503 is indeed a prime number, so your intuition was right. Prime numbers, as you mentioned, are numbers greater than 1 that are only divisible by 1 and themselves. To determine if a number is prime, dividing it by smaller prime numbers to see if it can be evenly divided is a common approach. Generally, if you’re working with a number like 503, you would check its divisibility against prime numbers up to the square root of that number. The square root of 503 is a bit more than 22, so we only need to consider prime numbers up to 22.
You’ve already tried 2, 3, and 5. 503 is not even, so it’s not divisible by 2. The digits of 503 don’t sum up to a multiple of 3, ruling that out. It doesn’t end in a 0 or 5, so it’s not divisible by 5 either. Then, we’d look at other prime numbers like 7, 11, 13, 17, and 19. In each case, you’ll find that 503 doesn’t divide evenly by any of them. Let’s take 7 as an example: 503 divided by 7 is approximately 71.857. Since there’s no even quotient, 503 isn’t divisible by 7. You’d find similar results for the others.
Because 503 can’t be divided without a remainder by any of these individual primes, it qualifies as a prime number itself. If you’re tackling large numbers, mathematicians often use more sophisticated algorithms, but for numbers of reasonable size, this basic method suffices. So, rest assured that 503 holds its place among the unique prime numbers!
