Prime p₀= 2568736714988896601 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 82 2 118 2 34 2 22 2 124 2 (?)
a_n: 0 2 6 8 90 92 210 212 246 248 270 272 396 398
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: 398
Found by: Penguin
db: batch=82, k=14, 4 82 118 34 22 124

SPT(16)	2568734468995531049	0 14 38 44 78 104 114 120 182 188 198 224 258 264 288 302	-2245993365552
SPT(16)	2568734800459535441	0 6 32 38 90 96 108 122 126 140 152 158 210 216 242 248	-1914529361160
STPT(10)	2568734859600996797	0 2 12 14 42 44 72 74 84 86	-1855387899804
SPT(16)	2568734892430569367	0 16 40 42 46 72 84 94 102 112 124 150 154 156 180 196	-1822558327234
SPT(18)	2568735073164920789	0 20 50 72 134 152 174 188 194 198 204 218 240 258 320 342 372 392	-1641823975812
SPT(16)	2568736643145276053	0 24 36 84 86 90 134 176 198 240 284 288 290 338 350 374	-71843620548
SPT(16)	2568736963131970027	0 12 22 34 36 82 106 124 132 150 174 220 222 234 244 256	248143073426
STPT(10)	2568737010783585251	0 2 36 38 78 80 120 122 156 158	295794688650
STPT(10)	2568737160130497407	0 2 42 44 102 104 162 164 204 206	445141600806
SPT(16)	2568737395544180011	0 30 60 130 138 142 160 172 198 210 228 232 240 310 340 370	680555283410
SPT(13)	2568737473665456539	0 18 24 54 108 120 144 168 180 234 264 270 288	758676559938