Prime p₀= 1258726703560012541 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 10 2 28 2 178 2 10 2 4 2 (?)
a_n: 0 2 96 98 108 110 138 140 318 320 330 332 336 338
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: 338
Found by: mcf2020
db: batch=77, k=14, 94 10 28 178 10 4

TPT(14)	1258726227375340991	0 2 36 38 66 68 78 80 156 158 168 170 288 290	-476184671550
STPT(10)	1258726328044025297	0 2 30 32 72 74 114 116 144 146	-375515987244
STPT(10)	1258726335891040109	0 2 18 20 30 32 42 44 60 62	-367668972432
SPT(16)	1258726459197098417	0 50 102 120 126 170 186 236 270 320 336 380 386 404 456 506	-244362914124
STPT(10)	1258726549277850449	0 2 18 20 30 32 42 44 60 62	-154282162092
STPT(10)	1258726670571317219	0 2 18 20 30 32 42 44 60 62	-32988695322
SPT(16)	1258726738937673553	0 10 78 84 106 108 114 130 174 190 196 198 220 226 294 304	35377661012
SPT(16)	1258726814782709929	0 40 42 48 72 90 142 144 208 210 262 280 304 310 312 352	111222697388
SPT(16)	1258726815998067011	0 32 50 156 170 176 182 200 252 270 276 282 296 402 420 452	112438054470
SPT(16)	1258727023254061259	0 68 84 134 138 150 174 188 210 224 248 260 264 314 330 398	319694048718
STPT(10)	1258727212864658819	0 2 42 44 60 62 78 80 120 122	509304646278