Prime p₀= 3327111445658289827 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 112 2 166 2 76 2 82 2 46 2 10 2 (?)
a_n: 0 2 114 116 282 284 360 362 444 446 492 494 504 506
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: 506
Found by: Roadranner
db: batch=83, k=14, 112 166 76 82 46 10

SPT(16)	3327110519444004361	0 6 18 46 48 96 106 120 136 150 160 208 210 238 250 256	-926214285466
TPT(14)	3327110544763453697	0 2 30 32 60 62 132 134 270 272 300 302 390 392	-900894836130
STPT(10)	3327110634615068669	0 2 18 20 30 32 42 44 60 62	-811043221158
SPT(16)	3327110881107243943	0 10 30 34 40 66 76 138 196 258 268 294 300 304 324 334	-564551045884
SPT(16)	3327110926145740411	0 16 28 72 138 168 222 306 322 406 460 490 556 600 612 628	-519512549416
SPT(16)	3327111107684648447	0 14 30 36 56 66 144 174 242 272 350 360 380 386 402 416	-337973641380
SPT(16)	3327111594803723681	0 26 36 50 92 126 128 138 170 180 182 216 258 272 282 308	149145433854
SPT(16)	3327112036142658097	0 6 10 42 66 76 120 126 130 136 180 190 214 246 250 256	590484368270
SPT(16)	3327112104500961181	0 12 16 52 58 72 118 126 142 150 196 210 216 252 256 268	658842671354
SPT(16)	3327112390754183639	0 2 24 44 60 72 80 144 170 234 242 254 270 290 312 314	945095893812
SPT(16)	3327112830247541851	0 6 18 28 46 90 96 102 106 112 118 162 180 190 202 208	1384589252024