Prime p₀= 395895194687953097 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 82 2 34 2 10 2 100 2 28 2 (?)
a_n: 0 2 90 92 174 176 210 212 222 224 324 326 354 356
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: 356
Found by: Cruncher Pete
db: batch=70, k=14, 88 82 34 10 100 28

SPT(14)	395895131587107661	0 40 106 112 160 190 210 292 312 342 390 396 462 502	-63100845436
TPT(12)	395895136947742739	0 2 72 74 102 104 108 110 180 182 192 194	-57740210358
SPT(14)	395895155954632309	0 22 48 52 82 100 114 118 132 150 180 184 210 232	-38733320788
SPT(14)	395895158815842187	0 12 40 42 46 52 126 130 204 210 214 216 244 256	-35872110910
SPT(14)	395895168544794827	0 6 42 44 80 84 96 140 152 156 192 194 230 236	-26143158270
SPT(14)	395895168746000551	0 28 78 82 96 108 118 180 190 202 216 220 270 298	-25941952546
SPT(14)	395895211590488593	0 36 46 60 78 90 144 190 244 256 274 288 298 334	16902535496
TPT(12)	395895215028034457	0 2 150 152 180 182 222 224 282 284 324 326	20340081360
SPT(14)	395895222096574091	0 30 38 48 56 66 92 126 152 162 170 180 188 218	27408620994
TPT(12)	395895226026566087	0 2 24 26 42 44 84 86 150 152 162 164	31338612990
SPT(14)	395895238255542719	0 24 38 42 50 72 74 78 80 102 110 114 128 152	43567589622