Prime p₀= 793578512798044031 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 148 2 58 2 40 2 106 2 58 2 (?)
a_n: 0 2 36 38 186 188 246 248 288 290 396 398 456 458
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: 458
Found by: Conan
db: batch=73, k=14, 34 148 58 40 106 58

SPT(16)	793577151481677371	0 12 42 68 158 176 200 216 272 288 312 330 420 446 476 488	-1361316366660
SPT(16)	793577268399944783	0 20 86 98 108 126 140 150 164 174 188 206 216 228 294 314	-1244398099248
TPT(14)	793577478491026457	0 2 42 44 114 116 174 176 222 224 270 272 384 386	-1034307017574
SPT(16)	793577719362393151	0 28 42 58 90 118 198 222 226 250 330 358 390 406 420 448	-793435650880
SPT(16)	793577900345524001	0 8 32 36 38 50 80 108 110 138 168 180 182 186 210 218	-612452520030
SPT(16)	793578004442919781	0 96 106 120 138 166 196 198 280 282 312 340 358 372 382 478	-508355124250
STPT(10)	793578539350697921	0 2 6 8 18 20 30 32 36 38	26552653890
STPT(10)	793578574641295769	0 2 18 20 30 32 42 44 60 62	61843251738
STPT(10)	793578890497436567	0 2 30 32 42 44 54 56 84 86	377699392536
SPT(16)	793578906927185831	0 18 48 56 60 78 90 102 116 128 140 158 162 170 200 218	394129141800
SPT(16)	793578938172913469	0 2 14 48 80 92 140 150 152 162 210 222 254 288 300 302	425374869438