Prime p₀= 401158701729503981 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 16 2 10 2 58 2 4 2 58 2 (?)
a_n: 0 2 18 20 30 32 90 92 96 98 156 158
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: 158
Found by: Cruncher Pete
db: batch=70, k=12, 16 10 58 4 58

SPT(14)	401158621356881233	0 28 60 94 126 156 186 208 238 268 300 334 366 394	-80372622748
SPT(14)	401158636268244353	0 48 80 98 108 114 120 134 140 146 156 174 206 254	-65461259628
SPT(14)	401158662242644429	0 12 78 100 114 154 204 208 258 298 312 334 400 412	-39486859552
SPT(14)	401158671908355019	0 40 112 148 162 192 228 274 310 340 354 390 462 502	-29821148962
SPT(14)	401158675891351951	0 28 46 70 72 102 108 160 166 196 198 222 240 268	-25838152030
TPT(14)	401158683562451957	0 2 30 32 72 74 84 86 114 116 132 134 240 242	-18167052024
SPT(14)	401158711617603857	0 14 26 54 60 74 134 186 246 260 266 294 306 320	9888099876
SPT(14)	401158724122430531	0 6 38 66 80 90 96 152 158 168 182 210 242 248	22392926550
SPT(14)	401158726524709289	0 14 50 92 108 152 234 248 330 374 390 432 468 482	24795205308
TPT(12)	401158727359007699	0 2 30 32 72 74 90 92 102 104 168 170	25629503718
SPT(16)	401158729289253269	0 42 60 78 102 110 162 228 284 350 402 410 434 452 470 512	27559749288