Prime p₀= 2826215144634997721 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 46 2 16 2 58 2 22 2 (?)
a_n: 0 2 60 62 90 92 138 140 156 158 216 218 240 242
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: 242
Found by: JayPi
db: batch=82, k=14, 58 28 46 16 58 22

SPT(16)	2826213925098075947	0 44 50 80 92 134 182 194 252 264 312 354 366 396 402 446	-1219536921774
SPT(16)	2826214178904463801	0 28 48 126 136 156 198 202 216 220 262 282 292 370 390 418	-965730533920
STPT(10)	2826214320951405227	0 2 30 32 42 44 54 56 84 86	-823683592494
SPT(16)	2826214516430756567	0 6 20 36 132 134 156 162 224 230 252 254 350 366 380 386	-628204241154
SPT(16)	2826214525793142997	0 42 64 66 120 144 190 196 210 216 262 286 340 342 364 406	-618841854724
SPT(16)	2826214927372007351	0 48 50 66 98 102 138 180 188 230 266 270 302 318 320 368	-217262990370
SPT(16)	2826215487977417897	0 20 50 92 110 114 140 162 194 216 242 246 264 306 336 356	343342420176
SPT(16)	2826215557587337249	0 22 34 78 88 102 120 148 174 202 220 234 244 288 300 322	412952339528
SPT(16)	2826215558401209581	0 6 32 66 122 132 150 192 266 308 326 336 392 426 452 458	413766211860
TPT(14)	2826215568615611069	0 2 132 134 162 164 198 200 258 260 300 302 330 332	423980613348
TPT(14)	2826216075850991597	0 2 54 56 72 74 90 92 102 104 114 116 144 146	931215993876