Prime p₀= 2313113883705370607 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 10 2 4 2 10 2 10 2 (?)
a_n: 0 2 12 14 24 26 30 32 42 44 54 56
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: 56
Found by: Orange Kid
db: batch=81, k=12, 2 10 2 10 2 4

SPT(16)	2313113456667925189	0 10 12 40 54 78 88 102 130 144 154 178 192 220 222 232	-427037445418
SPT(16)	2313113612525817221	0 66 80 92 102 108 110 128 150 168 170 176 186 198 212 278	-271179553386
SPT(16)	2313113667686854507	0 10 70 90 142 150 184 192 244 252 286 294 346 366 426 436	-216018516100
SPT(16)	2313113736202260091	0 36 46 52 66 90 106 132 190 216 232 256 270 276 286 322	-147503110516
SPT(16)	2313113815728258841	0 22 36 82 90 100 138 162 166 190 228 238 246 292 306 328	-67977111766
SPT(16)	2313113851443230809	0 10 12 24 58 64 78 124 138 184 198 204 238 250 252 262	-32262139798
SPT(16)	2313114071668551967	0 6 40 70 76 82 102 106 186 190 210 216 222 252 286 292	187963181360
STPT(10)	2313114092040816677	0 2 30 32 42 44 54 56 84 86	208335446070
STPT(10)	2313114109026905879	0 2 30 32 60 62 90 92 120 122	225321535272
TPT(14)	2313114264769762247	0 2 24 26 180 182 204 206 222 224 384 386 420 422	381064391640
SPT(16)	2313114277497505067	0 60 80 122 150 164 192 204 290 302 330 344 372 414 434 494	393792134460