Prime p₀= 2424262615518677111 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 40 2 46 2 28 2 40 2 76 2 (?)
a_n: 0 2 6 8 48 50 96 98 126 128 168 170 246 248
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: 248
Found by: Penguin
db: batch=82, k=14, 4 40 46 28 40 76

SPT(16)	2424261402939696503	0 14 18 36 74 78 86 128 156 198 206 210 248 266 270 284	-1212578980608
STPT(10)	2424261423584360819	0 2 18 20 30 32 42 44 60 62	-1191934316292
STPT(10)	2424261717496265399	0 2 18 20 30 32 42 44 60 62	-898022411712
SPT(16)	2424262053172147751	0 30 36 68 78 120 140 182 276 318 338 380 390 422 428 458	-562346529360
TPT(14)	2424262064265646667	0 2 54 56 192 194 234 236 240 242 264 266 270 272	-551253030444
STPT(10)	2424262571634169697	0 2 30 32 72 74 114 116 144 146	-43884507414
TPT(14)	2424262644405429689	0 2 30 32 78 80 138 140 168 170 198 200 252 254	28886752578
SPT(16)	2424262728050274733	0 34 40 46 58 66 124 130 264 270 328 336 348 354 360 394	112531597622
SPT(16)	2424263293923380831	0 32 56 102 108 122 152 168 290 306 336 350 356 402 426 458	678404703720
SPT(16)	2424263320804527263	0 8 14 54 74 78 138 140 144 146 206 210 230 270 276 284	705285850152
SPT(16)	2424263475043844047	0 22 34 40 82 106 124 150 346 372 390 414 456 462 474 496	859525166936