Prime p₀= 2680398786985309667 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 52 2 34 2 88 2 70 2 40 2 16 2 (?)
a_n: 0 2 54 56 90 92 180 182 252 254 294 296 312 314
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: 314
Found by: [SG-2W]Kurzer
db: batch=82, k=14, 52 34 88 70 40 16

SPT(16)	2680397680719079931	0 26 30 80 86 102 140 192 200 252 290 306 312 362 366 392	-1106266229736
TPT(14)	2680397720994274529	0 2 42 44 78 80 108 110 138 140 150 152 162 164	-1065991035138
TPT(14)	2680398433318943081	0 2 96 98 120 122 138 140 180 182 246 248 258 260	-353666366586
SPT(16)	2680398535545197461	0 16 22 66 88 100 102 126 172 196 198 210 232 276 282 298	-251440112206
SPT(16)	2680398650929956227	0 12 60 74 84 102 140 150 194 204 242 260 270 284 332 344	-136055353440
STPT(10)	2680398653640309629	0 2 18 20 30 32 42 44 60 62	-133345000038
SPT(16)	2680399346281249057	0 114 136 150 156 192 196 220 306 330 334 370 376 390 412 526	559295939390
STPT(10)	2680399487485094729	0 2 12 14 90 92 168 170 180 182	700499785062
SPT(16)	2680399705033955659	0 34 124 198 208 294 300 328 384 412 418 504 514 588 678 712	918048645992
SPT(16)	2680399853593419667	0 42 66 180 196 204 220 240 316 336 352 360 376 490 514 556	1066608110000
STPT(10)	2680400135436343289	0 2 12 14 30 32 48 50 60 62	1348451033622