Prime p₀= 2472092126956951691 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 16 2 28 2 22 2 106 2 28 2 (?)
a_n: 0 2 78 80 96 98 126 128 150 152 258 260 288 290
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: 290
Found by: Roadranner
db: batch=82, k=14, 76 16 28 22 106 28

SPT(16)	2472090549723222017	0 2 6 14 20 62 84 102 104 122 144 186 192 200 204 206	-1577233729674
SPT(16)	2472090736838189227	0 4 40 70 90 144 154 190 234 270 280 334 354 384 420 424	-1390118762464
SPT(16)	2472090965975951501	0 12 20 26 56 62 80 102 110 132 150 156 186 192 200 212	-1160981000190
SPT(16)	2472091036386352877	0 60 72 86 104 174 194 216 290 312 332 402 420 434 446 506	-1090570598814
SPT(16)	2472091487863771351	0 18 28 30 90 106 142 160 168 186 222 238 298 300 310 328	-639093180340
SPT(16)	2472091675975534009	0 22 28 78 108 112 220 244 348 372 480 484 514 564 570 592	-450981417682
STPT(10)	2472092376511025627	0 2 60 62 102 104 144 146 204 206	249554073936
TPT(14)	2472092414252804909	0 2 12 14 60 62 168 170 192 194 210 212 222 224	287295853218
TPT(14)	2472092432947608239	0 2 30 32 72 74 138 140 150 152 192 194 198 200	305990656548
STPT(10)	2472092476017006497	0 2 12 14 72 74 132 134 144 146	349060054806
SPT(20)	2472092654808329569	0 64 78 100 102 142 148 150 168 172 210 214 232 234 240 280 282 304 318 382	527851377878