Prime p₀= 959548038404418611 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 4 2 40 2 40 2 4 2 40 2 (?)
a_n: 0 2 30 32 36 38 78 80 120 122 126 128 168 170
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: 170
Found by: suriv
db: batch=76, k=14, 28 4 40 40 4 40

SPT(16)	959547140088265063	0 24 34 48 58 76 90 118 126 154 168 186 196 210 220 244	-898316153548
SPT(16)	959547321128697229	0 10 18 22 60 64 82 174 208 300 318 322 360 364 372 382	-717275721382
SPT(16)	959547603988859437	0 6 40 66 76 94 126 154 156 184 216 234 244 270 304 310	-434415559174
SPT(16)	959547930456451769	0 12 14 72 104 144 164 198 224 258 278 318 350 408 410 422	-107947966842
SPT(16)	959547947683323979	0 58 70 78 88 102 114 172 180 238 250 264 274 282 294 352	-90721094632
STPT(10)	959547959321087579	0 2 18 20 60 62 102 104 120 122	-79083331032
STPT(10)	959548038404418641	0 2 6 8 48 50 90 92 96 98	30
STPT(10)	959548153488276017	0 2 30 32 42 44 54 56 84 86	115083857406
STPT(10)	959548289879806169	0 2 12 14 90 92 168 170 180 182	251475387558
STPT(10)	959548372502177531	0 2 78 80 108 110 138 140 216 218	334097758920
STPT(10)	959548422612049091	0 2 6 8 48 50 90 92 96 98	384207630480