Prime p₀= 401158683562451957 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 40 2 10 2 28 2 16 2 106 2 (?)
a_n: 0 2 30 32 72 74 84 86 114 116 132 134 240 242
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 242
Found by: Cruncher Pete
db: batch=70, k=14, 28 40 10 28 16 106

TPT(12)	401158619521684691	0 2 30 32 36 38 60 62 78 80 168 170	-64040767266
SPT(14)	401158621356881233	0 28 60 94 126 156 186 208 238 268 300 334 366 394	-62205570724
SPT(14)	401158636268244353	0 48 80 98 108 114 120 134 140 146 156 174 206 254	-47294207604
SPT(14)	401158662242644429	0 12 78 100 114 154 204 208 258 298 312 334 400 412	-21319807528
SPT(14)	401158671908355019	0 40 112 148 162 192 228 274 310 340 354 390 462 502	-11654096938
SPT(14)	401158675891351951	0 28 46 70 72 102 108 160 166 196 198 222 240 268	-7671100006
TPT(12)	401158701729503981	0 2 18 20 30 32 90 92 96 98 156 158	18167052024
SPT(14)	401158711617603857	0 14 26 54 60 74 134 186 246 260 266 294 306 320	28055151900
SPT(14)	401158724122430531	0 6 38 66 80 90 96 152 158 168 182 210 242 248	40559978574
SPT(14)	401158726524709289	0 14 50 92 108 152 234 248 330 374 390 432 468 482	42962257332
TPT(12)	401158727359007699	0 2 30 32 72 74 90 92 102 104 168 170	43796555742