Prime p₀= 2568534287868140399 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 190 2 106 2 70 2 46 2 10 2 124 2 (?)
a_n: 0 2 192 194 300 302 372 374 420 422 432 434 558 560
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: 560
Found by: JayPi
db: batch=82, k=14, 190 106 70 46 10 124

SPT(16)	2568533316488095469	0 2 30 32 42 50 108 120 122 134 192 200 210 212 240 242	-971380044930
SPT(16)	2568533581426718407	0 22 36 60 64 66 102 106 150 154 190 192 196 220 234 256	-706441421992
SPT(16)	2568533686467017999	0 14 20 30 78 90 104 114 134 144 158 170 218 228 234 248	-601401122400
STPT(10)	2568533716242446387	0 2 30 32 42 44 54 56 84 86	-571625694012
STPT(10)	2568533772415576289	0 2 42 44 60 62 78 80 120 122	-515452564110
STPT(12)	2568533827241423147	0 2 12 14 30 32 54 56 72 74 84 86	-460626717252
STPT(10)	2568534543358157189	0 2 12 14 30 32 48 50 60 62	255490016790
TPT(14)	2568534545226597719	0 2 30 32 78 80 90 92 210 212 228 230 300 302	257358457320
SPT(16)	2568534699654132551	0 6 80 90 146 156 198 222 266 290 332 342 398 408 482 488	411785992152
STPT(10)	2568534777844597139	0 2 42 44 90 92 138 140 180 182	489976456740
SPT(16)	2568535370827062691	0 6 18 42 46 52 66 70 108 112 126 132 136 160 172 178	1082958922292