)	2577436196819308757	0 14 32 60 62 80 114 164 210 260 294 312 314 342 360 374	-58465023252
SPT(16)	2577436302743751011	0 36 56 72 96 180 260 300 302 342 422 506 530 546 566 602	47459419002
STPT(10)	2577436600738236707	0 2 30 32 42 44 54 56 84 86	345453904698
SPT(16)	2577436675567607551	0 18 76 78 90 96 106 148 150 192 202 208 220 222 280 298	420283275542
STPT(10)	2577436859488733477	0 2 42 44 72 74 102 104 144 146	604204401468
STPT(10)	2577437087442842291	0 2 6 8 18 20 30 32 36 38	832158510282