 The modal characterization of an essential property of an object as a property that an object must possess fits well with (at least one aspect of) our everyday understanding of the notion of essentiality, which often seems simply to be the notion of necessity. To say that something is essential for something else is typically just to say that the first is necessary for the second. But however well this account fits with (this aspect of) our everyday understanding of essentiality, it has some consequences that may be surprising: this characterization classifies the property of being such that there are infinitely many primes (or, perhaps, being such that there are infinitely many primes if the thing in question is existent) as essential to Socrates (as well as to all other things), since Socrates (like all other things) must have this property. Socrates must have this property for the simple reason that it is necessary that there are infinitely many primes. Moreover, this characterization classifies the property of being the sole member of the unit set \(\{2\}\) as essential to the number 2, given that it is necessary that 2 is the sole member of the unit set \(\{2\}\).