Prime p₀= 3679924313694048481 starts a Symmetric tuple of 13 consecutive primes (SPT).
d_n: 0 12 6 24 6 30 12 12 30 6 24 6 12 (?)
a_n: 0 12 18 42 48 78 90 102 132 138 162 168 180
All 13 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 180
Found by: [SG]KidDoesCrunch
db: batch=84, k=13, 12 6 24 6 30 12

SPT(16)	3679922958391989899	0 24 62 72 120 134 144 150 182 188 198 212 260 270 308 332	-1355302058582
STPT(10)	3679923057926812517	0 2 60 62 72 74 84 86 144 146	-1255767235964
SPT(16)	3679923213083548183	0 96 148 154 156 210 258 280 294 316 364 418 420 426 478 574	-1100610500298
STPT(10)	3679923301131862451	0 2 6 8 18 20 30 32 36 38	-1012562186030
STPT(10)	3679923419300167181	0 2 6 8 18 20 30 32 36 38	-894393881300
SPT(16)	3679923994705209863	0 8 30 44 68 86 108 140 204 236 258 276 300 314 336 344	-318988838618
STPT(10)	3679924637616254717	0 2 30 32 42 44 54 56 84 86	323922206236
STPT(10)	3679924773595962251	0 2 6 8 48 50 90 92 96 98	459901913770
SPT(16)	3679925236327475671	0 42 46 106 112 172 180 250 372 442 450 510 516 576 580 622	922633427190
SPT(22)	3679925707617846839	0 8 14 50 54 78 80 92 98 102 104 138 140 144 150 162 164 188 192 228 234 242	1393923798358
STPT(10)	3679926577199592677	0 2 42 44 72 74 102 104 144 146	2263505544196