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Which of the following CANNOT be the sum of two prime numbers?

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Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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New post 22 Jun 2020, 06:23
3
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A
B
C
D
E

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Question Stats:

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Which of the following CANNOT be the sum of two prime numbers?


A) 31
B) 38
C) 33
D) 36
E) 53
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Re: Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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New post 22 Jun 2020, 06:34
1
Explanation:

A. 29 + 2
B. 31 + 7
C. 31 + 2
D. 31 + 5
E. 53 is prime only

IMO-E
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Re: Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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New post 02 Jul 2020, 05:31
A) 31 = 29 + 2
B) 38 = 31 + 7
C) 33 = 31 + 2
D) 36 = 29 + 7
E) Can not be the sum of two prime numbers
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Re: Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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New post 02 Jul 2020, 07:01
3
In the options , there are 3 odd numbers and 2 even numbers given.

Odd+ Even = Odd
As there is only 1 prime number which is even i.e. 2
First, we need to check odd numbers in options :

31 = 29 + 2 (possible)
33 = 31 + 2 (possible)
53 = 51 + 2 ( not possible as 51 is not prime)

So, Answer is Option E
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Re: Which of the following CANNOT be the sum of two prime numbers?  [#permalink]

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New post 02 Jul 2020, 07:19
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There's a famous conjecture in Number Theory known as "Goldbach's Conjecture", which is true for every number anyone has looked at, but remains unproven for enormous numbers. That conjecture says "every even number greater than 2 can be written as a sum of two primes". So if you know in advance that's true for all the small even numbers, you can be certain this question has an odd answer.

If we can write an odd number as the sum of two primes, we need to use the prime 2, the only even prime, because it's only by adding an even and an odd that you get an odd sum. So to answer this question, we just need to find an answer that is not equal to 2 + p, where p is an odd prime, and 53 is right, because 51 is not prime (51 = 3*17).
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Re: Which of the following CANNOT be the sum of two prime numbers?   [#permalink] 02 Jul 2020, 07:19

Which of the following CANNOT be the sum of two prime numbers?

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