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

  • Thread starter Thread starter Ilikebugs
  • Start date Start date
  • Tags Tags
    Primes Sum
AI Thread Summary
To solve the problem of finding the sum of two primes that results in a two-digit odd integer, the discussion focuses on subtracting the count of such integers from 45. It is established that the sum of two primes must include the prime number 2 to yield an odd result, leading to the examination of the primality of n-2 for odd integers n. The conclusion reached is that there are 21 odd two-digit numbers where n-2 is prime, resulting in a final answer of 24. The conversation highlights the importance of correctly identifying prime numbers in this context. The analysis confirms that about half of the odd two-digit numbers cannot be expressed as a sum of two primes.
Ilikebugs
Messages
94
Reaction score
0
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)?
 

Attachments

  • potw 5.png
    potw 5.png
    41.7 KB · Views: 116
Mathematics news on Phys.org
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.
 
Last edited:
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
 
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
Thread 'Imaginary Pythagoras'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top