Prime p₀= 2623707718236801107 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 28 2 10 2 28 2 10 2 28 2 (?)
a_n: 0 2 30 32 42 44 72 74 84 86 114 116
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: 116
Found by: [SG-FC] hl
db: batch=82, k=12, 2 28 2 10 2 28

STPT(10)	2623706927897999729	0 2 42 44 60 62 78 80 120 122	-790338801378
SPT(16)	2623707048095757697	0 12 22 64 84 120 150 154 372 376 406 442 462 504 514 526	-670141043410
SPT(16)	2623707306128463403	0 10 24 30 34 58 76 94 150 168 186 210 214 220 234 244	-412108337704
SPT(16)	2623707485512426787	0 24 36 56 62 80 116 134 192 210 246 264 270 290 302 326	-232724374320
SPT(16)	2623707514901355427	0 30 52 72 112 136 172 186 220 234 270 294 334 354 376 406	-203335445680
SPT(16)	2623707634034533957	0 4 22 42 54 82 130 144 190 204 252 280 292 312 330 334	-84202267150
STPT(10)	2623708270577867021	0 2 6 8 48 50 90 92 96 98	552341065914
STPT(10)	2623708282841800127	0 2 30 32 42 44 54 56 84 86	564604999020
SPT(16)	2623708455552073933	0 16 30 60 96 138 148 198 406 456 466 508 544 574 588 604	737315272826
SPT(16)	2623708469532677101	0 12 40 46 78 108 136 178 240 282 310 340 372 378 406 418	751295875994
STPT(10)	2623708838542508081	0 2 30 32 78 80 126 128 156 158	1120305706974