Prime p₀= 928175247935016617 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 22 2 34 2 40 2 106 2 70 2 (?)
a_n: 0 2 30 32 54 56 90 92 132 134 240 242 312 314
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: 314
Found by: crashtech
db: batch=76, k=14, 28 22 34 40 106 70

SPT(16)	928174365266861431	0 10 12 28 70 102 136 138 160 162 196 228 270 286 288 298	-882668155186
SPT(16)	928174548828944821	0 40 48 52 66 106 148 150 178 180 222 262 276 280 288 328	-699106071796
STPT(10)	928174687529720999	0 2 18 20 30 32 42 44 60 62	-560405295618
STPT(10)	928174806685112759	0 2 48 50 90 92 132 134 180 182	-441249903858
STPT(10)	928174890022422167	0 2 30 32 72 74 114 116 144 146	-357912594450
STPT(10)	928175211867240437	0 2 60 62 72 74 84 86 144 146	-36067776180
STPT(10)	928175272302531401	0 2 30 32 78 80 126 128 156 158	24367514784
STPT(10)	928175341189218467	0 2 42 44 72 74 102 104 144 146	93254201850
STPT(10)	928175969319963107	0 2 42 44 72 74 102 104 144 146	721384946490
TPT(14)	928176465261498239	0 2 48 50 78 80 90 92 120 122 150 152 210 212	1217326481622
STPT(10)	928176471006096041	0 2 36 38 78 80 120 122 156 158	1223071079424