Prime p₀= 726257343869841137 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 16 2 22 2 16 2 58 2 10 2 (?)
a_n: 0 2 12 14 30 32 54 56 72 74 132 134 144 146
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: 146
Found by: [SG]steini
db: batch=73, k=14, 10 16 22 16 58 10

STPT(10)	726256165508153249	0 2 12 14 30 32 48 50 60 62	-1178361687888
SPT(16)	726256630020935249	0 8 42 68 80 84 92 120 122 150 158 162 174 200 234 242	-713848905888
SPT(16)	726256767094110713	0 6 30 68 86 128 174 200 264 290 336 378 396 434 458 464	-576775730424
STPT(10)	726256974262063217	0 2 30 32 42 44 54 56 84 86	-369607777920
STPT(10)	726257167712564351	0 2 78 80 108 110 138 140 216 218	-176157276786
SPT(16)	726257176318456637	0 12 30 32 56 116 126 144 152 170 180 240 264 266 284 296	-167551384500
SPT(16)	726257401496579143	0 28 70 90 100 118 144 174 214 244 270 288 298 318 360 388	57626738006
TPT(14)	726257580536004131	0 2 96 98 108 110 138 140 156 158 168 170 180 182	236666162994
SPT(16)	726257747966098003	0 18 28 60 66 94 96 106 108 118 120 148 154 186 196 214	404096256866
SPT(16)	726258077929732561	0 16 30 108 132 142 160 208 210 258 276 286 310 388 402 418	734059891424
STPT(10)	726258243764751947	0 2 12 14 42 44 72 74 84 86	899894910810