821 has 2 divisors, whose sum is σ = 822. Its totient is φ = 820.

The previous prime is 811. The next prime is 823. The reversal of 821 is 128.

821 is nontrivially palindromic in base 12.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 625 + 196 = 25^2 + 14^2 .

It is a cyclic number.

It is not a de Polignac number, because 821 - 2⁶ = 757 is a prime.

Together with 823, it forms a pair of twin primes.

It is a Chen prime.

It is a magnanimous number.

It is a pancake number, because a pancake can be divided into 821 parts by 40 straight cuts.

821 is an undulating number in base 12.

It is a plaindrome in base 6, base 9, base 15 and base 16.

It is a nialpdrome in base 10.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 821.

It is not a weakly prime, because it can be changed into another prime (823) by changing a digit.

It is a good prime.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 410 + 411.

It is an arithmetic number, because the mean of its divisors is an integer number (411).

It is an amenable number.

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

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

821 is an evil number, because the sum of its binary digits is even.

The product of its digits is 16, while the sum is 11.

The square root of 821 is about 28.6530975638. The cubic root of 821 is about 9.3637049156.

Adding to 821 its reverse (128), we get a palindrome (949).

The spelling of 821 in words is "eight hundred twenty-one", and thus it is an aban number.