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127 is a prime number

• 127 can be written using four 4's:

See also 113.

• 127 is the least n > 0 such that

n = pod(n2) + sod(n2),
where pod(k) and sod(k) denote the product and the sum of the digits of k, respectively.
127 has 2 divisors, whose sum is σ = 128. Its totient is φ = 126.

The previous prime is 113. The next prime is 131. The reversal of 127 is 721.

127 is nontrivially palindromic in base 2 and base 9.

It is a Cunningham number, because it is equal to 27-1.

127 is an esthetic number in base 13 and base 15, because in such bases its adjacent digits differ by 1.

It is a strong prime.

It is the 7-th Motzkin number.

It is a cyclic number.

It is a de Polignac number, because none of the positive numbers 2k-127 is a prime.

It is a super-2 number, since 2×1272 = 32258, which contains 22 as substring.

It is a Chen prime.

It is an alternating number because its digits alternate between odd and even.

127 is an undulating number in base 9.

127 is a lucky number.

127 is a nontrivial repdigit in base 2.

It is a plaindrome in base 2, base 4, base 8, base 10, base 13 and base 16.

It is a nialpdrome in base 2, base 6, base 12, base 14 and base 15.

It is a zygodrome in base 2.

It is a congruent number.

It is a panconsummate number.

It is a nontrivial repunit in base 2.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a good prime.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 63 + 64.

It is an arithmetic number, because the mean of its divisors is an integer number (64).

127 is a Friedman number, since it can be written as 2^7-1, using all its digits and the basic arithmetic operations.

127 is the 7-th hex number.

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

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

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

The product of its digits is 14, while the sum is 10.

The square root of 127 is about 11.2694276696. The cubic root of 127 is about 5.0265256953.

Adding to 127 its product of digits (14), we get a palindrome (141).

Adding to 127 its reverse (721), we get a palindrome (848).

It can be divided in two parts, 1 and 27, that added together give a triangular number (28 = T7).

The spelling of 127 in words is "one hundred twenty-seven", and thus it is an aban number and an iban number.