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You'll have to test whether 1823 can be divided by every number from 2 up to 42. You can stop there because 43 x 43 is bigger than 1823. You can test only prime numbers between 2 and 42, so 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41. 2 is out because 1823 is not even. 3 is out because 1 + 8 + 2 + 3 is 14, which does not divide by 3. 5 is out because 1823 does not end in 0 or 5. 7 is out because 182 - 3x2 = 176, which does not divide by 7. 11 is out because 182 - 3x1 = 179, which does not divide by 11. Then I run out of tricks to see if numbers can be divided by other numbers, so I test with a calculator. Everything gives a fraction. So 1823 is prime.
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