A positive integer n is defined as a "prime interlude" if n-1 and n+1 are both prime numbers. Which of the following is not a "prime interlude?"

Question

a.4
b.18
c.30
d.72
e.90

( First of all; What is a "prime interlude??")

I don't understand the question and don't know which answer to pick.

But this is what the book answer says: Once you figure out what "prime interlude" means (i.e,the integers immediately before and after your # are both prime), you're ready to tackle the answer choices:

(A)a 3 and 5 are both prime, so eliminate.

(B)18 17 and 19 are both prime, so eliminate.

(C)30 29 and 31 are both prime, so eliminate.

(D)72 71 and 73 are both prime, so eliminate.

(E)90 89 and 91 may both seem prime, but 91=7x13.

I don't understand. help me.

The answer book tells you a "prime interlude" occurs when BOTH the number before and the number after are prime number. Then it goes on to show that answers a,b,c,and d can be eliminated. Answer e has the 89 as a prime number BUT (and the answer book show you how) 91 is NOT a prime number because it can be factored into 7*13; therefore, since BOTH the number before AND the number after are not prime numbers, e is the correct answer.

A number is a 'prime interlude' if both the number above it and the number below it are prime numbers
I used to call them "twin primes"

eg. 11 and 13 are twin primes, they are 2 apart, so 12 would be a prime interlude

17 and 19 also work.

so let's look at the third choice, the 30
both 29, the number below it, and 31, the number above it, are primes.

for their last choice of 90, the number below it, the 89 IS prime, but the number above it, the 91 IS NOT prime, because 91 = 13x7

That is why E is the correct answer.

OOOOh! It took me a while but I understand now. In order for me to answer this problem I would have to know what a prime interlude is right?

Before I did not understand what you meant by "the # below it and the # above it" meant. I was thinking to myself: What #'s are you talking about and are you getting your answer out of thin air?????? By the # below you mean the # one less than the # given and the # above means the # up one greater than the number given. But the two #'s have to be prime in order for the middle # to be a "prime interlude." That's why it's called "PRIME" interclude.

Well here is one examples of a prime interclude that I made up to show that I understand.

1 and 3. 2 is the prime interlude because 1 and 3 are prime.

Another technique that I can use and that I made up myself is that I can remember what a prime interlude is the # in the "center" with the left and the right # prime because the prefix "inter" of the word interlude sounds like the word "CENTER." Don't you agree. Type a message to me back if you don't understand and I'll be glad to help you understand okay!

THANKS! : )

Ooooh THANKS A BUNCH! It took me a while but now I Completely understand. Just ask Reiny. : )

That souds ok to me.

I might have done better to say the number immediately before and the number immediately after. It might not have been so confusing to you then.

cool.

Answer 1

i don't understand the prime interlude ***
how can 18 be a prime number ??!!

Answer 2

Firstly we call Prime interlude as a number that is located between two prime numbers adjacent before and after that number.

From above given relation
4
18
30
72
90
Here,90 is not a prime interlude because the number after it is 91 that is not prime so to fullfil the criteria of a prime interlude the number after 90 shuld be prime

Further more

3-4-5 both number before and after 4 are prime that are 3 and 5

17-18-19 both number before and after 18 are prime that are 17 and 19

29-30-31 both number before and after 30 are prime that are 29 and 31

71-72-73 both number before and after 71 are prime that are 71 and 72

Hence the nukber that is not prime interlude is 91

Answer 3

Sorry 90*