Prime p₀= 775656461273850257 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 136 2 16 2 10 2 16 2 22 2 (?)
a_n: 0 2 24 26 162 164 180 182 192 194 210 212 234 236
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: 236
Found by: [SG]FX
db: batch=73, k=14, 22 136 16 10 16 22

SPT(16)	775655531638780459	0 24 42 64 78 108 142 148 234 240 274 304 318 340 358 382	-929635069798
SPT(16)	775655901939062731	0 12 46 82 90 112 126 130 138 142 156 178 186 222 256 268	-559334787526
STPT(10)	775655915379990011	0 2 6 8 48 50 90 92 96 98	-545893860246
STPT(12)	775655930559604229	0 2 18 20 42 44 78 80 102 104 120 122	-530714246028
SPT(16)	775655999849485943	0 18 48 86 114 116 128 138 146 156 168 170 198 236 266 284	-461424364314
STPT(10)	775656187497137069	0 2 12 14 30 32 48 50 60 62	-273776713188
SPT(16)	775656530069485777	0 76 84 94 114 172 196 202 234 240 264 322 342 352 360 436	68795635520
STPT(10)	775656581576576171	0 2 90 92 168 170 246 248 336 338	120302725914
STPT(10)	775656798279273941	0 2 30 32 60 62 90 92 120 122	337005423684
STPT(10)	775657091148213851	0 2 90 92 150 152 210 212 300 302	629874363594
STPT(10)	775657512115079327	0 2 30 32 42 44 54 56 84 86	1050841229070