Prime p₀= 2668587198099137141 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 64 2 10 2 58 2 16 2 88 2 40 2 (?)
a_n: 0 2 66 68 78 80 138 140 156 158 246 248 288 290
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: 290
Found by: [SG-FC] hl
db: batch=82, k=14, 64 10 58 16 88 40

SPT(16)	2668586557577352751	0 6 10 36 42 52 70 76 126 132 150 160 166 192 196 202	-640521784390
SPT(16)	2668586779592338391	0 12 50 72 96 108 140 176 252 288 320 332 356 378 416 428	-418506798750
SPT(16)	2668586810742262181	0 30 32 56 80 146 162 182 276 296 312 378 402 426 428 458	-387356874960
STPT(12)	2668586961295380821	0 2 36 38 48 50 78 80 90 92 126 128	-236803756320
STPT(10)	2668587048010639541	0 2 30 32 60 62 90 92 120 122	-150088497600
TPT(14)	2668587114815100251	0 2 78 80 216 218 276 278 318 320 420 422 456 458	-83284036890
STPT(10)	2668587274409325077	0 2 12 14 42 44 72 74 84 86	76310187936
SPT(16)	2668587643764429157	0 16 30 46 60 82 84 94 102 112 114 136 150 166 180 196	445665292016
SPT(16)	2668587824974925459	0 12 20 60 90 102 114 132 152 170 182 194 224 264 272 284	626875788318
STPT(10)	2668587908680663157	0 2 24 26 42 44 60 62 84 86	710581526016
STPT(10)	2668587924208438319	0 2 42 44 90 92 138 140 180 182	726109301178