Explanation:

The very first seven primes space 2, 3, 5, 7, 11, 13, and 17. Don"t forget around 2, the smallest prime number, and also the only even prime! adding these seven numbers provides a amount of 58, and 58/2 = 29.

You are watching: Which of the following groups of numbers are all prime numbers?


*


*


*


*


*


Explanation:

There room 8 possible numbers; 4,6,8,10,12,14,16,18.

One is not a element number, so only 8, 10, 12, 14, 16, and also 18 can be the amount of two different prime numbers.


Define a series of consecutive element numbers to it is in a series of numbers, every prime, in i m sorry there space no various other prime numbers in between them. These are not have to consecutive number themselves. For example, the number 5,7 and also 11 are consecutive element numbers, although they are not continually numbers.


If 

*
is the very first number in a collection of
*
element numbers, which of the following could not it is in the value of the last number in the series?


Explanation:

The primes, in order, are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, ...

 

We produce a few series:

*
 -> series length 2: 2,3

*
 -> series length 3: 3,5,7

*
 -> collection length 5: 5,7,11,13,17

*
 -> series length 7: 7,11,13,17,19,23,29

etc.

 

We deserve to then check out that, the the answers, just 47 and 31 remain probably correct answers. Now we have to decide i beg your pardon of those two are impossible. 

We can do another series, yet the 

*
collection has 11 state requiring united state to go further and also further up. If we perform this, we"ll discover that the terminates in ~ 47, definition that 31 should be the correct answer.

Another way, however, is to an alert that 29 is the end of the 

*
series. Due to the fact that 31 is the really next prime number, if we begin on 11, the collection that terminates in 31 would have to have length 7 together well. Every series after 
*
will certainly thus finish on a number bigger than 31, meaning we will certainly never complete on a 31.


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Example inquiry #4 : element Numbers


If 

*
is a element number, how many factors does 
*
have?


Possible Answers:
Correct answer:

*


Explanation:

The worth of

*
, or
*
, is the product of 
*
and
*
, for this reason it will certainly be divisible through 1, p, p, and also nothing rather (we know that the p’s room not divisible due to the fact that they space prime). As such p2 has specifically three factors.

(Alternatively, we have the right to plug in any type of prime number for p and see how numerous factors p2 has. For example, if p is 3, then the factors of p2, or 9, room 1, 3, and 9.)


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Example inquiry #1 : element Numbers


The sum of 4 consecutive integers is 210. Which among these 4 integers is prime?


Possible Answers:

49


57


53


47


51


Correct answer:

53


Explanation:

Let x represent the the smallest of the 4 numbers.

Then us can collection up the complying with equation:

*

*

*

*

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


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Example concern #6 : element Numbers


Which number is prime?


Possible Answers:
Correct answer:

*


Explanation:

A element number is a number with determinants of one and itself.

Let"s try to discover the factors.

*

*

*

*

*

It might not be straightforward to check out

*
 as a composite number, but if you recognize the divisibility dominion for 
*
 which is double the last digit and also subtract from the rest 
*
, you will certainly see 
*
 is no prime. 


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Example inquiry #1 : prime Numbers


Which is the the smallest prime number?


Possible Answers:
Correct answer:

*


Explanation:

The smallest prime number is actually 

*
*
 is not a prime nor a composite number. The is a unit. 


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Example inquiry #1 : prime Numbers


Which that the following is a element number?


Possible Answers:
Correct answer:

*


Explanation:

A element number is a number with determinants of one and also itself.

Let"s shot to discover the factors.

*

*

*

*

*

It might not be easy to see 

*
 as a composite number, but if you know the divisibility dominion for 
*
 which is double the last digit and subtract from the rest
*
, you will certainly see 
*
 is not prime. The divisibility ascendancy for 
*
 is include the exterior digits and if the amount matches the sum then that is divisible 
*
. The divisibility preeminence for 
*
 is if the digits have actually a amount divisible by 
*
, then it is
*
. All also numbers room composite numbers with the exemption of 
*
. So with these analyses, price is 
*


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Example question #9 : element Numbers


Which the the following is no prime?


Possible Answers:
Correct answer:

*


Explanation:

Since every one of the number don"t include to a sum of 

*
, and also we dont see any numbers een or finish in 
*
, let"s try the divisibility ascendancy for 
*
 which is double the critical digit and also subtract from the rest.

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*

*

*

*

*

Only 

*
 is divisible by 
*
 and is no prime and also therefore our answer. 

 


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Example inquiry #10 : prime Numbers


What are the first three element numbers?


Possible Answers:
Correct answer:

*


Explanation:

The smallest prime number is actually 

*
*
 is no a prime no one a composite number. It is a unit. This will remove the options with a 
*
 in them. The following prime numbers are 
*
. Ours answer is then 
*
*
 is a perfect square and also has much more than two factors 
*
.


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