Prime p₀= 2097858524598859667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 58 2 10 2 106 2 16 2 28 2 (?)
a_n: 0 2 12 14 72 74 84 86 192 194 210 212 240 242
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: 242
Found by: Ben
db: batch=80, k=14, 10 58 10 106 16 28

STPT(10)	2097857813257951091	0 2 6 8 48 50 90 92 96 98	-711340908576
TPT(14)	2097858081490334477	0 2 12 14 72 74 84 86 114 116 150 152 210 212	-443108525190
TPT(14)	2097858175578549029	0 2 18 20 72 74 90 92 270 272 282 284 372 374	-349020310638
STPT(10)	2097858266836838321	0 2 6 8 48 50 90 92 96 98	-257762021346
SPT(16)	2097858369450769043	0 18 44 60 84 108 128 140 174 186 206 230 254 270 296 314	-155148090624
SPT(16)	2097858476089814327	0 32 42 80 96 162 182 222 224 264 284 350 366 404 414 446	-48509045340
SPT(16)	2097858590620002751	0 16 36 46 52 72 76 88 90 102 106 126 132 142 162 178	66021143084
STPT(10)	2097858648611556539	0 2 42 44 60 62 78 80 120 122	124012696872
STPT(10)	2097859405480886777	0 2 30 32 72 74 114 116 144 146	880882027110
SPT(16)	2097859565016336113	0 6 48 66 90 128 144 146 168 170 186 224 248 266 308 314	1040417476446
TPT(14)	2097860240014221281	0 2 60 62 126 128 198 200 228 230 258 260 300 302	1715415361614