313 has 2 divisors, whose sum is σ = 314. Its totient is φ = 312.

The previous prime is 311. The next prime is 317.

It can be divided in two parts, 3 and 13, that added together give a 4-th power (16 = 2^{4}).

It is a happy number.

313 is nontrivially palindromic in base 2, base 10 and base 13.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 169 + 144 = 13^2 + 12^2 .

It is a palprime.

313 is a truncatable prime.

It is a cyclic number.

It is not a de Polignac number, because 313 - 2^{1} = 311 is a prime.

Together with 311, it forms a pair of twin primes.

313 is an undulating number in base 10 and base 13.

It is a plaindrome in base 5, base 9, base 15 and base 16.

It is a nialpdrome in base 12.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 296 and 305.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (311) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 156 + 157.

It is an arithmetic number, because the mean of its divisors is an integer number (157).

313 is the 13-th centered square number.

It is an amenable number.

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

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

313 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 9, while the sum is 7.

The square root of 313 is about 17.6918060130. The cubic root of 313 is about 6.7896613364.

The spelling of 313 in words is "three hundred thirteen", and thus it is an aban number and an oban number.

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