Prime p₀= 2540354552073003137 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 16 2 40 2 4 2 82 2 4 2 (?)
a_n: 0 2 24 26 42 44 84 86 90 92 174 176 180 182
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: 182
Found by: Paul
db: batch=82, k=14, 22 16 40 4 82 4

SPT(16)	2540353741013721739	0 64 78 138 142 162 172 250 252 330 340 360 364 424 438 502	-811059281398
STPT(10)	2540353749568507421	0 2 6 8 48 50 90 92 96 98	-802504495716
SPT(16)	2540353985012302913	0 26 56 60 116 180 194 224 276 306 320 384 440 444 474 500	-567060700224
SPT(16)	2540354054522198093	0 26 44 60 104 126 134 138 176 180 188 210 254 270 288 314	-497550805044
STPT(10)	2540354404026328007	0 2 30 32 42 44 54 56 84 86	-148046675130
SPT(16)	2540354471379818591	0 2 12 26 50 56 66 92 156 182 192 198 222 236 246 248	-80693184546
SPT(16)	2540355720271556611	0 6 12 22 36 40 78 88 120 130 168 172 186 196 202 208	1168198553474
SPT(16)	2540355910485193961	0 2 12 20 42 146 210 212 240 242 306 410 432 440 450 452	1358412190824
SPT(16)	2540355929260136359	0 12 28 54 64 94 130 142 150 162 198 228 238 264 280 292	1377187133222
STPT(10)	2540356038845384939	0 2 12 14 90 92 168 170 180 182	1486772381802
SPT(16)	2540356306677480701	0 42 78 86 116 146 176 186 212 222 252 282 312 320 356 398	1754604477564