Prime p₀= 2671001408098221851 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 106 2 10 2 10 2 16 2 16 2 (?)
a_n: 0 2 78 80 186 188 198 200 210 212 228 230 246 248
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: 248
Found by: JayPi
db: batch=82, k=14, 76 106 10 10 16 16

SPT(16)	2670999647675458573	0 24 28 36 60 108 136 138 286 288 316 364 388 396 400 424	-1760422763278
SPT(16)	2670999934956313379	0 12 20 60 68 152 168 170 210 212 228 312 320 360 368 380	-1473141908472
SPT(16)	2670999945628548089	0 14 20 24 84 98 108 128 234 254 264 278 338 342 348 362	-1462469673762
SPT(16)	2671000377690799313	0 38 54 68 80 120 150 158 186 194 224 264 276 290 306 344	-1030407422538
STPT(10)	2671000677962033927	0 2 42 44 72 74 102 104 144 146	-730136187924
TPT(14)	2671000933068878747	0 2 54 56 120 122 150 152 204 206 210 212 240 242	-475029343104
SPT(16)	2671002367722336181	0 10 30 66 72 132 162 172 216 226 256 316 322 358 378 388	959624114330
SPT(16)	2671002498841289681	0 90 120 146 168 180 186 210 236 260 266 278 300 326 356 446	1090743067830
STPT(10)	2671003222013337707	0 2 12 14 42 44 72 74 84 86	1813915115856
STPT(10)	2671003516999039721	0 2 36 38 168 170 300 302 336 338	2108900817870
SPT(16)	2671004283480833681	0 2 38 62 78 86 140 212 216 288 342 350 366 390 426 428	2875382611830