Prime p₀= 2570422261707279767 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 52 2 46 2 10 2 94 2 58 2 (?)
a_n: 0 2 30 32 84 86 132 134 144 146 240 242 300 302
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: 302
Found by: Orange Kid
db: batch=82, k=14, 28 52 46 10 94 58

SPT(16)	2570420124848878567	0 12 40 42 52 82 100 150 172 222 240 270 280 282 310 322	-2136858401200
SPT(16)	2570420296712950037	0 12 14 44 80 96 104 114 122 132 140 156 192 222 224 236	-1964994329730
STPT(10)	2570420932106836049	0 2 48 50 90 92 132 134 180 182	-1329600443718
TPT(14)	2570421102552479549	0 2 72 74 162 164 258 260 270 272 282 284 300 302	-1159154800218
STPT(10)	2570421302247768881	0 2 6 8 18 20 30 32 36 38	-959459510886
TPT(14)	2570421660154170629	0 2 48 50 78 80 102 104 120 122 240 242 252 254	-601553109138
SPT(16)	2570422316956262891	0 6 20 26 38 66 68 72 146 150 152 180 192 198 212 218	55248983124
TPT(14)	2570422962037451867	0 2 24 26 132 134 150 152 162 164 294 296 342 344	700330172100
SPT(16)	2570423152498590877	0 4 24 90 120 192 222 232 234 244 274 346 376 442 462 466	890791311110
STPT(10)	2570423327441391839	0 2 18 20 30 32 42 44 60 62	1065734112072
SPT(16)	2570423485539152213	0 14 66 104 126 150 174 180 230 236 260 284 306 344 396 410	1223831872446