65537 has 2 divisors, whose sum is σ = 65538. Its totient is φ = 65536.

The previous prime is 65521. The next prime is 65539. The reversal of 65537 is 73556.

65537 is nontrivially palindromic in base 2, base 4 and base 16.

It is a Cunningham number, because it is equal to 2¹⁶+1.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 65536 + 1 = 256^2 + 1^2 .

It is a cyclic number.

It is not a de Polignac number, because 65537 - 2⁴ = 65521 is a prime.

Together with 65539, it forms a pair of twin primes.

It is a Chen prime.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 65537.

It is not a weakly prime, because it can be changed into another prime (65539) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a good prime.

It is a Pierpont prime, being equal to 2¹⁶ ⋅ 3⁰ + 1.

In principle, a polygon with 65537 sides can be constructed with ruler and compass.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 32768 + 32769.

It is an arithmetic number, because the mean of its divisors is an integer number (32769).

It is a Proth number, since it is equal to 1 ⋅ 2¹⁶ + 1 and 1 < 2¹⁶.

2⁶⁵⁵³⁷ is an apocalyptic number.

It is an amenable number.

65537 is a deficient number, since it is larger than the sum of its proper divisors (1).

65537 is an equidigital number, since it uses as much as digits as its factorization.

65537 is an evil number, because the sum of its binary digits is even.

The product of its digits is 3150, while the sum is 26.

The square root of 65537 is about 256.0019531175. The cubic root of 65537 is about 40.3176786609.

The spelling of 65537 in words is "sixty-five thousand, five hundred thirty-seven".