407821 has 2 divisors, whose sum is σ = 407822. Its totient is φ = 407820.

The previous prime is 407807. The next prime is 407833. The reversal of 407821 is 128704.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 372100 + 35721 = 610^2 + 189^2 .

It is a cyclic number.

It is not a de Polignac number, because 407821 - 2⁵ = 407789 is a prime.

It is a super-3 number, since 3×407821³ = 203483880133345983, which contains 333 as substring.

407821 is a lucky number.

It is equal to p₃₄₄₃₈ and since 407821 and 34438 have the same sum of digits, it is a Honaker prime.

It is a junction number, because it is equal to n+sod(n) for n = 407792 and 407801.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (407801) by changing a digit.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 203910 + 203911.

It is an arithmetic number, because the mean of its divisors is an integer number (203911).

2⁴⁰⁷⁸²¹ is an apocalyptic number.

It is an amenable number.

407821 is a deficient number, since it is larger than the sum of its proper divisors (1).

407821 is an equidigital number, since it uses as much as digits as its factorization.

407821 is an odious number, because the sum of its binary digits is odd.

The product of its (nonzero) digits is 448, while the sum is 22.

The square root of 407821 is about 638.6086438500. The cubic root of 407821 is about 74.1577472476.

The spelling of 407821 in words is "four hundred seven thousand, eight hundred twenty-one".