417821 has 2 divisors, whose sum is σ = 417822. Its totient is φ = 417820.

The previous prime is 417811. The next prime is 417839. The reversal of 417821 is 128714.

Added to its reverse (128714) it gives a triangular number (546535 = T₁₀₄₅).

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 319225 + 98596 = 565^2 + 314^2 .

It is a cyclic number.

It is not a de Polignac number, because 417821 - 2¹⁰ = 416797 is a prime.

It is a Sophie Germain prime.

It is a Curzon number.

It is a congruent number.

It is not a weakly prime, because it can be changed into another prime (417811) by changing a digit.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 208910 + 208911.

It is an arithmetic number, because the mean of its divisors is an integer number (208911).

2⁴¹⁷⁸²¹ is an apocalyptic number.

It is an amenable number.

417821 is a deficient number, since it is larger than the sum of its proper divisors (1).

417821 is an equidigital number, since it uses as much as digits as its factorization.

417821 is an evil number, because the sum of its binary digits is even.

The product of its digits is 448, while the sum is 23.

The square root of 417821 is about 646.3907486962. The cubic root of 417821 is about 74.7589893105.

Adding to 417821 its reverse (128714), we get a triangular number (546535 = T₁₀₄₅).

The spelling of 417821 in words is "four hundred seventeen thousand, eight hundred twenty-one".