3967 has 2 divisors, whose sum is σ = 3968. Its totient is φ = 3966.

The previous prime is 3947. The next prime is 3989. The reversal of 3967 is 7693.

3967 is nontrivially palindromic in base 16.

It is a weak prime.

3967 is a truncatable prime.

It is a cyclic number.

It is a de Polignac number, because none of the positive numbers 2^k-3967 is a prime.

It is a Carol number, being equal to (2⁶ - 1)² - 2.

It is a lonely number, since its distance to closest prime (3947) sets a new record.

3967 is an undulating number in base 16.

It is a plaindrome in base 12.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (3907) 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, 1983 + 1984.

It is an arithmetic number, because the mean of its divisors is an integer number (1984).

2³⁹⁶⁷ is an apocalyptic number.

3967 is a deficient number, since it is larger than the sum of its proper divisors (1).

3967 is an equidigital number, since it uses as much as digits as its factorization.

3967 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 1134, while the sum is 25.

The square root of 3967 is about 62.9841249840. The cubic root of 3967 is about 15.8302363903.

It can be divided in two parts, 396 and 7, that multiplied together give a palindrome (2772).

The spelling of 3967 in words is "three thousand, nine hundred sixty-seven".