Prime p₀= 2681443634735894867 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 58 2 46 2 28 2 40 2 58 2 (?)
a_n: 0 2 42 44 102 104 150 152 180 182 222 224 282 284
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: 284
Found by: JayPi
db: batch=82, k=14, 40 58 46 28 40 58

STPT(12)	2681442596119014449	0 2 12 14 72 74 78 80 138 140 150 152	-1038616880418
SPT(16)	2681442712500483523	0 4 18 28 30 54 124 186 268 330 400 424 426 436 450 454	-922235411344
SPT(16)	2681442746464712933	0 20 30 44 96 126 138 140 294 296 308 338 390 404 414 434	-888271181934
STPT(12)	2681443142741128037	0 2 42 44 54 56 60 62 72 74 114 116	-491994766830
SPT(16)	2681443506312107351	0 12 20 50 72 90 92 140 210 258 260 278 300 330 338 350	-128423787516
SPT(16)	2681443516024281431	0 8 12 42 66 68 90 92 306 308 330 332 356 386 390 398	-118711613436
STPT(10)	2681443677423907577	0 2 24 26 42 44 60 62 84 86	42688012710
SPT(16)	2681443791280281827	0 42 60 74 86 90 126 192 224 290 326 330 342 356 374 416	156544386960
STPT(10)	2681443825033351907	0 2 42 44 72 74 102 104 144 146	190297457040
SPT(16)	2681444385991766987	0 12 56 86 92 146 180 182 210 212 246 300 306 336 380 392	751255872120
SPT(16)	2681444622940297441	0 30 40 42 112 132 156 190 258 292 316 336 406 408 418 448	988204402574