PSAT Math : How to find out if a number is prime
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Example Questions
Example Question #1 : How To Find Out If A Number Is Prime
The sum of the first seven prime numbers divided by two is
61
29
24
58
33
29
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.
Example Question #1 : How To Find Out If A Number Is Prime
If 
Plug in a prime number such as 
Example Question #1 : Prime Numbers
How many integers between 2 and 20, even only, can be the sum of two different prime numbers?
There are 8 possible numbers; 4,6,8,10,12,14,16,18.
One is not a prime number, so only 8, 10, 12, 14, 16, and 18 can be the sum of two different prime numbers.
Example Question #1 : Prime Numbers
Define a series of consecutive prime numbers to be a series of numbers, each prime, in which there are no other prime numbers between them. These are not necessarily consecutive numbers themselves. For example, the numbers 5,7 and 11 are consecutive prime numbers, although they are not consecutive numbers.
If 
The primes, in order, are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, ...
We create a few series:
etc.
We can then see that, of the answers, only 47 and 31 remain possibly correct answers. Now we need to decide which of those two are impossible.
We could do another series, but the 
Another way, however, is to notice that 29 is the end of the 
Example Question #1 : How To Find Out If A Number Is Prime
If 
The value of 
(Alternatively, we can plug in any prime number for p and see how many factors p2 has. For example, if p is 3, then the factors of p2, or 9, are 1, 3, and 9.)
Example Question #2 : Prime Numbers
The sum of four consecutive integers is 210. Which one of these four integers is prime?
57
51
49
53
47
53
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.
Example Question #292 : Arithmetic
Which of the following is equal to the sum of the five smallest prime numbers?
25
28
27
33
18
28
It is important to know what a prime number is in order to answer this question. A prime number is defined as any positive integer that is divisible only by the number 1 and itself. For example, 17 is a prime number because its only factors are 1 and 17.
The first five prime numbers are 2, 3, 5, 7, and 11. Remember, 1 is not a prime number, and 2 is the only even prime.
Therefore, the sum of the five smallest prime numbers is 28.
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