• 10541² = 111112681 is the smallest square that contains exactly six digits '1'.

---

10541 has 4 divisors (see below), whose sum is σ = 10752. Its totient is φ = 10332.

The previous prime is 10531. The next prime is 10559. The reversal of 10541 is 14501.

10541 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4, and also an emirpimes, since its reverse is a distinct semiprime: 14501 = 17 ⋅853.

It is a cyclic number.

It is not a de Polignac number, because 10541 - 2⁶ = 10477 is a prime.

It is a super-2 number, since 2×10541² = 222225362, which contains 22 as substring.

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

It is a Duffinian number.

It is a plaindrome in base 8.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (10501) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 20 + ... + 146.

It is an arithmetic number, because the mean of its divisors is an integer number (2688).

2¹⁰⁵⁴¹ is an apocalyptic number.

It is an amenable number.

10541 is a deficient number, since it is larger than the sum of its proper divisors (211).

10541 is an equidigital number, since it uses as much as digits as its factorization.

10541 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 210.

The product of its (nonzero) digits is 20, while the sum is 11.

The square root of 10541 is about 102.6693722587. The cubic root of 10541 is about 21.9260603148.

The spelling of 10541 in words is "ten thousand, five hundred forty-one".