Prime p₀= 2496866344609301657 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 16 2 106 2 28 2 28 2 (?)
a_n: 0 2 12 14 24 26 42 44 150 152 180 182 210 212
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: 212
Found by: Penguin
db: batch=82, k=14, 10 10 16 106 28 28

SPT(16)	2496864729323570783	0 6 14 84 86 114 134 156 218 240 260 288 290 360 368 374	-1615285730874
STPT(10)	2496865265275254647	0 2 42 44 72 74 102 104 144 146	-1079334047010
STPT(10)	2496865836627254219	0 2 180 182 210 212 240 242 420 422	-507982047438
STPT(10)	2496865864806440249	0 2 48 50 90 92 132 134 180 182	-479802861408
TPT(14)	2496865944941639231	0 2 6 8 30 32 36 38 120 122 156 158 210 212	-399667662426
SPT(16)	2496866092558434733	0 10 24 126 190 196 204 208 246 250 258 264 328 430 444 454	-252050866924
SPT(16)	2496866419812622727	0 44 60 104 122 192 210 216 350 356 374 444 462 506 522 566	75203321070
TPT(14)	2496866641010780711	0 2 78 80 168 170 180 182 318 320 336 338 486 488	296401479054
SPT(16)	2496866764692880907	0 54 62 84 104 126 140 162 164 186 200 222 242 264 272 326	420083579250
STPT(10)	2496866798258299079	0 2 18 20 30 32 42 44 60 62	453648997422
STPT(10)	2496867204501901241	0 2 6 8 48 50 90 92 96 98	859892599584