7523

7523 is a positive integer that follows 7522 and precedes 7524. In standard decimal notation it is written as 7523.

In mathematics, 7523 is a prime number, meaning it has no positive divisors other than 1 and itself. A straightforward check against primes up to the square root of 7523 confirms its primality; thus its prime factorization is simply 7523.

For those who consider different numeral systems, 7523 has the following representations: in binary it is 1110101100011, in octal it is 16543, and in hexadecimal it is 1D63. In decimal, the sum of its digits is 17, so 7523 is not divisible by 3 or 9; as an odd number, it is not divisible by 2 or 5. The digits 7, 5, 2, and 3 are all prime numbers, so the decimal digits themselves are prime digits.

One can also express 7523 as a sum of powers of two: 7523 = 4096 + 2048 + 1024 + 256 + 64 + 32 + 2 + 1, which corresponds to its binary representation. As a prime, 7523 has a distinct role in number theory as an indivisible unit under multiplication, and it participates in various prime-based considerations such as modular arithmetic and prime-testing demonstrations.