3251 has 2 divisors, whose sum is σ = 3252. Its totient is φ = 3250.

The previous prime is 3229. The next prime is 3253. The reversal of 3251 is 1523.

3251 is an esthetic number in base 7, because in such base its adjacent digits differ by 1.

It is a strong prime.

It is an emirp because it is prime and its reverse (1523) is a distict prime.

It is a cyclic number.

It is not a de Polignac number, because 3251 - 2⁶ = 3187 is a prime.

Together with 3253, it forms a pair of twin primes.

It is a Chen prime.

It is a nialpdrome in base 16.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 3251.

It is not a weakly prime, because it can be changed into another prime (3253) by changing a digit.

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

It is a good prime.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 1625 + 1626.

It is an arithmetic number, because the mean of its divisors is an integer number (1626).

2³²⁵¹ is an apocalyptic number.

3251 is the 26-th centered decagonal number.

3251 is a deficient number, since it is larger than the sum of its proper divisors (1).

3251 is an equidigital number, since it uses as much as digits as its factorization.

3251 is an odious number, because the sum of its binary digits is odd.

The product of its digits is 30, while the sum is 11.

The square root of 3251 is about 57.0175411606. The cubic root of 3251 is about 14.8139994150.

Subtracting from 3251 its sum of digits (11), we obtain a triangular number (3240 = T₈₀).

Adding to 3251 its reverse (1523), we get a palindrome (4774).

Subtracting from 3251 its reverse (1523), we obtain a cube (1728 = 12³).

The spelling of 3251 in words is "three thousand, two hundred fifty-one".