5743

5743 is a positive integer and, in the realm of number theory, it is a prime number. It is odd and greater than two, placing it among the primes that are often used in mathematical examples and algorithmic tests.

Primality and properties: 5743 is not divisible by any prime number up to 73. Its square root is about 75.8, so checking primes up to 73 suffices to confirm its primality. Additionally, 5743 ≡ 3 (mod 4), a congruence with consequence: a prime congruent to 3 modulo 4 cannot be expressed as a sum of two squares.

Representations: In hexadecimal, 5743 is 0x166F. In binary, it is 1011001101111. The decimal digit sum is 5 + 7 + 4 + 3 = 19, which is not a multiple of 3, consistent with its non-divisibility by 3.

Context and usage: As a prime, 5743 appears in mathematical tables and lists of primes used for reference, educational demonstrations, and computational examples. Like other primes, it has no nontrivial factors, a property that underpins various testing and explanatory contexts in number theory. See also prime number and list of prime numbers for related topics.