A prime number is a number with factors of one and itself.

Let's try to find the factors.

It may not be easy to see as a composite number, but if you know the divisibility rule for which is double the last digit and subtract from the rest , you will see is not prime.

The first seven primes are 2, 3, 5, 7, 11, 13, and 17. Don't forget about 2, the smallest prime number, and also the only even prime! Adding these seven numbers gives a sum of 58, and 58/2 = 29.

A prime number is a number with factors of one and itself.

Let's try to find the factors.

It may not be easy to see as a composite number, but if you know the divisibility rule for which is double the last digit and subtract from the rest, you will see is not prime. The divisibility rule for is add the outside digits and if the sum matches the sum then it is divisible . The divisibility rule for is if the digits have a sum divisible by , then it is . All even numbers are composite numbers with the exception of . So with these analyses, answer is .

Since all the numbers are odd and don't end with a , let's check the basic divisbility rule. The divisibility rule for is if the digits have a sum divisible by , then it is.

Based on this analysis, only is divisible by and therefore not prime and is our answer.

This will require us to know the divisibility rule of . The reason for this choice is that some of the numbers are palindromes like so we eliminate . For the three digit numbers, the divisibility rule for is add the outside digits and if the sum matches the sum then it is divisible. Let's see.

Based on this test, is not divisible by and is our answer.

The smallest prime number is actually . is not a prime nor a composite number. It is a unit. This will eliminate the choices with a in them. The next prime numbers are . Our answer is then . is a perfect square and has more than two factors .

Let x represent the smallest of the four numbers.

Then we can set up the following equation:

Therefore the four numbers are 51, 52, 53, 54. The only prime in this list is 53.

Plug in a prime number such as and evaluate all the possible solutions. Note that the question asks which value COULD be prime, not which MUST BE prime. As soon as your number-picking yields a prime number, you have satisfied the "could be prime" standard and know that you have a correct answer.

The order of the prime numbers start from . is not prime as it's a unit. is a composite number. So our fourth smallest prime number is .

The value of , or , is the product of and , so it will be divisible by 1, p, p * p, and nothing else (we know that the p’s are not divisible because they are prime). Therefore _p_2 has exactly three factors.

(Alternatively, we can plug in any prime number for p and see how many factors _p_2 has. For example, if p is 3, then the factors of _p_2, or 9, are 1, 3, and 9.)