5419

5419 is a natural number that follows 5418 and precedes 5420. It is four digits long and occurs in various numerical contexts as a representative example of primes and modular arithmetic.

In mathematics, 5419 is a prime number. It is odd and not divisible by 2, 3, or 5. A divisibility check up to the square root of 5419 (which is about 73.6) confirms that it has no positive divisors other than 1 and itself. As a prime, its only positive divisors are 1 and 5419.

From a digit and base perspective, the decimal digits of 5419 are 5, 4, 1, and 9, all distinct. The sum of digits is 19, giving a digital root of 1. In other common bases, 5419 equals 1010100101011 in binary and 0x152B in hexadecimal.

A notable number-theoretic property is that 5419 ≡ 3 (mod 4). Primes with this congruence cannot be expressed as a sum of two squares. This aligns with the general theorem: primes congruent to 3 modulo 4 do not have representations as a^2 + b^2 with integers a and b.

Because it is prime, 5419 also serves as a modulus in modular arithmetic, where arithmetic is performed in the ring of integers modulo 5419, forming a finite field under addition and multiplication (excluding zero divisors). In everyday contexts, 5419 may appear as an identifier, code, or example value in mathematical discussions.