4167 has 6 divisors (see below), whose sum is σ = 6032. Its totient is φ = 2772.

The previous prime is 4159. The next prime is 4177. The reversal of 4167 is 7614.

Added to its reverse (7614) it gives a triangular number (11781 = T₁₅₃).

It is not a de Polignac number, because 4167 - 2³ = 4159 is a prime.

It is an Ulam number.

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

It is a Duffinian number.

It is a plaindrome in base 15.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (4127) 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 in 5 ways as a sum of consecutive naturals, for example, 223 + ... + 240.

4167 is a Friedman number, since it can be written as 71+4^6, using all its digits and the basic arithmetic operations.

2⁴¹⁶⁷ is an apocalyptic number.

4167 is a deficient number, since it is larger than the sum of its proper divisors (1865).

4167 is a wasteful number, since it uses less digits than its factorization.

4167 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 469 (or 466 counting only the distinct ones).

The product of its digits is 168, while the sum is 18.

The square root of 4167 is about 64.5523043741. The cubic root of 4167 is about 16.0919188384.

Adding to 4167 its reverse (7614), we get a triangular number (11781 = T₁₅₃).

It can be divided in two parts, 4 and 167, that added together give a palindrome (171).

The spelling of 4167 in words is "four thousand, one hundred sixty-seven".