Prime p₀= 2949884562312727799 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 160 2 46 2 40 2 10 2 124 2 (?)
a_n: 0 2 48 50 210 212 258 260 300 302 312 314 438 440
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: 440
Found by: ginga
db: batch=82, k=14, 46 160 46 40 10 124

SPT(16)	2949883590739678301	0 8 18 48 62 80 92 108 200 216 228 246 260 290 300 308	-971573049498
SPT(16)	2949883638731500753	0 16 60 76 78 84 106 130 144 168 190 196 198 214 258 274	-923581227046
STPT(10)	2949883729179029969	0 2 18 20 30 32 42 44 60 62	-833133697830
STPT(10)	2949883776951551507	0 2 12 14 42 44 72 74 84 86	-785361176292
SPT(16)	2949883801696686391	0 12 40 42 60 78 96 120 238 262 280 298 316 318 346 358	-760616041408
SPT(16)	2949884461385586059	0 18 24 98 114 144 170 180 242 252 278 308 324 398 404 422	-100927141740
STPT(10)	2949885047995679609	0 2 12 14 90 92 168 170 180 182	485682951810
STPT(10)	2949885106184290739	0 2 48 50 90 92 132 134 180 182	543871562940
SPT(16)	2949885172275626213	0 44 66 68 114 140 150 156 248 254 264 290 336 338 360 404	609962898414
SPT(18)	2949885390151651727	0 66 72 102 116 200 210 216 230 252 266 272 282 366 380 410 416 482	827838923928
SPT(16)	2949885621177155131	0 6 28 58 76 120 132 168 190 226 238 282 300 330 352 358	1058864427332