Explanation:

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

You are watching: What is the sum of the first five prime numbers?

Explanation:

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

One is no a element number, so only 8, 10, 12, 14, 16, and 18 have the right to be the amount of two different prime numbers.

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

If

is the an initial number in a collection of
element numbers, i m sorry 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 create a few series:

-> collection length 2: 2,3

-> series length 3: 3,5,7

-> series length 5: 5,7,11,13,17

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

etc.

We have the right to then watch that, that the answers, just 47 and also 31 remain maybe correct answers. Now we should decide i m sorry of those two are impossible.

We might do an additional series, however the

collection has 11 terms requiring us to walk further and further up. If we execute this, we"ll find that it terminates in ~ 47, meaning that 31 must be the correct answer.

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

series. Due to the fact that 31 is the really next element number, if we start on 11, the series that terminates in 31 would need to have length 7 as well. Every series after
will certainly thus finish on a number bigger than 31, definition we will never complete on a 31.

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### Example concern #4 : element Numbers

If

is a prime number, how numerous factors does
have?

Explanation:

The value of

, or
, is the product of
and also
, so it will certainly be divisible by 1, p, p, and nothing else (we understand that the p’s room not divisible because they are prime). As such p2 has exactly three factors.

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

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### Example inquiry #1 : prime Numbers

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

47

51

53

49

57

53

Explanation:

Let x represent the the smallest of the four numbers.

Then we can set up the following equation:

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

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### Example inquiry #6 : element Numbers

Which number is prime?

Explanation:

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

Let"s try to find the factors.

It may not be basic to see

as a composite number, yet if you understand the divisibility ascendancy for
which is dual the last digit and also subtract from the rest
, you will see
is not prime.

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### Example question #1 : element Numbers

Which is the smallest prime number?

Explanation:

The the smallest prime number is actually

is no a prime nor a composite number. It is a unit.

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### Example inquiry #8 : prime Numbers

Which of the following is a prime number?

Explanation:

A prime number is a number with components of one and itself.

Let"s try to discover the factors.

It might not be basic to see

as a composite number, yet if you recognize the divisibility dominion for
which is dual the critical digit and subtract native the rest
, you will certainly see
is not prime. The divisibility preeminence for
is add the exterior digits and if the amount matches the sum then it is divisible
. The divisibility rule for
is if the digits have a sum divisible by
, climate it is
. All also numbers are composite numbers with the exemption of
. So with these analyses, price is

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### Example concern #9 : prime Numbers

Which the the following is no prime?

Explanation:

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

, and also we dont see any numbers een or finish in
, let"s shot the divisibility dominion for
which is dual the last digit and also subtract from the rest.

Only

is divisible by
and is no prime and therefore ours answer.

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### Example inquiry #10 : element Numbers

What space the very first three element numbers?

Explanation:

The smallest prime number is actually

is not a prime nor a composite number. It is a unit. This will remove the options with a
in them. The following prime numbers are
. Our answer is then
is a perfect square and has much more than two factors
.

See more: Why Is Friar Laurence To Blame For The Deaths Of Romeo And Juliet

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