Prime p₀= 2326666697564161409 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 52 2 58 2 76 2 28 2 70 2 (?)
a_n: 0 2 18 20 72 74 132 134 210 212 240 242 312 314
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: 314
Found by: [SG-2W]Kurzer
db: batch=81, k=14, 16 52 58 76 28 70

SPT(16)	2326665292707408853	0 6 18 30 36 46 58 120 124 186 198 208 214 226 238 244	-1404856752556
SPT(18)	2326665335761067003	0 6 44 66 84 104 108 120 140 204 224 236 240 260 278 300 338 344	-1361803094406
STPT(10)	2326665504019630589	0 2 12 14 90 92 168 170 180 182	-1193544530820
SPT(16)	2326665715735281883	0 48 54 58 76 96 138 154 210 226 268 288 306 310 316 364	-981828879526
SPT(16)	2326665762949194869	0 38 42 72 90 102 108 158 222 272 278 290 308 338 342 380	-934614966540
SPT(16)	2326666289966934143	0 44 54 60 134 138 140 144 170 174 176 180 254 260 270 314	-407597227266
TPT(16)	2326666865788196159	0 2 42 44 48 50 60 62 90 92 132 134 222 224 228 230	168224034750
TPT(14)	2326666930080281651	0 2 90 92 120 122 126 128 168 170 198 200 300 302	232516120242
STPT(10)	2326667387918416157	0 2 24 26 42 44 60 62 84 86	690354254748
STPT(12)	2326667586575995721	0 2 78 80 90 92 156 158 168 170 246 248	889011834312
STPT(10)	2326668174377226857	0 2 72 74 102 104 132 134 204 206	1476813065448