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

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The discussion centers on determining the number of two-digit odd integers that can be expressed as the sum of two prime numbers, specifically focusing on the calculation of 45 minus this count. The conclusion reached is that 24 two-digit odd integers cannot be expressed as the sum of two primes. The reasoning involves checking the primality of n-2, where n represents any odd two-digit number, confirming that there are 21 such integers where n-2 is prime.

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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)?
 

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

True, I missed one. Corrected though
 

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