MHB Sum of 2 Primes: 45 - (2 Digit Integer)?

[Ilikebugs]

View attachment 6519 I think that we have to get all 2 digit odd numbers that can be expressed as the sum of 2 primes and subtract that from 45, so I think that the answer would be 45-(number of 2 digit integers n that are prime and have n-2 be prime as well)?

 

[Greg]

I think that we have to get all 2 digit odd numbers that can be expressed as the sum of 2 primes and subtract that from 45, so I think that the answer would be 45-(number of 2 digit integers n that are prime and have n-2 be prime as well)?

$n$ doesn't have to be prime.

 

[vidyarth]

The question seems interesting. The answer is $24$. That is, about half of the odd 2-didit numbers cannot be expressed as a sum of two primes. The proof is simple. The sum if two primes must contain $2$, for otherwise the number cannot be odd. Thus, we have just check the primality of $n-2$ , where $n$ is any odd number.

 

[Ilikebugs]

Arent there 21 odd 2 digit numbers where n-2 is prime, so its 24?

 

[vidyarth]

Arent there 21 odd 2 digit numbers where n-2 is prime, so its 24?

True, I missed one. Corrected though