Prime p₀= 4506143215669726931 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 40 2 46 2 28 2 130 2 208 2 (?)
a_n: 0 2 66 68 108 110 156 158 186 188 318 320 528 530
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: 530
Found by: [SG-2W]Kurzer
db: batch=85, k=14, 64 40 46 28 130 208

STPT(10)	4506142157573729339	0 2 42 44 60 62 78 80 120 122	-1058095997592
TPT(14)	4506142676111300501	0 2 6 8 270 272 336 338 396 398 408 410 420 422	-539558426430
STPT(10)	4506143024207252927	0 2 30 32 72 74 114 116 144 146	-191462474004
STPT(10)	4506143027094211157	0 2 12 14 72 74 132 134 144 146	-188575515774
SPT(16)	4506143073623477933	0 36 50 78 84 114 126 180 194 248 260 290 296 324 338 374	-142046248998
SPT(16)	4506143130412472761	0 58 132 136 142 172 240 262 276 298 366 396 402 406 480 538	-85257254170
SPT(16)	4506143605728898691	0 6 32 42 120 132 176 182 210 216 260 272 350 360 386 392	390059171760
SPT(18)	4506143880947434699	0 18 28 30 70 84 88 100 108 130 138 150 154 168 208 210 220 238	665277707768
SPT(16)	4506144462322660463	0 8 36 50 56 98 138 176 180 218 258 300 306 320 348 356	1246652933532
SPT(16)	4506144600073120393	0 28 30 46 58 76 130 148 168 186 240 258 270 286 288 316	1384403393462
SPT(16)	4506144623530776487	0 4 16 24 34 46 60 66 94 100 114 126 136 144 156 160	1407861049556