Prime p₀= 865686180172579397 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 70 2 160 2 28 2 136 2 28 2 (?)
a_n: 0 2 60 62 132 134 294 296 324 326 462 464 492 494
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: 494
Found by: Frank [NT]
db: batch=73, k=14, 58 70 160 28 136 28

SPT(16)	865684521532333171	0 18 30 82 102 120 126 130 138 142 148 166 186 238 250 268	-1658640246226
SPT(16)	865685456087759443	0 16 24 48 94 108 118 136 138 156 166 180 226 250 258 274	-724084819954
SPT(16)	865685653112208001	0 12 16 40 72 112 126 132 190 196 210 250 282 306 310 322	-527060371396
STPT(12)	865685815548451967	0 2 12 14 54 56 60 62 102 104 114 116	-364624127430
SPT(16)	865686086092240073	0 24 50 78 84 96 146 168 176 198 248 260 266 294 320 344	-94080339324
SPT(16)	865686135308054143	0 28 88 154 160 168 178 180 208 210 220 228 234 300 360 388	-44864525254
SPT(16)	865686210522254981	0 6 32 80 90 132 140 146 186 192 200 242 252 300 326 332	30349675584
STPT(10)	865686262649473019	0 2 18 20 30 32 42 44 60 62	82476893622
SPT(16)	865686594424709963	0 20 24 66 90 156 240 248 306 314 398 464 488 530 534 554	414252130566
STPT(10)	865687042161863357	0 2 42 44 72 74 102 104 144 146	861989283960
TPT(14)	865687147007565851	0 2 36 38 66 68 78 80 150 152 258 260 300 302	966834986454