In discussing the unique factorization of numbers in Elementary Number Theory, Underwood Dudley devised a new number system:
“Consider the integers 1, 5, 9, 13, 17,…; that is, all integers of the form 
, 
We will call an element of this set prome if it has no divisors other than 1 and itself in the set. For example, 21 is prome, whereas 
is not."
, We will call an element of this set prome if it has no divisors other than 1 and itself in the set. For example, 21 is prome, whereas is not."Write a function to determine whether a number is prome. Take 1 to be not prome.
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Underwood Dudley seems to be prone (prome?) to joking -- as befits anyone bearing such a cromulent name --: these are usually called Hilbert primes or S-primes instead.