Sure, let's go step by step to address the question.
1. List of Even Numbers Between 40 and 60:
We start by identifying all the even numbers in the given range 40 to 60.
These even numbers are:
[tex]\[ 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60 \][/tex]
2. Showing Each Even Number is the Sum of Two Prime Numbers:
We need to express each of these even numbers as the sum of two prime numbers.
- 40:
[tex]\( 40 = 3 + 37 \)[/tex]
Both 3 and 37 are prime numbers.
- 42:
[tex]\( 42 = 5 + 37 \)[/tex]
Both 5 and 37 are prime numbers.
- 44:
[tex]\( 44 = 3 + 41 \)[/tex]
Both 3 and 41 are prime numbers.
- 46:
[tex]\( 46 = 3 + 43 \)[/tex]
Both 3 and 43 are prime numbers.
- 48:
[tex]\( 48 = 5 + 43 \)[/tex]
Both 5 and 43 are prime numbers.
- 50:
[tex]\( 50 = 3 + 47 \)[/tex]
Both 3 and 47 are prime numbers.
- 52:
[tex]\( 52 = 5 + 47 \)[/tex]
Both 5 and 47 are prime numbers.
- 54:
[tex]\( 54 = 7 + 47 \)[/tex]
Both 7 and 47 are prime numbers.
- 56:
[tex]\( 56 = 3 + 53 \)[/tex]
Both 3 and 53 are prime numbers.
- 58:
[tex]\( 58 = 5 + 53 \)[/tex]
Both 5 and 53 are prime numbers.
- 60:
[tex]\( 60 = 7 + 53 \)[/tex]
Both 7 and 53 are prime numbers.
3. Summary of Results:
We have shown that each even number between 40 and 60 can be expressed as the sum of two prime numbers. Here is the summary:
[tex]\[
\begin{align*}
40 & = 3 + 37 \\
42 & = 5 + 37 \\
44 & = 3 + 41 \\
46 & = 3 + 43 \\
48 & = 5 + 43 \\
50 & = 3 + 47 \\
52 & = 5 + 47 \\
54 & = 7 + 47 \\
56 & = 3 + 53 \\
58 & = 5 + 53 \\
60 & = 7 + 53 \\
\end{align*}
\][/tex]
This concludes the detailed, step-by-step solution to the problem.
