Prime p₀= 11557339774586657 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 58 2 10 2 58 2 70 2 46 2 (?)
a_n: 0 2 60 62 72 74 132 134 204 206 252 254
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: 254
Found by: UBT - Timbo
db: batch=62, k=12, 58 10 58 70 46

SPT(14)	11557302708040337	0 24 26 44 54 66 72 134 140 152 162 180 182 206	-37066546320
SPT(14)	11557303762820999	0 2 14 24 78 80 170 192 282 284 338 348 360 362	-36011765658
SPT(14)	11557305809421277	0 12 42 54 66 70 76 90 96 100 112 124 154 166	-33965165380
SPT(14)	11557322537991001	0 6 18 22 46 88 102 256 270 312 336 340 352 358	-17236595656
SPT(14)	11557325142370243	0 10 46 66 70 78 88 108 118 126 130 150 186 196	-14632216414
SPT(14)	11557331803784131	0 16 40 52 66 72 82 156 166 172 186 198 222 238	-7970802526
SPT(14)	11557341222154153	0 6 30 34 54 154 166 258 270 370 390 394 418 424	1447567496
SPT(14)	11557346652864407	0 2 6 14 26 30 36 140 146 150 162 170 174 176	6878277750
SPT(14)	11557348528061551	0 10 22 78 102 112 118 180 186 196 220 276 288 298	8753474894
SPT(14)	11557348822635293	0 14 18 38 60 104 110 144 150 194 216 236 240 254	9048048636
SPT(14)	11557353738556903	0 70 76 78 96 156 246 250 340 400 418 420 426 496	13963970246