10100113 has 2 divisors, whose sum is σ = 10100114. Its totient is φ = 10100112.

The previous prime is 10100107. The next prime is 10100117. The reversal of 10100113 is 31100101.

It is a happy number.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 8162449 + 1937664 = 2857^2 + 1392^2 .

It is an emirp because it is prime and its reverse (31100101) is a distict prime.

It is a cyclic number.

It is not a de Polignac number, because 10100113 - 2²¹ = 8002961 is a prime.

It is a super-2 number, since 2×10100113² = 204024565225538, which contains 22 as substring.

It is a junction number, because it is equal to n+sod(n) for n = 10100096 and 10100105.

It is not a weakly prime, because it can be changed into another prime (10100117) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 5050056 + 5050057.

It is an arithmetic number, because the mean of its divisors is an integer number (5050057).

Almost surely, 2^10100113 is an apocalyptic number.

It is an amenable number.

10100113 is a deficient number, since it is larger than the sum of its proper divisors (1).

10100113 is an equidigital number, since it uses as much as digits as its factorization.

10100113 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 3, while the sum is 7.

The square root of 10100113 is about 3178.0674945633. The cubic root of 10100113 is about 216.1600394299.

Adding to 10100113 its reverse (31100101), we get a palindrome (41200214).

The spelling of 10100113 in words is "ten million, one hundred thousand, one hundred thirteen".