Prime p₀= 2004322110262311557 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 172 2 4 2 28 2 52 2 34 2 40 2 (?)
a_n: 0 2 174 176 180 182 210 212 264 266 300 302 342 344
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: 344
Found by: Landjunge
db: batch=80, k=14, 172 4 28 52 34 40

SPT(16)	2004321170983304179	0 10 12 30 40 114 144 168 184 208 238 312 322 340 342 352	-939279007378
SPT(16)	2004321660448262863	0 10 16 24 58 70 148 154 180 186 264 276 310 318 324 334	-449814048694
SPT(16)	2004321689894101009	0 18 42 70 154 160 168 234 238 304 312 318 402 430 454 472	-420368210548
SPT(16)	2004322006942548781	0 52 210 222 228 250 262 298 342 378 390 412 418 430 588 640	-103319762776
TPT(14)	2004322101053683247	0 2 42 44 102 104 114 116 132 134 300 302 354 356	-9208628310
SPT(16)	2004322108279139359	0 34 40 42 60 84 102 138 154 190 208 232 250 252 258 292	-1983172198
SPT(16)	2004322743573200917	0 16 54 60 94 130 210 234 256 280 360 396 430 436 474 490	633310889360
SPT(16)	2004322991590460257	0 30 66 84 90 94 114 210 226 322 342 346 352 370 406 436	881328148700
STPT(10)	2004323097553006091	0 2 36 38 78 80 120 122 156 158	987290694534
TPT(14)	2004323615863883849	0 2 42 44 150 152 162 164 192 194 300 302 342 344	1505601572292
SPT(16)	2004323632109954513	0 44 78 108 114 144 180 186 218 224 260 290 296 326 360 404	1521847642956