Prime p₀= 2114997816576441959 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 70 2 16 2 22 2 16 2 46 2 (?)
a_n: 0 2 108 110 180 182 198 200 222 224 240 242 288 290
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: 290
Found by: Landjunge
db: batch=80, k=14, 106 70 16 22 16 46

TPT(14)	2114996362574696747	0 2 54 56 234 236 240 242 252 254 282 284 354 356	-1454001745212
STPT(10)	2114997020872722977	0 2 12 14 42 44 72 74 84 86	-795703718982
SPT(16)	2114997156322538561	0 2 8 12 86 156 188 192 236 240 272 342 416 420 426 428	-660253903398
SPT(16)	2114997644000265419	0 2 24 44 72 80 108 128 174 194 222 230 258 278 300 302	-172576176540
TPT(14)	2114997644818461911	0 2 6 8 126 128 138 140 156 158 180 182 210 212	-171757980048
SPT(16)	2114997734612738959	0 42 78 88 130 142 184 198 244 258 300 312 354 364 400 442	-81963703000
SPT(16)	2114997847809675649	0 10 22 42 60 84 132 144 160 172 220 244 262 282 294 304	31233233690
SPT(16)	2114997864680691629	0 18 38 62 72 90 122 132 140 150 182 200 210 234 254 272	48104249670
STPT(10)	2114998026862833947	0 2 42 44 102 104 162 164 204 206	210286391988
SPT(16)	2114998310645259497	0 12 20 30 54 56 72 86 90 104 120 122 146 156 164 176	494068817538
TPT(14)	2114998320529362239	0 2 12 14 72 74 102 104 108 110 210 212 318 320	503952920280