Prime p₀= 1246849753340407079 starts a Symmetric tuple of 12 consecutive primes, which form 6 twin primes (STPT).
d_n: 0 2 10 2 28 2 4 2 28 2 10 2 (?)
a_n: 0 2 12 14 42 44 48 50 78 80 90 92
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: 92
Found by: Cruncher Pete
db: batch=77, k=12, 2 10 2 28 2 4

SPT(16)	1246849118688621653	0 14 60 126 170 176 234 240 254 260 318 324 368 434 480 494	-634651785426
SPT(16)	1246849121116556339	0 2 12 44 74 78 92 128 144 180 194 198 228 260 270 272	-632223850740
SPT(16)	1246849183492896787	0 40 66 82 100 202 214 216 220 222 234 336 354 370 396 436	-569847510292
STPT(10)	1246849314532474529	0 2 30 32 60 62 90 92 120 122	-438807932550
STPT(10)	1246849564077411641	0 2 6 8 48 50 90 92 96 98	-189262995438
SPT(16)	1246849566883014803	0 8 38 66 104 174 200 230 354 384 410 480 518 546 576 584	-186457392276
STPT(10)	1246849766754276437	0 2 30 32 42 44 54 56 84 86	13413869358
SPT(16)	1246849938877752941	0 26 30 56 180 186 218 240 266 288 320 326 450 476 480 506	185537345862
STPT(10)	1246850135656078451	0 2 36 38 78 80 120 122 156 158	382315671372
STPT(10)	1246850157489338159	0 2 18 20 30 32 42 44 60 62	404148931080
SPT(16)	1246850358981601457	0 12 14 42 56 84 144 146 150 152 212 240 254 282 284 296	605641194378