Prime p₀= 2563266939775760081 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 10 2 100 2 28 2 76 2 46 2 (?)
a_n: 0 2 66 68 78 80 180 182 210 212 288 290 336 338
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: 338
Found by: Penguin
db: batch=82, k=14, 64 10 100 28 76 46

TPT(14)	2563265766485567621	0 2 30 32 36 38 78 80 90 92 258 260 288 290	-1173290192460
STPT(10)	2563265931990652547	0 2 84 86 162 164 240 242 324 326	-1007785107534
STPT(10)	2563265948730962939	0 2 48 50 60 62 72 74 120 122	-991044797142
STPT(10)	2563265992976831267	0 2 30 32 72 74 114 116 144 146	-946798928814
STPT(10)	2563266425458686929	0 2 42 44 60 62 78 80 120 122	-514317073152
TPT(14)	2563266831288643001	0 2 60 62 168 170 198 200 210 212 228 230 240 242	-108487117080
SPT(16)	2563267053415992971	0 6 20 32 48 50 66 78 80 92 108 110 126 138 152 158	113640232890
STPT(10)	2563267228342720967	0 2 12 14 42 44 72 74 84 86	288566960886
SPT(16)	2563267692991202137	0 24 42 142 202 210 234 240 244 250 274 282 342 442 460 484	753215442056
STPT(10)	2563267793296464011	0 2 6 8 18 20 30 32 36 38	853520703930
SPT(16)	2563268182398499441	0 22 60 76 82 106 120 136 162 178 192 216 222 238 276 298	1242622739360