Here are patterns and proofs I have collected for the reigns of Queen Anne and for George I.

In the first 3 cases, these pieces were made under the Master of the Mint at the time , Sir Isaac Newton. This was his day job when he wasnt figuring out the physical laws of the universe.

I would be less than surprised if the 1713 and 1717 farthings shown here were personally handled by him as the quantities minted were miniscule. No currency farthings were minted during the reign of Queen Anne (r 1702-1714). This was due to the insistence of influential people to make the farthings out of pure copper, but at that time there was no means to reliably do so. They were subjected to the "hammer test" of the time, and too high a percentage of pieces subjected to the blow cracked or split. As to the copper piece shown, rumours of its rarity had persisted for decades, to the point where murder was attempted on at least one occasion in the hopes of obtaining one. It ended up that the rumours were incorrect, but well less than 1000 were probably made. 

As to the 1713 silver piece, Peck variety 747, this is very rare. the 1717 lacquered proof is from the collection of Colin Cooke, who amassed probably the greatest collection of farthings of all time. This piece is extremely rare, with likely less than 10 made.