Prime p₀= 4044855408973640927 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 46 2 130 2 16 2 28 2 10 2 (?)
a_n: 0 2 24 26 72 74 204 206 222 224 252 254 264 266
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: 266
Found by: Alnitak2019
db: batch=84, k=14, 22 46 130 16 28 10

STPT(10)	4044854401557676697	0 2 42 44 72 74 102 104 144 146	-1007415964230
SPT(16)	4044854430627039187	0 12 30 60 64 70 100 112 114 126 156 162 166 196 214 226	-978346601740
SPT(16)	4044854572267891757	0 44 56 90 92 96 134 176 180 222 260 264 266 300 312 356	-836705749170
STPT(10)	4044854672687643509	0 2 30 32 60 62 90 92 120 122	-736285997418
SPT(16)	4044854799230500961	0 6 18 68 72 102 122 132 206 216 236 266 270 320 332 338	-609743139966
SPT(16)	4044854850560803681	0 36 90 112 132 138 142 178 180 216 220 226 246 268 322 358	-558412837246
SPT(18)	4044855635464561847	0 44 56 114 122 140 152 186 194 312 320 354 366 384 392 450 462 506	226490920920
SPT(13)	4044855890912765707	0 6 42 60 102 120 126 132 150 192 210 246 252	481939124780
STPT(10)	4044856206469118039	0 2 18 20 30 32 42 44 60 62	797495477112
SPT(16)	4044856220933083007	0 74 92 126 132 174 176 182 204 210 212 254 260 294 312 386	811959442080
SPT(16)	4044856355179091581	0 12 52 72 120 126 142 156 202 216 232 238 286 306 346 358	946205450654