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OK, you've got us. The jig is up. There is no use for absurdly large prime numbers—yet (we’ll explain that eventually). Slightly less ludicrous prime numbers do have a point, which we'll describe here.
One modern day instance of practical use for prime numbers is in RSA encryption, which allows two parties to pass secret messages back and forth using independent encryption and decryption codes. In RSA, someone who wants to receive a private message will publish a product of two large prime numbers as their "public key," which senders can use to encrypt messages intended for the key publisher.