# Lesson: Prime Numbers

## Comment on Prime Numbers

### Hi Brent,

Hi Brent,

Do you have the video slides for this lesson available for download? I know you have some available in linkedin.

Thanks! ### Hi bcc123,

Hi bcc123,

We don't have slides for each individual video lesson. However, we do have slides that cover all of GMAT math here: https://www.slideshare.net/GMATPrepNow_free/gmat-math-flashcards and here: https://gmatclub.com/forum/new-resource-interactive-flashcards-for-gmat-...

### sir doubt

sir doubt
https://gmatclub.com/forum/if-x-y-y-1-and-y-is-a-prime-number-less-than-11-which-of-the-f-223453.html ### Happy to help!

Happy to help!

My step-by-step solution can be found here: https://gmatclub.com/forum/if-x-y-y-1-and-y-is-a-prime-number-less-than-...

Cheers,
Brent

### Is the positive integer x

Is the positive integer x even?

(1) (x - 1) is a prime number
(2) (x^2 - 1) is a prime number

statement 1 = if x = 3 then x-1 is prime
if x = 6 then x-1 is prime
so insuff
statement 2
x^2-1 = prime
only 2 satisfies this
so suff
is this approach correct??? ### Perfect approach!

Perfect approach!

Cheers,
Brent

### Hi Brent, could you please

https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-either-a-multiple-of-2-an-127362.html ### Hi Brent here's another one I

Hi Brent here's another one I need your help with

https://gmatclub.com/forum/set-s-consists-of-more-than-two-integers-are-all-the-numbers-in-set-s-152717.html ### https://gmatclub.com/forum/if

https://gmatclub.com/forum/if-p-is-a-positive-integer-is-p-a-prime-number-172237.html
sir in statement 1 how to know which values to test? In this question, we're asked whether p is a prime number.
The GMAT loves to test whether students are aware that 2 is a prime number (in fact 2 is the ONLY prime number that's even). In fact, 2, 3 are the ONLY two consecutive primes.
So, that's why I tested p = 2

Notice that 2 and 3 (aka, p and p+1) have TWO factors each (making them both prime)
So, at that point, I started looking for 2 consecutive integers that each have FOUR factors each, which would make those values NOT prime numbers (aka composite numbers).

Do 3 & 4 work? No, 3 has two factors, and 4 has three factors.
Do 4 & 5 work? No, 4 has three factors, and 5 has two factors.
Do 5 & 6 work? No, 5 has two factors, and 6 has four factors.
.
.
.
Do 14 & 15 work? YES! 14 has FOUR factors, and 15 has FOUR factors.

Cheers,
Brent

### https://gmatclub.com/forum

https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-either-a-multiple-of-2-an-127362.html

I'm not sure if the approach I used is right:

Number of multiples of 2 between 2 and 30:

2(1) ... 2(15) 15 - 1 + 1 = 15
Take away 1 as its integers below 30
So total is 14

Number of odd prime numbers below 30:

9

Sum of positive multiples of 2 and odd prime numbers:

2 + 19 = 21
2 + 23 = 25
4 + 23 = 27

Any other calculations would have resulted in overlap and repetition. So total numbers that satisfied the statement was: 14+9+3 = 26

Where am I going wrong and how could this have been done much much more simpler in under 2 mins? Your list is missing 9 and 15

9 = 2 + 7
15 = 2 + 13

Here's m full solution: https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-e...

### In your approach, what's the

In your approach, what's the rationale behind choosing the smallest odd prime 3 as opposed to 5 or 7? ### Choosing 3 ensures that I don

Choosing 3 ensures that I don't miss any values.

That said, in this particular example, I could have chosen 5 or 7 and still reached the correct answer, but it's still best to start with the smallest odd prime.

For example, if I had chosen 11, then I would have missed the opportunity to get 9 as one of the possible values.

Cheers,
Brent

### https://gmatclub.com/forum

https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-either-a-multiple-of-2-an-127362.html
i did not get the 30 second approach given by Bunuel Bunuel's solution is pretty much the same as my 30-second solution (at https://gmatclub.com/forum/how-many-positive-integers-less-than-30-are-e...). The main difference is that Bunuel uses fewer words :-)

Cheers,
Brent

### https://gmatclub.com/forum/if

https://gmatclub.com/forum/if-the-integer-n-is-greater-than-1-is-n-equal-to-94720.html ### The product of all the prime

The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5

Prime numbers are 2,3,5,7,11,13,17,19.

To approximate the product of those prime numbers we can do the following:
2*5=10
3*7=20
11*19=200
13*17=200

Now lets multiply 10*20*200*200=8000000 and according to scientific notation the result should be written as 8*10^6.

If to take calculator and make a precise calculation the answer is also 10^6. Do I understand it correctly? Please help me out. Thank you. However, you need to recognize that your approximations are all a bit smaller than than the actual products.
For example, 11 x 19 = 209 (not 200), and 13 x 17 = 221 (not 200) etc.
So, your product of 8 x 10^6 is a bit LESS THAN the actual answer.
If we round UP, we get: 8 x 10^6 ≈ 10 x 10^6 ≈ 10^7

Here's my full solution: https://gmatclub.com/forum/the-product-of-all-the-prime-numbers-less-tha...

Does that help?

Cheers,
Brent

Hi Brent, I don't see how this explanation holds good for a set with, say, 4 or 5 numbers. Could you please help on this?

Thanks!
Kashaf This is a crazy tricky question!!

The solution wouldn't hold up if there were 4 or 5 numbers. However, since we're not told how many numbers there are, it's possible that there are 3 numbers (if we knew there were 4 or 5 numbers in the set, statement 1 would be sufficient. So, the only way statement 1 is not sufficient is when there are only 3 numbers in the set).

However, when we combine the two statements, we can be certain that all of the numbers are negative.

Does that help?

Cheers,
Brent

### Was hoping this was asked.

Was hoping this was asked. Solution threw me off plus I don't understand how we account for Statement 2, the Prime component of it all. ### Statement 2: The product of

Statement 2: The product of the smallest and largest integers in the list is a prime number.
The product of two prime numbers is composite (e.g., 3 x 5 = 15, and 15 is composite)
The product of a prime number and a composite number is composite (i.e., non-prime).
The product of two composite numbers is composite.

So, the are two ways for the product of two integers to be prime
- One number is 1 and the other number is prime (e.g., 1 x 7 = 7, and 7 is prime)
- One number is -1 and the other number is the negative of a prime number (e.g., -1 x -3 = 3, and 3 is prime)

I hope that helps.

### Question: https://gmatclub

Question: https://gmatclub.com/forum/if-each-of-the-two-digits-x-and-y-is-distinct-137998.html

Hi Brent,

For this question, I spent over 1 minute to confirm if 97 and 79 are primes. Do we need to memorize primes till 100 for the GMAT? Thanks. 