Prime p₀= 554358353409958481 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 82 2 16 2 28 2 106 2 28 2 (?)
a_n: 0 2 66 68 150 152 168 170 198 200 306 308 336 338
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: 338
Found by: emoga
db: batch=57, k=14, 64 82 16 28 106 28

TPT(12)	554358315206687399	0 2 72 74 102 104 132 134 168 170 198 200	-38203271082
SPT(14)	554358318404652709	0 28 48 54 70 90 100 132 142 162 178 184 204 232	-35005305772
TPT(14)	554358322052083511	0 2 18 20 30 32 48 50 156 158 186 188 240 242	-31357874970
TPT(12)	554358322444422227	0 2 30 32 42 44 210 212 240 242 312 314	-30965536254
SPT(14)	554358326969061107	0 42 114 122 146 150 152 234 236 240 264 272 344 386	-26440897374
SPT(14)	554358348171981589	0 12 42 60 90 112 168 172 228 250 280 298 328 340	-5237976892
TPT(12)	554358359057740661	0 2 6 8 90 92 138 140 156 158 228 230	5647782180
SPT(14)	554358370891203209	0 8 30 60 78 80 108 140 168 170 188 218 240 248	17481244728
SPT(14)	554358373727080631	0 8 20 42 60 98 158 192 252 290 308 330 342 350	20317122150
SPT(16)	554358395999958161	0 108 182 210 288 296 306 308 360 362 372 380 458 486 560 668	42589999680
SPT(14)	554358418063396399	0 34 48 84 88 90 118 120 148 150 154 190 204 238	64653437918