Prime p₀= 796266763820935079 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 118 2 124 2 10 2 58 2 58 2 (?)
a_n: 0 2 72 74 192 194 318 320 330 332 390 392 450 452
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: 452
Found by: Theadalus
db: batch=73, k=14, 70 118 124 10 58 58

SPT(16)	796265951185087843	0 4 6 40 48 70 76 144 160 228 234 256 264 298 300 304	-812635847236
SPT(16)	796266121629824191	0 10 48 78 108 118 132 142 168 178 192 202 232 262 300 310	-642191110888
SPT(16)	796266133486153609	0 30 42 70 88 112 118 174 208 264 270 294 312 340 352 382	-630334781470
SPT(18)	796266299937936661	0 40 52 70 72 96 106 126 192 226 292 312 322 346 348 366 378 418	-463882998418
TPT(14)	796266429073409417	0 2 30 32 54 56 60 62 90 92 114 116 144 146	-334747525662
SPT(18)	796266716986644989	0 44 68 78 114 120 144 180 260 288 368 404 428 434 470 480 504 548	-46834290090
STPT(10)	796266770447668571	0 2 6 8 18 20 30 32 36 38	6626733492
SPT(16)	796267136966562263	0 66 74 114 156 164 200 246 248 294 330 338 380 420 428 494	373145627184
STPT(10)	796267137537561761	0 2 30 32 78 80 126 128 156 158	373716626682
STPT(10)	796267288964061281	0 2 6 8 48 50 90 92 96 98	525143126202
TPT(14)	796267423561894901	0 2 138 140 156 158 168 170 180 182 198 200 276 278	659740959822