"You know that Gallium is rarer than gold."

This is a bit misleading. Although gallium does not exist in the elemental form (zero oxidation state) naturally, it does occur naturally as gallium (3+ oxidation state) compounds. Gallium is obtained as a by product of mining, processing other metals, etc. Although there may be a lot more gold than gallium in the world, this means specifically "in the world that has been taken out of the ground". The natural abundance in the earth's crust of gold = 0.0000031% and gallium = 0.0019%, so there is a lot more gallium in the earth's crust than gold. As far as I know, there is no gallium mining specifically (no significant demand, yet!).

Just an FYI,

Cheers,

Quan