Prime p₀= 2310548642851986497 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 118 2 40 2 4 2 40 2 76 2 (?)
a_n: 0 2 42 44 162 164 204 206 210 212 252 254 330 332
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: 332
Found by: FritzB
db: batch=81, k=14, 40 118 40 4 40 76

SPT(16)	2310546432015691267	0 4 12 16 66 76 100 180 256 336 360 370 420 424 432 436	-2210836295230
STPT(10)	2310546453297379397	0 2 42 44 72 74 102 104 144 146	-2189554607100
STPT(10)	2310546500222118251	0 2 30 32 120 122 210 212 240 242	-2142629868246
SPT(16)	2310546550714429999	0 10 34 52 124 132 144 174 178 208 220 228 300 318 342 352	-2092137556498
STPT(10)	2310547227469124459	0 2 12 14 90 92 168 170 180 182	-1415382862038
SPT(13)	2310547636344911723	0 48 60 96 138 180 198 216 258 300 336 348 396	-1006507074774
SPT(16)	2310548814451955081	0 6 26 32 60 68 90 102 176 188 210 218 246 252 272 278	171599968584
STPT(10)	2310548884802917007	0 2 12 14 42 44 72 74 84 86	241950930510
SPT(16)	2310548888215087489	0 4 34 48 78 84 90 100 102 112 118 124 154 168 198 202	245363100992
SPT(16)	2310549305246198239	0 10 72 88 100 108 132 138 214 220 244 252 264 280 342 352	662394211742
SPT(16)	2310549968191085377	0 40 54 72 82 130 144 162 172 190 204 252 262 280 294 334	1325339098880