Prime p₀= 4092749865807811301 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 16 2 22 2 16 2 10 2 28 2 (?)
a_n: 0 2 18 20 36 38 60 62 78 80 90 92 120 122
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: 122
Found by: [AF>WildWildWest]Sebastien
db: batch=84, k=14, 16 16 22 16 10 28

SPT(16)	4092749068762905503	0 24 68 78 108 138 164 168 236 240 266 296 326 336 380 404	-797044905798
SPT(16)	4092749191089948031	0 88 102 108 166 196 222 238 240 256 282 312 370 376 390 478	-674717863270
TPT(14)	4092749313959631317	0 2 12 14 24 26 54 56 102 104 114 116 192 194	-551848179984
STPT(10)	4092749601097795607	0 2 30 32 72 74 114 116 144 146	-264710015694
SPT(16)	4092749707932653983	0 10 36 48 64 150 186 208 216 238 274 360 376 388 414 424	-157875157318
SPT(16)	4092749789081393213	0 30 96 98 134 140 180 204 230 254 294 300 336 338 404 434	-76726418088
SPT(16)	4092750197081681437	0 16 60 66 100 112 120 180 196 256 264 276 310 316 360 376	331273870136
STPT(10)	4092750251155918019	0 2 48 50 90 92 132 134 180 182	385348106718
SPT(16)	4092750491358333653	0 24 36 78 90 116 144 210 224 290 318 344 356 398 410 434	625550522352
SPT(13)	4092750542742079601	0 36 126 138 168 258 318 378 468 498 510 600 636	676934268300
STPT(10)	4092750545774243159	0 2 78 80 120 122 162 164 240 242	679966431858