509 has 2 divisors, whose sum is σ = 510. Its totient is φ = 508.

The previous prime is 503. The next prime is 521. The reversal of 509 is 905.

509 = 12^{2} + 13^{2} + 14^{2}.

509 is nontrivially palindromic in base 4.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 484 + 25 = 22^2 + 5^2 .

It is a cyclic number.

It is a de Polignac number, because none of the positive numbers 2^{k}-509 is a prime.

It is a Sophie Germain prime.

It is a Chen prime.

It is an alternating number because its digits alternate between odd and even.

509 is a modest number, since divided by 9 gives 5 as remainder.

It is a Curzon number.

It is a plaindrome in base 15.

It is a nialpdrome in base 8.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 493 and 502.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (503) by changing a digit.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 254 + 255.

It is an arithmetic number, because the mean of its divisors is an integer number (255).

It is an amenable number.

509 is a deficient number, since it is larger than the sum of its proper divisors (1).

509 is an equidigital number, since it uses as much as digits as its factorization.

509 is an evil number, because the sum of its binary digits is even.

The product of its (nonzero) digits is 45, while the sum is 14.

The square root of 509 is about 22.5610283454. The cubic root of 509 is about 7.9843443827.

Subtracting from 509 its product of nonzero digits (45), we obtain a palindrome (464).

The spelling of 509 in words is "five hundred nine", and thus it is an aban number and an oban number.

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