What happens when unlimited demand hits supply constraints?

Central banks trading their paper money for gold indicates that gold is more valuable in the eyes of the people who can devalue money through inflation.

In a free market, when demand increases, prices would normally rise to a level that constrains demand.

But central bank demand is unrestrained. No price is too high when you can print money.

The gold (and silver) supply is limited. Central bank demand is unlimited.

The price of gold and silver will increase. Central banks are banking on it.