TITLE: Every integer greater than 1 is divisible by at least one prime. Can anyone please express this in logical notation
QUESTION [0 upvotes]: Every integer greater than 1 is divisible by at least one prime.
Can anyone please express this in logical notation

REPLY [0 votes]: Using these auxiliary predicates respectively for divisibility and primality:

$(m ~|~ n) \equiv \exists k: k* m = n$,
$Prime(n) \equiv (n > 1) \land\forall m( m ~|~n \rightarrow (m = n ~\lor~ m = 1))$,

you can express it as follows:

$\forall n \in \mathbb{Z}(n > 1 \rightarrow \exists m \in \mathbb{N}: Prime(m) ~\land~ m ~|~ n)$
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