Prime p₀= 2668587114815100251 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 136 2 58 2 40 2 100 2 34 2 (?)
a_n: 0 2 78 80 216 218 276 278 318 320 420 422 456 458
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: [SG-FC] hl
db: batch=82, k=14, 76 136 58 40 100 34

STPT(10)	2668585649327176721	0 2 6 8 18 20 30 32 36 38	-1465487923530
SPT(16)	2668586557577352751	0 6 10 36 42 52 70 76 126 132 150 160 166 192 196 202	-557237747500
SPT(16)	2668586779592338391	0 12 50 72 96 108 140 176 252 288 320 332 356 378 416 428	-335222761860
SPT(16)	2668586810742262181	0 30 32 56 80 146 162 182 276 296 312 378 402 426 428 458	-304072838070
STPT(12)	2668586961295380821	0 2 36 38 48 50 78 80 90 92 126 128	-153519719430
STPT(10)	2668587048010639541	0 2 30 32 60 62 90 92 120 122	-66804460710
TPT(14)	2668587198099137141	0 2 66 68 78 80 138 140 156 158 246 248 288 290	83284036890
STPT(10)	2668587274409325077	0 2 12 14 42 44 72 74 84 86	159594224826
SPT(16)	2668587643764429157	0 16 30 46 60 82 84 94 102 112 114 136 150 166 180 196	528949328906
SPT(16)	2668587824974925459	0 12 20 60 90 102 114 132 152 170 182 194 224 264 272 284	710159825208
STPT(10)	2668587908680663157	0 2 24 26 42 44 60 62 84 86	793865562906