1013 has 2 divisors, whose sum is σ = 1014. Its totient is φ = 1012.

The previous prime is 1009. The next prime is 1019. The reversal of 1013 is 3101.

1013 is nontrivially palindromic in base 14.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 529 + 484 = 23^2 + 22^2 .

It is a cyclic number.

It is not a de Polignac number, because 1013 - 2^{2} = 1009 is a prime.

It is a Sophie Germain prime.

1013 is an undulating number in base 14.

It is a Curzon number.

It is the 8-th primeval number, because it sets a new record (14) in the number of distinct primes that is it possible to write using its digits.

It is a plaindrome in base 9, base 13 and base 15.

It is a nialpdrome in base 4 and base 11.

It is a zygodrome in base 4.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 988 and 1006.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (1019) by changing a digit.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 506 + 507.

It is equal to the Eulerian number *A*(10, 1).

It is an arithmetic number, because the mean of its divisors is an integer number (507).

1013 is the 23-rd centered square number.

It is an amenable number.

1013 is a deficient number, since it is larger than the sum of its proper divisors (1).

1013 is an equidigital number, since it uses as much as digits as its factorization.

1013 is an evil number, because the sum of its binary digits is even.

The product of its (nonzero) digits is 3, while the sum is 5.

The square root of 1013 is about 31.8276609257. The cubic root of 1013 is about 10.0431469001.

The spelling of 1013 in words is "one thousand, thirteen".

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