How old was Hamlet and were I can find it in the story?

Hamlet returns from England where he was supposed to have been killed, according to King Claudius' plan. But he has escaped and is back in Denmark. He is at the castle graveyard. He meets his good friend Horatio there, and they come across two gravediggers, referred to as Clown One and Clown Two. The gravediggers are cheerfully going about their business, throwing up dirt and bones, when they are engaged in conversation by Hamlet and Horatio. Here, in Act 5, Scene 1, is the telling exchange:

HAMLET

...How long hast thou been a grave-maker?

FIRST CLOWN:

Of all the days i' the year, I came to't that day that our last king Hamlet overcame Fortinbras.

HAMLET:

How long is that since?

FIRST CLOWN:

Cannot you tell that? Every fool can tell that. It was the very day that young Hamlet was born—he that is mad, and sent into England.

HAMLET:

Ay, marry, why was he sent into England?

FIRST CLOWN:

Why, because a was mad. A shall recover his wits there; or, if a do not, 'tis no great matter there.

HAMLET:

Why?

FIRST CLOWN:

'Twill not he seen in him there. There the men are as mad as he.

HAMLET:

How came he mad?

FIRST CLOWN:

Very strangely, they say.

HAMLET:

How 'strangely'?

FIRST CLOWN:

Faith, e'en with losing his wits.

HAMLET:

Upon what ground?

FIRST CLOWN:

Why, here in Denmark. I have been sexton here, man and boy, thirty years.

That puts Hamlet's age squarely at thirty. I suppose one could say that he doesn't act his age, but I don't see why not. And it doesn't contradict the fact that Yorick has been dead for twenty-three years; that means that he died when Hamlet was seven... plenty of time for young Hamlet to ride on the jester's back and remember him fondly. And besides, this gravedigger seems to have all his wits about him (and then some), and there's no reason to doubt him. I'm sticking with thirty.