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

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Thanks!In summary, the conversation discusses finding all 2 digit odd numbers that can be expressed as the sum of 2 primes and subtracting them from 45. The answer is 24, as about half of the odd 2-digit numbers cannot be expressed as a sum of two primes. The proof involves checking the primality of n-2, where n is any odd number. After correction, the final count of such numbers is 24.
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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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  • #2
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.
 
  • #3
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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  • #4
Arent there 21 odd 2 digit numbers where n-2 is prime, so its 24?
 
  • #5
Ilikebugs said:
Arent there 21 odd 2 digit numbers where n-2 is prime, so its 24?

True, I missed one. Corrected though
 

1. What is the sum of 2 primes when 45 is subtracted from a 2-digit integer?

The sum of 2 primes when 45 is subtracted from a 2-digit integer is the result of adding together two prime numbers that, when subtracted from a 2-digit integer, equal 45. For example, if the 2-digit integer is 67, the sum of 2 primes would be 11 and 23, since 67 - 11 - 23 = 45.

2. How do you find the 2 primes in this problem?

To find the 2 primes in this problem, you can use a process called prime factorization. This involves breaking down the 2-digit integer into its prime factors, and then testing different combinations of those factors to see which ones add up to 45. Alternatively, you can use a prime number calculator to quickly identify the 2 primes.

3. Can the 2 primes be the same number?

No, the 2 primes in this problem cannot be the same number. In order for the equation to be valid, the two numbers must be different prime numbers. This is because a prime number can only be divided by 1 and itself, so if the two numbers were the same, the result of the equation would always be 0.

4. Is there a limit to the 2-digit integer that can be used in this problem?

Technically, there is no limit to the 2-digit integer that can be used in this problem. However, as the 2-digit integer gets larger, the potential combinations of 2 primes that add up to 45 become more complex and may require more time and effort to find. For practical purposes, it is best to stick to 2-digit integers that are not too large.

5. What is the significance of finding the sum of 2 primes when 45 is subtracted from a 2-digit integer?

There is no specific scientific significance to this problem. It is simply a mathematical exercise that can help improve your skills in prime factorization and number theory. However, the concept of finding the sum of 2 primes has been used in cryptography to create secure encryption algorithms.

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