4139

4139 is a natural number that follows 4138 and precedes 4140. In mathematics, it is a prime number and is congruent to 3 modulo 4, which implies it cannot be expressed as the sum of two squares.

Despite that, 4139 can be written as a sum of three squares. One explicit representation is 4139 = 63^2 + 11^2 + 7^2. The number is also the difference of two consecutive squares: 4139 = 2070^2 − 2069^2, since (2070 − 2069)(2070 + 2069) = 1 × 4139.

In common numeral systems, 4139 is represented as 1000000101011 in binary and as 0x102B in hexadecimal. The decimal digits sum to 17, giving a digital root of 8.

Additional context: as a prime, 4139 falls within the sequence of prime numbers and has no positive divisors other than 1 and itself. Its properties as a 4k+3 prime influence certain number-theoretic representations, such as the impossibility of a two-square decomposition, while still permitting representations as sums of three squares.