Determine the validity of the number problem

[chwala]

Homework Statement

ii. Find a number between $30$ and $50$which shows the statement is false.

Relevant Equations

numbers

my question is on part ii. Only,

the marking scheme indicates that the answer is $38=31+7$ only. My question is why is this False? $38$ is an even number, $7$ and $31$ are two different prime numbers and their sum gives us $38$!
i would say$32=13+17+2$
$31=13+17+1$

which is false, ooooh! unless the value indicated above is only true for value $38$ and not any other value between $30$ and $50$. English was a problem there...

 

[Office_Shredder]

It says it needs to be summed in two different ways. For example 16=11+5 and also 16=13+3, you need two different sums of two primes.

 

[chwala]

It says it needs to be summed in two different ways. For example 16=11+5 and also 16=13+3, you need two different sums of two primes.

Aaargh I see that now...thanks

 

[chwala]

Aaargh I see that now...thanks
$32=29+3=13+19$

 

[Office_Shredder]

So 32 it's not a counterexample. The claim is you can do this for all even numbers, and the solution says that 38 is the counterexample.

 

[chwala]

I agree,I understand now...its very clear. The claim is false because of $38$ as you have clearly shown...Thank you once again...

 

[chwala]

So 32 it's not a counterexample. The claim is you can do this for all even numbers, and the solution says that 38 is the counterexample.

True, whereas in the even numbers like
$32= 3+29 = 13+19$ [3 to 13 (+10)...therefore for 29 (-10) = 19]
$34=5+29 = 11+23$ [5 to 11 (+ 6)...therefore for 29 ( -6) = 23]

Now the number $38$ can only be expressed in the form $38= 7+31$ and no any other combination.