Explanation:

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

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*


*


*


*


*


Explanation:

There are 8 feasible numbers; 4,6,8,10,12,14,16,18.

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


Define a collection of consecutive element numbers to it is in a collection of numbers, each prime, in which there room no other prime numbers between them. These room not have to consecutive numbers themselves. Because that example, the numbers 5,7 and 11 room consecutive prime numbers, although they space not continually numbers.


If 

*
is the first number in a collection of
*
prime numbers, i beg your pardon of the following might not be the worth 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:

*
 -> collection length 2: 2,3

*
 -> series length 3: 3,5,7

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

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

etc.

 

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

We might do an additional series, but the 

*
collection has 11 terms requiring us to walk further and further up. If we carry out this, we"ll discover that it terminates in ~ 47, an interpretation that 31 need to be the correct answer.

Another way, however, is to notification that 29 is the end of the 

*
series. Because 31 is the an extremely next prime number, if we begin on 11, the series that terminates in 31 would have to have length 7 together well. Every series after 
*
will thus end on a number bigger than 31, meaning we will certainly never end up on a 31.


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Example concern #4 : element Numbers


If 

*
is a prime number, how plenty of factors does 
*
have?


Possible Answers:
Correct answer:

*


Explanation:

The worth of

*
, or
*
, is the product of 
*
and also
*
, for this reason it will certainly be divisible by 1, p, p, and nothing else (we know that the p’s room not divisible since they space prime). Because of this p2 has exactly three factors.

(Alternatively, we deserve to plug in any kind of prime number because that p and see how countless factors p2 has. Because that example, if p is 3, climate the factors of p2, or 9, are 1, 3, and also 9.)


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Example question #1 : prime Numbers


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


Possible Answers:

49


57


53


47


51


Correct answer:

53


Explanation:

Let x stand for the smallest of the 4 numbers.

Then we can collection up the adhering to equation:

*

*

*

*

Therefore the four numbers are 51, 52, 53, 54. The only prime in this list 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 factors of one and also itself.

Let"s shot to uncover the factors.

*

*

*

*

*

It might not be easy to watch

*
 as a composite number, but if you recognize the divisibility preeminence for 
*
 which is dual the last digit and also subtract indigenous the rest 
*
, you will certainly see 
*
 is not 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 no a prime no one a composite number. The is a unit. 


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Example inquiry #1 : prime Numbers


Which that the complying with is a element number?


Possible Answers:
Correct answer:

*


Explanation:

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

Let"s shot to uncover the factors.

*

*

*

*

*

It might not be basic to see 

*
 as a composite number, but if you know the divisibility rule for 
*
 which is double the last digit and subtract native the rest
*
, you will see 
*
 is no prime. The divisibility dominance for 
*
 is include the exterior digits and also if the amount matches the sum then it is divisible 
*
. The divisibility dominance for 
*
 is if the digits have actually a amount divisible by 
*
, climate it is
*
. All even numbers are composite numbers through the exception of 
*
. So through these analyses, prize is 
*


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Example concern #9 : prime Numbers


Which that the following is no prime?


Possible Answers:
Correct answer:

*


Explanation:

Since all of the digits don"t include to a amount of 

*
, and also we not see any type of numbers een or finish in 
*
, let"s try the divisibility ascendancy for 
*
 which is double the last digit and also subtract native the rest.

See more: 2000 Ford Expedition Fuse Box Location, Ford Expedition (Un93 1997

*

*

*

*

*

Only 

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

 


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Example inquiry #10 : prime Numbers


What space the very first three element numbers?


Possible Answers:
Correct answer:

*


Explanation:

The the smallest prime number is actually 

*
*
 is no a prime no one a composite number. The is a unit. This will remove the options with a 
*
 in them. The following prime number are 
*
. Our answer is then 
*
*
 is a perfect square and has an ext than 2 factors 
*
.


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