Prime p₀= 2946407525555562119 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 16 2 22 2 16 2 130 2 16 2 (?)
a_n: 0 2 60 62 78 80 102 104 120 122 252 254 270 272
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: 272
Found by: ginga
db: batch=82, k=14, 58 16 22 16 130 16

SPT(16)	2946406224915597293	0 14 36 78 80 84 104 120 134 150 170 174 176 218 240 254	-1300639964826
STPT(10)	2946406867394071091	0 2 6 8 48 50 90 92 96 98	-658161491028
TPT(14)	2946406872207912317	0 2 42 44 84 86 114 116 120 122 150 152 180 182	-653347649802
STPT(10)	2946407121511172321	0 2 30 32 60 62 90 92 120 122	-404044389798
STPT(10)	2946407200476713159	0 2 42 44 90 92 138 140 180 182	-325078848960
SPT(16)	2946407514010714477	0 10 22 64 66 196 204 246 280 322 330 460 462 504 516 526	-11544847642
TPT(14)	2946408157199147747	0 2 12 14 30 32 54 56 72 74 150 152 162 164	631643585628
SPT(16)	2946409363625655601	0 58 60 88 102 120 150 192 196 238 268 286 300 328 330 388	1838070093482
SPT(16)	2946409513591792013	0 80 90 120 150 174 188 198 230 240 254 278 308 338 348 428	1988036229894
SPT(16)	2946409687577810533	0 24 28 46 48 66 70 120 184 234 238 256 258 276 280 304	2162022248414
TPT(16)	2946410084072120507	0 2 30 32 84 86 90 92 204 206 252 254 342 344 504 506	2558516558388