Prime p₀= 2768818597388577761 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 148 2 148 2 4 2 22 2 (?)
a_n: 0 2 30 32 60 62 210 212 360 362 366 368 390 392
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: [B^S]ABoskovich
db: batch=82, k=14, 28 28 148 148 4 22

SPT(16)	2768817940381263787	0 4 22 30 66 90 136 144 202 210 256 280 316 324 342 346	-657007313974
SPT(16)	2768818136777071019	0 18 32 42 84 92 134 144 158 168 210 218 260 270 284 302	-460611506742
SPT(16)	2768818156177712399	0 18 24 62 78 92 98 164 228 294 300 314 330 368 374 392	-441210865362
STPT(10)	2768818364185581707	0 2 24 26 42 44 60 62 84 86	-233202996054
SPT(16)	2768818397462697317	0 6 96 132 170 176 194 264 332 402 420 426 464 500 590 596	-199925880444
STPT(10)	2768818462068893327	0 2 30 32 60 62 90 92 120 122	-135319684434
STPT(10)	2768819004665205389	0 2 42 44 60 62 78 80 120 122	407276627628
SPT(16)	2768819233984340533	0 64 90 96 100 118 120 124 150 154 156 174 178 184 210 274	636595762772
TPT(14)	2768819830234337639	0 2 42 44 102 104 132 134 138 140 168 170 240 242	1232845759878
SPT(16)	2768820173272064243	0 78 296 330 336 356 390 428 468 506 540 560 566 600 818 896	1575883486482
STPT(10)	2768820253213330529	0 2 48 50 90 92 132 134 180 182	1655824752768