78137 has 2 divisors, whose sum is σ = 78138. Its totient is φ = 78136.

The previous prime is 78121. The next prime is 78139. The reversal of 78137 is 73187.

It is a strong prime.

It can be written as a sum of positive squares in only one way, i.e., 72361 + 5776 = 269^2 + 76^2 .

It is a cyclic number.

It is not a de Polignac number, because 78137 - 2⁴ = 78121 is a prime.

It is a super-2 number, since 2×78137² = 12210781538, which contains 22 as substring.

Together with 78139, 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 78137.

It is not a weakly prime, because it can be changed into another prime (78139) by changing a digit.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 39068 + 39069.

It is an arithmetic number, because the mean of its divisors is an integer number (39069).

2⁷⁸¹³⁷ is an apocalyptic number.

It is an amenable number.

78137 is a deficient number, since it is larger than the sum of its proper divisors (1).

78137 is an equidigital number, since it uses as much as digits as its factorization.

78137 is an evil number, because the sum of its binary digits is even.

The product of its digits is 1176, while the sum is 26.

The square root of 78137 is about 279.5299626158. The cubic root of 78137 is about 42.7515873241.

Subtracting from 78137 its reverse (73187), we obtain a triangular number (4950 = T₉₉).

It can be divided in two parts, 781 and 37, that added together give a palindrome (818).

The spelling of 78137 in words is "seventy-eight thousand, one hundred thirty-seven".