What did Shakespeare mean in King Richard III when he said that ‘G’ Of Edward’s heirs the murderer shall be?

Question

Plots have I laid, inductions dangerous,
By drunken prophecies, libels and dreams,
To set my brother Clarence and the King
In deadly hate, the one against the other:
And if King Edward be as true and just
As I am subtle, false and treacherous,
This day should Clarence closely be mew’d up,
About a prophecy, which says that ‘G’
Of Edward’s heirs the murderer shall be –
Dive, thoughts, down to my soul: here Clarence comes.
(Spoken by Richard (Act 1, Scene 1))

In King Richard III by Shakespeare the above sentences are part of the soliloquy of Richard III, son of King Edward. Now my question: when he said alone

This day should Clarence closely be mew’d up,
About a prophecy, which says that ‘G’
Of Edward’s heirs the murderer shall be –
Dive, thoughts, down to my soul: here Clarence comes.

What did he mean by 'G'? Is that the first letter of his name prophesized by the three witches later?

Answer 1

Richard has three older brothers: Edward (king Edward IV); Edmund, Earl of Rutland; and George, Duke of Clarence. If Richard wants to mount the throne, he needs to get rid of his brothers and of his oldest brothers two sons (Edward V and Richard, Duke of York).

This day should Clarence closely be mew’d up,
About a prophecy, which says that ‘G’
Of Edward’s heirs the murderer shall be –

"Mew'd up" means "confined". The reason why Edward IV sends Clarence to the Tower is a prophecy that Shakespeare most likely found in The Mirror for Magistrates:

A prophecy was found which sayd a G,
Of Edwardes children should destruccion be.
Me to be G, because my name was George
My brother thought, and therfor did me hate.
(Quoted in King Richard III, edited by Antony Hammond. The Arden Shakespeare. Methuen, 1981)

In other words, Edward IV's two sons would be killed by someone whose name begins with a "G". This is the prophecy that Clarence talks about a few lines later:

And from the cross-row plucks the letter G.
And says a wizard told him that by G
His issue disinherited should be;
And, for my name of George begins with G,
It follows in his thought that I am he.

Answer 2

It becomes clear a few lines later when Richard is talking to Clarence. Clarence is actually George, the Duke of Clarence. It's all part of Richard's plot to remove Clarence by spreading terrible rumors to set King Edward against him. (Edward is Richard's older brother, incidentally, not his father.)

The prophecy actually comes true later, though--Richard starts out as the Duke of Gloucester, and he has Edward's heirs killed. It's one of those wonderful equivocal things that Shakespeare loved to do.