• 137 can be written using four 4's:

137 has 2 divisors, whose sum is σ = 138. Its totient is φ = 136.

The previous prime is 131. The next prime is 139. The reversal of 137 is 731.

137 is an esthetic number in base 6 and base 16, because in such bases its adjacent digits differ by 1.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 121 + 16 = 11^2 + 4^2 .

137 is a truncatable prime.

It is a cyclic number.

It is not a de Polignac number, because 137 - 2^{6} = 73 is a prime.

Together with 139, it forms a pair of twin primes.

It is a Chen prime.

It is a pancake number, because a pancake can be divided into 137 parts by 16 straight cuts.

It is the 7-th primeval number, because it sets a new record (11) in the number of distinct primes that is it possible to write using its digits.

It is a plaindrome in base 6, base 10, base 11, base 14 and base 16.

It is a nialpdrome in base 8, base 12, base 13 and base 15.

It is a congruent number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 68 + 69.

It is an arithmetic number, because the mean of its divisors is an integer number (69).

It is an amenable number.

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

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

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

The product of its digits is 21, while the sum is 11.

The square root of 137 is about 11.7046999107. The cubic root of 137 is about 5.1551367355.

Adding to 137 its reverse (731), we get a palindrome (868).

It can be divided in two parts, 13 and 7, that multiplied together give a triangular number (91 = T_{13}).

The spelling of 137 in words is "one hundred thirty-seven", and thus it is an aban number.

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