Prime p₀= 253163979352630301 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 124 2 88 2 10 2 28 2 10 2 (?)
a_n: 0 2 126 128 216 218 228 230 258 260 270 272
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: 272
Found by: desktop64
db: batch=69, k=12, 124 88 10 28 10

SPT(14)	253163929458669067	0 12 34 46 76 90 112 144 166 180 210 222 244 256	-49893961234
TPT(12)	253163930734302611	0 2 6 8 36 38 90 92 126 128 210 212	-48618327690
SPT(14)	253163938461215027	0 2 12 50 56 60 96 140 176 180 186 224 234 236	-40891415274
SPT(14)	253163949369856181	0 12 20 62 108 116 122 126 132 140 186 228 236 248	-29982774120
SPT(14)	253163958126849799	0 30 60 82 102 112 120 130 138 148 168 190 220 250	-21225780502
SPT(14)	253163970884778641	0 6 8 18 20 78 98 120 140 198 200 210 212 218	-8467851660
SPT(14)	253163981392142417	0 2 36 72 132 182 186 200 204 254 314 350 384 386	2039512116
SPT(16)	253163996501946923	0 50 56 60 74 158 198 210 254 266 306 390 404 408 414 464	17149316622
SPT(14)	253164030547555019	0 44 50 68 72 110 132 140 162 200 204 222 228 272	51194924718
SPT(14)	253164035296557523	0 10 40 106 108 130 136 138 144 166 168 234 264 274	55943927222
SPT(14)	253164062409867383	0 54 74 84 90 98 108 350 360 368 374 384 404 458	83057237082