Prime p₀= 1264820804396973959 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 4 2 160 2 76 2 22 2 (?)
a_n: 0 2 18 20 42 44 48 50 210 212 288 290 312 314
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: 314
Found by: rlacr
db: batch=77, k=14, 16 22 4 160 76 22

SPT(16)	1264820141927460857	0 30 60 134 182 194 204 212 312 320 330 342 390 464 494 524	-662469513102
STPT(10)	1264820181308028011	0 2 6 8 18 20 30 32 36 38	-623088945948
STPT(10)	1264820402491155269	0 2 42 44 90 92 138 140 180 182	-401905818690
SPT(16)	1264820664879695179	0 12 34 90 130 142 144 180 232 268 270 282 322 378 400 412	-139517278780
TPT(14)	1264820735613084047	0 2 12 14 102 104 192 194 210 212 234 236 294 296	-68783889912
STPT(10)	1264820784571239191	0 2 6 8 18 20 30 32 36 38	-19825734768
SPT(16)	1264821045795810571	0 22 46 52 76 78 136 138 160 162 220 222 246 252 276 298	241398836612
SPT(16)	1264821322853174893	0 24 28 78 108 114 120 174 214 268 274 280 310 360 364 388	518456200934
SPT(16)	1264821425481114157	0 30 42 46 52 60 82 100 126 144 166 174 180 184 196 226	621084140198
STPT(10)	1264821530210458679	0 2 18 20 30 32 42 44 60 62	725813484720
SPT(16)	1264821810828299323	0 4 36 46 84 88 96 136 138 178 186 190 228 238 270 274	1006431325364