Prime p₀= 1056924027427874729 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 58 2 10 2 64 2 40 2 58 2 (?)
a_n: 0 2 30 32 90 92 102 104 168 170 210 212 270 272
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: 272
Found by: =Lupus=
db: batch=76, k=14, 28 58 10 64 40 58

SPT(16)	1056921871611789923	0 26 38 48 68 84 98 110 174 186 200 216 236 246 258 284	-2155816084806
STPT(10)	1056921892916024297	0 2 30 32 42 44 54 56 84 86	-2134511850432
SPT(16)	1056922252475657401	0 16 18 66 70 72 82 88 120 126 136 138 142 190 192 208	-1774952217328
SPT(16)	1056922774174777001	0 18 20 32 62 66 86 122 126 162 182 186 216 228 230 248	-1253253097728
STPT(10)	1056923768112935477	0 2 42 44 72 74 102 104 144 146	-259314939252
SPT(18)	1056923896869383789	0 8 12 78 108 120 122 140 158 162 180 198 200 212 242 308 312 320	-130558490940
STPT(10)	1056924821110205141	0 2 6 8 48 50 90 92 96 98	793682330412
SPT(16)	1056924851354344477	0 30 60 102 112 130 154 196 240 282 306 324 334 376 406 436	823926469748
SPT(16)	1056924878279201801	0 30 78 80 90 126 128 146 402 420 422 458 468 470 518 548	850851327072
TPT(14)	1056924940393719581	0 2 18 20 60 62 120 122 186 188 198 200 288 290	912965844852
SPT(16)	1056925174889414609	0 18 38 102 108 128 212 218 234 240 324 344 350 414 434 452	1147461539880