# Answer to Question #13769 in Visual Basic for with

Question #13769

Given a range of integers by its lower and upper limit, print a list of all even numbers and their Goldbach composition.

Example:

Input lower limit: 9

Input upper limit: 20

Output:

10 = 3 + 7

12 = 5 + 7

14 = 3 + 11

16 = 3 + 13

18 = 5 + 13

20 = 3 + 17

Example:

Input lower limit: 9

Input upper limit: 20

Output:

10 = 3 + 7

12 = 5 + 7

14 = 3 + 11

16 = 3 + 13

18 = 5 + 13

20 = 3 + 17

Expert's answer

Module Module1

Sub Main()

Dim lowerlimit As Integer

Dim upperlimit As Integer

Console.WriteLine("Input lower limit: ")

lowerlimit = Integer.Parse(Console.ReadLine())

Console.WriteLine("Input upper limit: ")

upperlimit = Integer.Parse(Console.ReadLine())

For i As Integer = lowerlimit To upperlimit

If i Mod 2 = 0 Then

Show(i)

End If

Next

Console.ReadLine()

End Sub

Private Sub Show(ByVal number As Integer)

Dim N As Integer = number

Dim isprime(N) As Boolean

For i As Integer = 2 To N - 1

isprime(i) = True

Next

For i As Integer = 2 To N

If (i * i < N) Then

If isprime(i) Then

For j As Integer = i To N

If i * j < N Then

isprime(i * j) = False

End If

Next

End If

End If

Next

Dim primes As Integer = 0

For i As Integer = 2 To N - 1

If isprime(i) Then

primes = primes + 1

End If

Next

Dim list(primes) As Integer

Dim nn As Integer = 0

For i As Integer = 0 To N - 1

If isprime(i) Then

nn = nn + 1

list(nn) = i

End If

Next

Dim left As Integer = 0

Dim right As Integer = primes - 1

While left <= right

If (list(left) + list(right) = N) Then

Exit While

ElseIf (list(left) + list(right) < N) Then

left = left + 1

Else

right = right - 1

End If

End While

If (list(left) + list(right) = N) Then

Console.WriteLine(N.ToString() + " = " + list(left).ToString() + " + " + list(right).ToString())

Else

Console.WriteLine(N.ToString() + " not expressible as sum of two primes")

End If

End Sub

End Module

Sub Main()

Dim lowerlimit As Integer

Dim upperlimit As Integer

Console.WriteLine("Input lower limit: ")

lowerlimit = Integer.Parse(Console.ReadLine())

Console.WriteLine("Input upper limit: ")

upperlimit = Integer.Parse(Console.ReadLine())

For i As Integer = lowerlimit To upperlimit

If i Mod 2 = 0 Then

Show(i)

End If

Next

Console.ReadLine()

End Sub

Private Sub Show(ByVal number As Integer)

Dim N As Integer = number

Dim isprime(N) As Boolean

For i As Integer = 2 To N - 1

isprime(i) = True

Next

For i As Integer = 2 To N

If (i * i < N) Then

If isprime(i) Then

For j As Integer = i To N

If i * j < N Then

isprime(i * j) = False

End If

Next

End If

End If

Next

Dim primes As Integer = 0

For i As Integer = 2 To N - 1

If isprime(i) Then

primes = primes + 1

End If

Next

Dim list(primes) As Integer

Dim nn As Integer = 0

For i As Integer = 0 To N - 1

If isprime(i) Then

nn = nn + 1

list(nn) = i

End If

Next

Dim left As Integer = 0

Dim right As Integer = primes - 1

While left <= right

If (list(left) + list(right) = N) Then

Exit While

ElseIf (list(left) + list(right) < N) Then

left = left + 1

Else

right = right - 1

End If

End While

If (list(left) + list(right) = N) Then

Console.WriteLine(N.ToString() + " = " + list(left).ToString() + " + " + list(right).ToString())

Else

Console.WriteLine(N.ToString() + " not expressible as sum of two primes")

End If

End Sub

End Module

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