Prime p₀= 740346300223923059 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 16 2 40 2 40 2 34 2 10 2 (?)
a_n: 0 2 60 62 78 80 120 122 162 164 198 200 210 212
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: 212
Found by: Theadalus
db: batch=73, k=14, 58 16 40 40 34 10

TPT(14)	740345592570185687	0 2 42 44 114 116 204 206 360 362 402 404 450 452	-707653737372
STPT(12)	740345613050743109	0 2 42 44 90 92 132 134 180 182 222 224	-687173179950
TPT(14)	740345811716599481	0 2 30 32 96 98 108 110 150 152 180 182 198 200	-488507323578
SPT(16)	740345843525152883	0 18 30 50 54 126 140 146 168 174 188 260 264 284 296 314	-456698770176
SPT(16)	740346081834334177	0 54 100 132 144 180 186 222 244 280 286 322 334 366 412 466	-218389588882
SPT(16)	740346118870533173	0 8 50 60 104 108 186 216 218 248 326 330 374 384 426 434	-181353389886
SPT(16)	740346466165427501	0 6 18 20 72 86 90 102 146 158 162 176 228 230 242 248	165941504442
STPT(10)	740346584861106701	0 2 30 32 78 80 126 128 156 158	284637183642
SPT(16)	740346716914537027	0 42 52 84 114 136 142 232 234 324 330 352 382 414 424 466	416690613968
SPT(16)	740346726829681297	0 6 34 46 54 72 76 120 166 210 214 232 240 252 280 286	426605758238
STPT(10)	740346928141972817	0 2 12 14 42 44 72 74 84 86	627918049758