Prime p₀= 2278652471057823359 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 40 2 4 2 22 2 4 2 40 2 (?)
a_n: 0 2 42 44 48 50 72 74 78 80 120 122
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: 122
Found by: Orange Kid
db: batch=81, k=12, 2 40 2 4 2 22

SPT(18)	2278651394122265759	0 18 62 80 132 134 174 182 192 200 210 218 258 260 312 330 374 392	-1076935557600
SPT(16)	2278651396692434833	0 66 90 94 150 154 166 240 304 378 390 394 450 454 478 544	-1074365388526
SPT(16)	2278651479898838657	0 26 60 114 120 134 170 174 182 186 222 236 242 296 330 356	-991158984702
SPT(16)	2278651849563658787	0 30 44 54 66 72 92 96 140 144 164 170 182 192 206 236	-621494164572
STPT(10)	2278652354281347659	0 2 18 20 30 32 42 44 60 62	-116776475700
SPT(18)	2278652421155677393	0 16 24 36 78 106 120 154 156 178 180 214 228 256 298 310 318 334	-49902145966
STPT(10)	2278652539759373819	0 2 18 20 30 32 42 44 60 62	68701550460
SPT(16)	2278652816906933903	0 8 36 80 140 156 186 210 284 308 338 354 414 458 486 494	345849110544
STPT(10)	2278652994932487461	0 2 36 38 78 80 120 122 156 158	523874664102
SPT(16)	2278653071259394849	0 28 40 42 54 64 78 82 90 94 108 118 130 132 144 172	600201571490
STPT(10)	2278653145867925327	0 2 54 56 72 74 90 92 144 146	674810101968