Prime p₀= 337585922606882687 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 118 2 166 2 16 2 28 2 22 2 (?)
a_n: 0 2 84 86 204 206 372 374 390 392 420 422 444 446
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: 446
Found by: Cruncher Pete
db: batch=70, k=14, 82 118 166 16 28 22

SPT(14)	337585863040969889	0 62 78 80 114 140 162 260 282 308 342 344 360 422	-59565912798
SPT(14)	337585873987337809	0 42 52 54 58 78 120 172 214 234 238 240 250 292	-48619544878
STPT(10)	337585879752945149	0 2 18 20 30 32 42 44 60 62	-42853937538
TPT(12)	337585881750285167	0 2 72 74 84 86 102 104 114 116 150 152	-40856597520
SPT(14)	337585913579030371	0 6 28 72 90 100 210 238 348 358 376 420 442 448	-9027852316
SPT(14)	337585916704087039	0 10 18 28 48 72 94 108 130 154 174 184 192 202	-5902795648
SPT(14)	337585927666921411	0 18 30 52 60 106 130 168 192 238 246 268 280 298	5060038724
SPT(14)	337585941990879977	0 2 20 24 30 66 80 96 110 146 152 156 174 176	19383997290
SPT(14)	337585948199344639	0 18 22 28 40 60 70 90 100 120 132 138 142 160	25592461952
SPT(14)	337585964262745379	0 32 42 102 140 152 194 198 240 252 290 350 360 392	41655862692
TPT(12)	337586008929273281	0 2 36 38 48 50 78 80 90 92 210 212	86322390594