820321 has 2 divisors, whose sum is σ = 820322. Its totient is φ = 820320.

The previous prime is 820319. The next prime is 820331. The reversal of 820321 is 123028.

It is a happy number.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 819025 + 1296 = 905^2 + 36^2 .

It is a cyclic number.

It is not a de Polignac number, because 820321 - 2¹ = 820319 is a prime.

Together with 820319, it forms a pair of twin primes.

It is an Ulam number.

It is a junction number, because it is equal to n+sod(n) for n = 820295 and 820304.

It is not a weakly prime, because it can be changed into another prime (820331) 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 as a sum of consecutive naturals, namely, 410160 + 410161.

It is an arithmetic number, because the mean of its divisors is an integer number (410161).

2⁸²⁰³²¹ is an apocalyptic number.

It is an amenable number.

820321 is a deficient number, since it is larger than the sum of its proper divisors (1).

820321 is an equidigital number, since it uses as much as digits as its factorization.

820321 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 96, while the sum is 16.

The square root of 820321 is about 905.7157390705. The cubic root of 820321 is about 93.6112281682.

Adding to 820321 its reverse (123028), we get a palindrome (943349).

The spelling of 820321 in words is "eight hundred twenty thousand, three hundred twenty-one".