Below is a prime number problem. Before I launch into my prime number post, why don’t you take a minute or two to crack the problem?

*x^3 = n. If the units digit of n is a prime number, then indicate each of the following that could be the value of x.*

* *

*[A] 1*

*[B] 2*

*[C] 3*

*[D] 5*

*[E] 7*

*[F] 8 *

*[G] 9*

* *

Problems dealing with prime numbers are very common on the GRE. To have a chance of getting an easy prime number question correct, you must know the following two pieces of information:

One is NOT a prime number.

Two is the only even prime number.

Now, go back to the prime number question above, and see if there is anything you would change. Let’s start with [A]. 1^3 results in 1. Knowing that 1 is not a prime, we can eliminate [A].

We can also eliminate [B] because 2^3 equals 8, and we have to ensure that the units digit of n, and not x, is a prime.

Now another piece of information is important:

3, 5, 7, 11, 13, 17, 19

These are the prime numbers you should be able to rattle off the top of your head the way you can your address and phone number.

3^3 is our first candidate because n = 27, and the units digit is 7, a prime. [C]

Next we have 5^3 = 125. 5 is a prime. [D]

7^3 = 343. The units digit is 3 so we know that [E] is the answer. It is important to note that you do not need to multiply 7 x7 x 7. You only have to look for the units digit. 7 x 7 = 49. Multiply the final 7 by the 9 in 49 and that yields a 3 as a units digit.

[F] 8 is a tricky one. Clearly 8 isn’t a prime number. But 8 is the value of x. 8^3 is 512. And 2, if you remember from above, is a prime. So, [F] works.

Finally we have 9^3 = 729. The units digit is not a prime, as 9 is not a prime. So, we omit [G[.

The final answer then is [C], [D], [E], [F]

Prime number problems can of course come in many different varieties. I’ll be posting more prime number examples soon. But, as long as you know the above fundamentals, you can build off that information and tackle even the most difficult prime number questions.

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Hi Chris,

When it comes to prime numbers, why aren’t there any negative primes? Could you please enlighten me on whether negative prime numbers exist, and if yes, whether or not they’re included in the GRE?

Excellent questions, Abhishek!

Overall, a number is prime if it has only two factors: 1 and itself. And only positive integers are said to be prime. We do not apply the distinction “prime” or “not prime” to negative integers, zero, or to non-integers.

Hope this clears up your doubts!

Thanks a lot! 😀

You’re very welcome 🙂 Happy studying!

Hi Chris,

I don’t understand why 512 is a prime number. It is divisible by 2.

Hi Ken,

‘512’ itself is not a prime number, but the question is stating only that the units of a number must be prime. In this case, the units digit of 512 is 2, which is a prime.

Hopefully that clears things up 🙂

3> 27 yes

5> 125 yes

7 > **3 yes

8> **2 yes

9> **9 no

CDEF