Prime p₀= 1266504953141698979 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 76 2 58 2 58 2 40 2 (?)
a_n: 0 2 60 62 90 92 168 170 228 230 288 290 330 332
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: 332
Found by: Megacruncher
db: batch=77, k=14, 58 28 76 58 58 40

SPT(16)	1266503539552750139	0 50 60 78 110 120 138 180 200 242 260 270 302 320 330 380	-1413588948840
SPT(16)	1266503707900900583	0 20 44 56 66 80 86 140 174 228 234 248 258 270 294 314	-1245240798396
SPT(16)	1266503909161178293	0 156 166 180 264 300 310 328 336 354 364 400 484 498 508 664	-1043980520686
TPT(14)	1266503984946647099	0 2 48 50 78 80 90 92 132 134 162 164 210 212	-968195051880
STPT(10)	1266504288671348939	0 2 42 44 60 62 78 80 120 122	-664470350040
SPT(16)	1266504355559124373	0 6 18 40 54 58 60 90 124 154 156 160 174 196 208 214	-597582574606
STPT(10)	1266505422704629319	0 2 42 44 60 62 78 80 120 122	469562930340
SPT(16)	1266505624041288079	0 4 52 72 82 102 124 144 190 210 232 252 262 282 330 334	670899589100
TPT(14)	1266505731589481321	0 2 168 170 198 200 240 242 246 248 306 308 318 320	778447782342
TPT(14)	1266506324694856559	0 2 18 20 222 224 228 230 312 314 408 410 450 452	1371553157580
SPT(16)	1266506530762150283	0 8 90 114 138 144 170 194 204 228 254 260 284 308 390 398	1577620451304