How do you know the prime number between 25 and 50?

Answer 1

50 is just 1 above 49, which is 7 squared. We know that 50 is even, so it is not prime, and 49 certainly isn't. So if any number under 49 is not prime, it must be divisible by a Prime number less than 7, i.e. 2, 3, or 5. So any odd number less than 49 that is not divisible by 3 or 5 is prime. Furthermore, we know that the multiples of 5 end in 0 or 5, and the digits in a multiple of 3 add up to a multiple of 3. So just take all the odd numbers from 27 to 47 and throw away the ones that end in 5. Of the remaining numbers, the ones whose digits don't add up to a multiple of 3 (if the sum is more than 9, add its digits until you get a single digit and see if it is 3, 6, or 9) are prime.