Prime p₀= 39996012627725639 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 76 2 22 2 28 2 136 2 40 2 (?)
a_n: 0 2 78 80 102 104 132 134 270 272 312 314
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: 314
Found by: ChelseaOilman
db: batch=65, k=12, 76 22 28 136 40

SPT(14)	39995940940282697	0 6 30 42 56 60 90 122 152 156 170 182 206 212	-71687442942
SPT(14)	39995950471743691	0 28 46 78 90 106 126 130 150 166 178 210 228 256	-62155981948
SPT(14)	39995952839041327	0 16 34 64 66 76 90 130 144 154 156 186 204 220	-59788684312
SPT(14)	39995978902679237	0 6 20 32 42 74 110 126 162 194 204 216 230 236	-33725046402
SPT(14)	39995987123335589	0 2 30 78 92 108 134 168 194 210 224 272 300 302	-25504390050
STPT(10)	39995990337783449	0 2 12 14 30 32 48 50 60 62	-22289942190
SPT(14)	39996029606225117	0 12 24 42 54 62 140 144 222 230 242 260 272 284	16978499478
SPT(14)	39996029735062633	0 16 24 36 40 46 58 66 78 84 88 100 108 124	17107336994
STPT(10)	39996048583980077	0 2 30 32 42 44 54 56 84 86	35956254438
TPT(12)	39996051110321177	0 2 60 62 102 104 240 242 312 314 384 386	38482595538
SPT(14)	39996095232457321	0 102 150 156 166 180 222 226 268 282 292 298 346 448	82604731682