Prime p₀= 2577878791537156337 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 22 2 94 2 142 2 76 2 58 2 (?)
a_n: 0 2 60 62 84 86 180 182 324 326 402 404 462 464
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: 464
Found by: [SG-FC] hl
db: batch=82, k=14, 58 22 94 142 76 58

SPT(16)	2577876944343555703	0 10 36 120 136 156 234 246 274 286 364 384 400 484 510 520	-1847193600634
SPT(16)	2577877293704698717	0 4 6 42 72 120 144 156 160 172 196 244 274 310 312 316	-1497832457620
SPT(20)	2577877617180718289	0 24 30 42 54 72 114 138 152 170 192 210 224 248 290 308 320 332 338 362	-1174356438048
SPT(16)	2577877733458510097	0 72 84 116 132 174 180 222 284 326 332 374 390 422 434 506	-1058078646240
SPT(16)	2577877998416053819	0 12 24 30 40 100 120 150 154 184 204 264 274 280 292 304	-793121102518
TPT(14)	2577878112709065557	0 2 24 26 54 56 72 74 150 152 240 242 264 266	-678828090780
SPT(16)	2577879077690431441	0 28 36 40 58 78 136 156 190 210 268 288 306 310 318 346	286153275104
STPT(10)	2577879152604566429	0 2 12 14 90 92 168 170 180 182	361067410092
STPT(10)	2577879491540563619	0 2 48 50 90 92 132 134 180 182	700003407282
SPT(16)	2577879582686629673	0 8 20 60 78 96 140 156 158 174 218 236 254 294 306 314	791149473336
STPT(10)	2577879709708397837	0 2 30 32 42 44 54 56 84 86	918171241500