Prime p₀= 813864873117418457 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 10 2 28 2 94 2 40 2 58 2 (?)
a_n: 0 2 12 14 24 26 54 56 150 152 192 194 252 254
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: 254
Found by: Theadalus
db: batch=73, k=14, 10 10 28 94 40 58

STPT(10)	813864573247441907	0 2 42 44 72 74 102 104 144 146	-299869976550
SPT(16)	813864580773010231	0 6 10 28 70 100 142 166 192 216 258 288 330 348 352 358	-292344408226
SPT(16)	813864661648199809	0 22 42 88 124 168 174 228 274 328 334 378 414 460 480 502	-211469218648
SPT(13)	813864710755686911	0 12 60 102 132 168 180 192 228 258 300 348 360	-162361731546
SPT(16)	813864763427954573	0 24 26 38 44 80 84 114 140 170 174 210 216 228 230 254	-109689463884
STPT(12)	813864804645016769	0 2 12 14 72 74 78 80 138 140 150 152	-68472401688
SPT(16)	813865938099672569	0 14 24 48 90 128 210 234 248 272 354 392 434 458 468 482	1064982254112
SPT(16)	813865968446057099	0 2 42 80 132 158 174 210 212 248 264 290 342 380 420 422	1095328638642
SPT(16)	813866131133763431	0 38 50 138 152 182 192 240 260 308 318 348 362 450 462 500	1258016344974
STPT(10)	813866384970592769	0 2 12 14 30 32 48 50 60 62	1511853174312
STPT(10)	813866484799710239	0 2 18 20 30 32 42 44 60 62	1611682291782