Brand new name for a brand new this

(With reference to this post here.)

It’s Alice’s turn and she controls Zimone and has a Fling, an Awaken the Woods, and a fragmentize in hand. She controls 2 Forests (green mana), a Plains (white mana), a mountain (red mana), as well as two lands that are here because they can be sacrificed.

Both Alice and Bob have infinite mana colorless mana made via an artifact that can untap itself for more mana.

Bob has 10 life and controls a Wasteland and two Forests. He has a Nourishing Shoal in hand. He also controls a Battle of Wits and has 250 cards in his library.

To win before Bob does next turn, Alice needs to create a large creature token with Zimone by casting Awaken the Woods, and at end step Fling the token. However, Bob with his infinite mana can cast an arbitrarily large Nourishing Shoal, gaining 10^100 life for example. Alice will try to Fragmentize the Monolith that Bob controls. In response he will generate the mana to cast the giant Shoal and he has to pick a number.

Then, Alice can cast Awaken the Woods to make her land count a prime number that is bigger than 10^100 so that at end of turn, she can Fling the Primo token at Bob’s face. However, once the trigger goes on the stack to make the token, Bob can Wasteland any of Alice’s non basic lands to make her total land count a composite number, making no token.

But, Alice has a trick! She can sacrifice one of her own Havenwood Battle grounds to make her number of lands 2 less in combination with a wasteland. This would allow her to still have a prime number if she chose the larger of a pair of twin primes as her target land count.

The question is this: Can Alice always make a number of lands bigger than any other number so that if Bob destroys one of her lands, she can sacrifice another, remaining at a prime number, and making the token to Fling for the win?

Somebody reblog with that one Sonic fandub meme of "what the FUCK are you talking about", because that is the EXACT emotion I'm experiencing here.

In plain English:

Alice and Bob are playing Magic: the Gathering. If Alice does nothing, Bob will win next turn.

Bob's current position allows him to respond to anything Alice does by doing a Stupid Card Trick that grants him an arbitrarily large number of hit points. By "arbitrarily large", we mean that Bob can pick any number he wants, but it has to be finite; i.e., he can't say "infinity plus one".

Alice's plan is to do something that will break the setup that permits Bob's Stupid Card Trick, thereby forcing him to pick a number of hit points for it to give him before he loses it. Alice will then follow up with her own Stupid Card Trick which allows her to deal an arbitrarily large amount of damage.

So all Alice needs to do is say a number that's larger than the number Bob said, and she wins, right?

Well, not quite. Unlike Bob's Stupid Card Trick, Alice's Stupid Card Trick only works if the number she picks is prime. If anything Bob does in response prevents her from picking a prime number, she does no damage, and Bob wins next turn.

It so happens that Bob does have the ability to respond in a way that reduces the number Alice picked by one. Any prime number minus one is non-prime, so this counters Alice's Stupid Card Trick.

But: Alice has the ability to counter Bob's counter by reducing the number she picked by a further one. This puts her back in business if and only if the prime number she picked in the first place is still prime after having two subtracted from it.

The question is, then: is it guaranteed that Alice can always pick a prime number that's larger than Bob's number and is still prime after having two subtracted from it, no matter what number Bob picks?