Prime p₀= 4506334453131882977 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 70 2 46 2 28 2 28 2 22 2 (?)
a_n: 0 2 60 62 132 134 180 182 210 212 240 242 264 266
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: 266
Found by: Stony666
db: batch=85, k=14, 58 70 46 28 28 22

SPT(16)	4506332704405678373	0 44 54 66 86 96 104 156 248 300 308 318 338 350 360 404	-1748726204604
SPT(16)	4506332710320798233	0 18 38 66 78 108 128 158 258 288 308 338 350 378 398 416	-1742811084744
STPT(10)	4506332879337569039	0 2 42 44 90 92 138 140 180 182	-1573794313938
TPT(14)	4506333750302548457	0 2 54 56 102 104 192 194 210 212 252 254 270 272	-702829334520
STPT(10)	4506333769574452997	0 2 30 32 42 44 54 56 84 86	-683557429980
SPT(16)	4506334415959826431	0 28 100 120 130 150 178 210 220 252 280 300 310 330 402 430	-37172056546
STPT(10)	4506334524716891609	0 2 78 80 120 122 162 164 240 242	71585008632
STPT(10)	4506334778122178297	0 2 90 92 102 104 114 116 204 206	324990295320
STPT(10)	4506335069254168229	0 2 48 50 60 62 72 74 120 122	616122285252
STPT(10)	4506335541250008197	0 2 30 32 42 44 54 56 84 86	1088118125220
STPT(10)	4506335744205345959	0 2 18 20 30 32 42 44 60 62	1291073462982