Prime p₀= 2362414499519082467 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 10 2 118 2 4 2 40 2 16 2 (?)
a_n: 0 2 42 44 54 56 174 176 180 182 222 224 240 242
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: 242
Found by: Landjunge
db: batch=81, k=14, 40 10 118 4 40 16

STPT(10)	2362412649460368119	0 2 18 20 30 32 42 44 60 62	-1850058714348
SPT(22)	2362412757405047863	0 10 24 28 46 70 76 138 174 214 234 280 300 340 376 438 444 468 486 490 504 514	-1742114034604
SPT(16)	2362413028950384491	0 50 60 92 102 126 132 146 156 170 176 200 210 242 252 302	-1470568697976
SPT(16)	2362413039770686013	0 66 68 80 86 90 96 108 128 140 146 150 156 168 170 236	-1459748396454
SPT(16)	2362413701099730899	0 54 90 104 108 140 192 222 230 260 312 344 348 362 398 452	-798419351568
SPT(16)	2362414047830112179	0 38 54 92 102 134 150 164 198 212 228 260 270 308 324 362	-451688970288
STPT(10)	2362414548406715351	0 2 6 8 48 50 90 92 96 98	48887632884
STPT(10)	2362414736886656057	0 2 12 14 72 74 132 134 144 146	237367573590
SPT(16)	2362414847583853163	0 30 44 90 98 104 114 140 288 314 324 330 338 384 398 428	348064770696
SPT(16)	2362414926976785299	0 68 80 104 150 168 182 234 248 300 314 332 378 402 414 482	427457702832
STPT(10)	2362414958803374029	0 2 42 44 60 62 78 80 120 122	459284291562