Prime p₀= 2563458361244615759 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 28 2 82 2 16 2 136 2 10 2 (?)
a_n: 0 2 108 110 138 140 222 224 240 242 378 380 390 392
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: 392
Found by: JayPi
db: batch=82, k=14, 106 28 82 16 136 10

SPT(16)	2563456510126579117	0 66 72 124 136 154 156 186 190 220 222 240 252 304 310 376	-1851118036642
TPT(14)	2563456941095144819	0 2 30 32 60 62 102 104 132 134 138 140 168 170	-1420149470940
STPT(10)	2563457136192024617	0 2 150 152 210 212 270 272 420 422	-1225052591142
SPT(16)	2563457199618441631	0 30 36 58 60 66 82 88 120 126 142 148 150 172 178 208	-1161626174128
SPT(16)	2563457537680042037	0 14 24 116 140 150 192 236 240 284 326 336 360 452 462 476	-823564573722
STPT(10)	2563458128259713987	0 2 30 32 42 44 54 56 84 86	-232984901772
SPT(16)	2563458437307684451	0 16 52 120 138 150 162 168 190 196 208 220 238 306 342 358	76063068692
STPT(10)	2563459007981592731	0 2 6 8 48 50 90 92 96 98	646736976972
SPT(16)	2563459137770386057	0 16 34 42 66 126 166 184 192 210 250 310 334 342 360 376	776525770298
SPT(16)	2563459481175975203	0 20 66 96 98 104 120 204 350 434 450 456 458 488 534 554	1119931359444
STPT(10)	2563459539192939857	0 2 30 32 42 44 54 56 84 86	1177948324098