Prime p₀= 2356510644395716031 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 88 2 34 2 10 2 40 2 124 2 (?)
a_n: 0 2 60 62 150 152 186 188 198 200 240 242 366 368
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: 368
Found by: Landjunge
db: batch=81, k=14, 58 88 34 10 40 124

SPT(16)	2356508403612431137	0 40 76 130 132 136 144 172 174 202 210 214 216 270 306 346	-2240783284894
STPT(10)	2356508627111502011	0 2 36 38 78 80 120 122 156 158	-2017284214020
SPT(16)	2356508731107246269	0 8 14 80 114 140 198 218 234 254 312 338 372 438 444 452	-1913288469762
STPT(10)	2356508768242248671	0 2 6 8 18 20 30 32 36 38	-1876153467360
TPT(16)	2356510344213099077	0 2 12 14 24 26 54 56 90 92 174 176 222 224 300 302	-300182616954
SPT(16)	2356510642811964763	0 18 36 70 88 106 108 126 148 166 168 186 204 238 256 274	-1583751268
SPT(16)	2356511113673383301	0 8 32 50 56 110 116 176 192 252 258 312 318 336 360 368	469277667270
SPT(16)	2356511457152333711	0 2 60 62 66 90 102 158 240 296 308 332 336 338 396 398	812756617680
SPT(16)	2356511725766002729	0 18 58 70 82 130 138 162 298 322 330 378 390 402 442 460	1081370286698
SPT(16)	2356512270212814761	0 42 50 60 116 132 152 180 182 210 230 246 302 312 320 362	1625817098730
SPT(16)	2356512286204566773	0 6 24 26 30 38 44 56 78 90 96 104 108 110 128 134	1641808850742