Prime p₀= 1267582131670075787 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 28 2 88 2 64 2 142 2 4 2 (?)
a_n: 0 2 24 26 54 56 144 146 210 212 354 356 360 362
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: 362
Found by: HenkM
db: batch=77, k=14, 22 28 88 64 142 4

SPT(16)	1267580669206385447	0 12 26 30 86 104 110 132 134 156 162 180 236 240 254 266	-1462463690340
SPT(16)	1267580779115317301	0 6 20 32 48 78 120 140 228 248 290 320 336 348 362 368	-1352554758486
SPT(16)	1267581031115608961	0 6 20 36 50 66 68 92 96 120 122 138 152 168 182 188	-1100554466826
SPT(16)	1267581370021135583	0 18 30 120 128 144 170 186 218 234 260 276 284 374 386 404	-761648940204
TPT(14)	1267581703114190411	0 2 36 38 48 50 120 122 126 128 180 182 276 278	-428555885376
SPT(16)	1267581932061015491	0 50 56 60 68 98 156 176 330 350 408 438 446 450 456 506	-199609060296
SPT(16)	1267582472404782323	0 14 26 30 114 126 140 150 170 180 194 206 290 294 306 320	340734706536
TPT(14)	1267582482287046857	0 2 42 44 114 116 120 122 150 152 204 206 252 254	350616971070
STPT(10)	1267582491629074589	0 2 42 44 90 92 138 140 180 182	359958998802
SPT(16)	1267582521127196831	0 12 30 56 86 96 98 152 186 240 242 252 282 308 326 338	389457121044
STPT(10)	1267582596738935759	0 2 18 20 60 62 102 104 120 122	465068859972