• Deleting all the even digits from 2⁴⁰¹³ we obtain a prime of 610 digits.

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4013 has 2 divisors, whose sum is σ = 4014. Its totient is φ = 4012.

The previous prime is 4007. The next prime is 4019. The reversal of 4013 is 3104.

It is a balanced prime because it is at equal distance from previous prime (4007) and next prime (4019).

It can be written as a sum of positive squares in only one way, i.e., 3844 + 169 = 62^2 + 13^2 .

It is a cyclic number.

It is a de Polignac number, because none of the positive numbers 2^k-4013 is a prime.

It is a super-2 number, since 2×4013² = 32208338, which contains 22 as substring.

It is a plaindrome in base 14.

It is a nialpdrome in base 8.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (4019) by changing a digit.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 2006 + 2007.

It is an arithmetic number, because the mean of its divisors is an integer number (2007).

It is an amenable number.

4013 is a deficient number, since it is larger than the sum of its proper divisors (1).

4013 is an equidigital number, since it uses as much as digits as its factorization.

4013 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 12, while the sum is 8.

The square root of 4013 is about 63.3482438588. The cubic root of 4013 is about 15.8911887681.

Adding to 4013 its reverse (3104), we get a palindrome (7117).

Subtracting from 4013 its reverse (3104), we obtain a palindrome (909).

It can be divided in two parts, 401 and 3, that added together give a palindrome (404).

The spelling of 4013 in words is "four thousand, thirteen".