Prime p₀= 1268667892005967109 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 76 2 10 2 100 2 16 2 40 2 (?)
a_n: 0 2 60 62 138 140 150 152 252 254 270 272 312 314
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: mikey
db: batch=77, k=14, 58 76 10 100 16 40

SPT(16)	1268666203229093969	0 18 48 54 62 80 108 144 188 224 252 270 278 284 314 332	-1688776873140
SPT(16)	1268666270962195201	0 10 18 42 46 52 76 118 120 162 186 192 196 220 228 238	-1621043771908
STPT(12)	1268666392741717337	0 2 42 44 54 56 90 92 102 104 144 146	-1499264249772
SPT(16)	1268667044911677683	0 6 74 84 86 96 110 150 230 270 284 294 296 306 374 380	-847094289426
SPT(16)	1268667257148677257	0 60 106 112 172 202 216 232 270 286 300 330 390 396 442 502	-634857289852
STPT(10)	1268667423952302131	0 2 6 8 18 20 30 32 36 38	-468053664978
STPT(10)	1268668042781830697	0 2 30 32 42 44 54 56 84 86	150775863588
STPT(10)	1268668178941336487	0 2 30 32 72 74 114 116 144 146	286935369378
STPT(10)	1268668248146985767	0 2 42 44 72 74 102 104 144 146	356141018658
STPT(10)	1268668267947329069	0 2 18 20 30 32 42 44 60 62	375941361960
TPT(14)	1268668304119511591	0 2 18 20 36 38 48 50 330 332 426 428 468 470	412113544482