Prime p₀= 1231782164396053799 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: biodoc
db: batch=77, k=12, 2 10 2 4 2 22

SPT(16)	1231780836811419721	0 22 88 126 166 180 192 276 292 376 388 402 442 480 546 568	-1327584634078
TPT(14)	1231780996051830491	0 2 36 38 126 128 150 152 156 158 168 170 276 278	-1168344223308
SPT(16)	1231781113640362403	0 18 24 26 30 66 104 126 128 150 188 224 228 230 236 254	-1050755691396
STPT(12)	1231781465031017429	0 2 18 20 90 92 168 170 240 242 258 260	-699365036370
TPT(14)	1231781465031017429	0 2 18 20 90 92 168 170 240 242 258 260 312 314	-699365036370
STPT(10)	1231781710703941919	0 2 18 20 30 32 42 44 60 62	-453692111880
STPT(10)	1231782341922577811	0 2 36 38 78 80 120 122 156 158	177526524012
STPT(10)	1231782383909499941	0 2 30 32 78 80 126 128 156 158	219513446142
STPT(10)	1231782449066487599	0 2 78 80 180 182 282 284 360 362	284670433800
SPT(16)	1231782620348506927	0 16 30 52 54 60 72 82 84 94 106 112 114 136 150 166	455952453128
SPT(16)	1231782650172239303	0 26 50 54 68 206 230 246 248 264 288 426 440 444 468 494	485776185504