Prime p₀= 2350775445012765299 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 4 2 22 2 4 2 10 2 (?)
a_n: 0 2 12 14 18 20 42 44 48 50 60 62
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: 62
Found by: Time_Traveler
db: batch=81, k=12, 2 10 2 4 2 22

STPT(10)	2350774568850418769	0 2 60 62 240 242 420 422 480 482	-876162346530
SPT(16)	2350774740520162081	0 28 42 66 100 118 126 142 186 202 210 228 262 286 300 328	-704492603218
TPT(14)	2350774772114970371	0 2 30 32 60 62 78 80 186 188 216 218 288 290	-672897794928
SPT(16)	2350774846904805163	0 6 36 58 100 108 118 138 178 198 208 216 258 280 310 316	-598107960136
SPT(16)	2350774850206949923	0 28 30 54 78 130 136 154 180 198 204 256 280 304 306 334	-594805815376
SPT(16)	2350774884163859831	0 6 18 32 98 116 140 152 186 198 222 240 306 320 332 338	-560848905468
SPT(16)	2350775509726448117	0 20 62 66 80 120 122 164 312 354 356 396 410 414 456 476	64713682818
STPT(10)	2350775524584583277	0 2 24 26 42 44 60 62 84 86	79571817978
SPT(16)	2350775621058954409	0 112 150 190 220 232 258 294 298 334 360 372 402 442 480 592	176046189110
STPT(10)	2350775963066259161	0 2 66 68 138 140 210 212 276 278	518053493862
STPT(10)	2350776006637717829	0 2 42 44 60 62 78 80 120 122	561624952530