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VB 6 Helper Newsletter
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Rod Stephens
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Mar 06, 2009 13:25 PST
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Sorry for the long hiatus. My latest book is keeping me WAY busier than
I would like. Unfortunately that's likely to continue for a while.
But I wanted to send something out for a couple of reasons:
- DevX posted a special report called "Move to the Future with
Multicore Code" (http://www.devx.com/SpecialReports/Door/40893). It
includes links to 9 DevX articles about multicore programming including
my two "Getting Started with the .NET Task Parallel Library" and
"Getting Started with the .NET Task Parallel Library: Multicore Case
Studies."
- I've added a new section in BooksToKeep.com for Christopher Moore.
I was amazed to find that I had forgotten his books when I recently
finished "Island of the Sequined Love Nun." It's absolutely hilarious!
My favorite of his so far.
- This week also features some kind of interesting stories that came
out of out local elementary school’s fifth grade Math Olympiad group (in
VB 6 and .NET versions). They're pretty optional but include a useful
factorization function.
Have a great week and thanks for subscribing!
Rod
RodSte-@vb-helper.com
Books To Keep: http://www.BooksToKeep.com
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*** Now Available ***
Beginning Database Design Solutions
http://www.amazon.com/exec/obidos/ASIN/0470385499/vbhelper/
Visual Basic 2008 Programmer's Reference
http://www.amazon.com/exec/obidos/ASIN/0470182628/vbhelper/
==========
VB6 Contents:
1. New HowTo: Calculate the prime factors of a product of primes plus or
minus 1 in Visual Basic 6
2. New HowTo: Calculate the prime factors of numbers of the form 999997
in Visual Basic 6
Both Contents:
3. New Links
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<VB6>
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1. New HowTo: Calculate the prime factors of a product of primes plus or
minus 1 in Visual Basic 6
http://www.vb-helper.com/howto_prime_products.html
http://www.vb-helper.com/HowTo/howto_prime_products.zip
In around 300 BC, Euclid proved that there are an infinite number of
primes using this argument:
Suppose there are a finite number of primes and they are p1, p2,
..., pn. Then none of can divide the value:
p1 * p2 * ... * Pn + 1
So this new number is also prime, contradicting the assumption that
p1, p2, ..., pn are all of the primes.
Recently someone suggested a similar technique for finding a big prime.
The idea is to take the product of the first N primes and then add or
subtract 1.
Unfortunately this method doesn't work. While the new number is not
divisible by the primes you use to build the number, there may be other
primes beyond those (but still smaller than the square root of the new
number) that divide it.
This program demonstrates this by calculating products of the first N
primes and then finding their prime factors.
The following code shows the program's Form_Load event handler. It
calculates products of the first 1, 2, ..., 9 primes and calls function
Factors to display their prime factors.
Private Sub Form_Load()
Dim primes() As String
Dim result As String
Dim i As Integer
Dim j As Integer
Dim num As Long
Dim txt As String
primes = Split("2,3,5,7,11,13,17,19,23", ",")
result = ""
For i = LBound(primes) To UBound(primes)
num = 1
txt = ""
For j = LBound(primes) To i
txt = txt & " x " & primes(j)
num = num * CLng(primes(j))
Next j
txt = Mid$(txt, 3)
num = num - 1
result = result & txt & " - 1 = " & Format$(num) & " = " &
Factors(num) & vbCrLf
num = num + 2
result = result & txt & " + 1 = " & Format$(num) & " = " &
Factors(num) & vbCrLf
Next i
txtResult.Text = result
txtResult.SelStart = 0
txtResult.SelLength = 0
End Sub
The Factors function is the only part of this program that is really
generally useful. It returns a string listing a number's prime factors.
The function starts by pulling factors of 2 out of the number. As long
as the number is divisible by 2, the program adds a 2 to the output and
divides the number by 2.
Eventually the number becomes odd (there may be remaining odd factors
or, if the number is a power of two, then this step reduces the number
to 1). At that point, the program starts pulling out odd factors.
Starting with the test factor value 3, if the test factor value divides
the number evenly, then the program adds it to the output and divides
the test factor from the number. If the test factor doesn't divide the
number evenly, then the program adds 2 to the test factor to consider
the next odd number.
The program repeats this step until the test factor is greater than the
square root of the remaining number. At that point, whatever is left of
the number is prime.
' Return the number's prime factors.
Private Function Factors(ByVal num As Long) As String
Dim result As String
result = ""
' Take out the 2s.
Do While num Mod 2 = 0
' This is a factor.
result = result & " x 2"
num = num \ 2
Loop
' Take out other primes.
Dim factor As Long
factor = 3
Do While factor * factor <= num
If num Mod factor = 0 Then
' This is a factor.
result = result & " x " & Format$(factor)
num = num \ factor
Else
factor = factor + 1
End If
Loop
If num > 1 Then result = result & " x " & Format$(num)
If Len(result) = 0 Then
result = "1"
Else
result = Mid$(result, 3)
End If
Factors = result
End Function
Incidentally, the first example that p1 * p2 * ... * pn - 1 is non prime
is:
2 x 3 x 5 x 7 - 1 = 209 = 11 x 19
The first example that p1 * p2 * ... * pn + 1 is non prime is:
2 x 3 x 5 x 7 x 11 x 13 + 1 = 30031 = 59 x 509
Also go to
ncenews.org/view/generic/id/36979/title/Largest_known_prime_number_found
for an interesting article about the largest known prime number (as of
September 28, 2008). It has around 13 million digits!
==========
2. New HowTo: Calculate the prime factors of numbers of the form 999997
in Visual Basic 6
http://www.vb-helper.com/howto_nines_prime.html
http://www.vb-helper.com/HowTo/howto_nines_prime.zip
Recently a bunch of fifth graders were asked to think of the largest
prime numbers they could. A lot of them wrote numbers of the form
99999997. It's easy to see that these are not divisible by 2 or 5.
Because the digits aren't divisible by 3, the number is also not
divisible by 3 (most of them knew that trick).
In fact, the first several numbers in this format 7, 97, and 997 are
prime, and it's not easy to tell whether larger numbers of this sort are
prime in your head.
This program writes out several numbers in this format and displays
their prime factors.
The program's Form_Load event handler loops through nine of these
numbers, calling function Factors to display their prime factors.
Private Sub Form_Load()
Dim result As String
Dim nine As String
Dim i As Integer
Dim num As Long
result = ""
nine = "7"
For i = 1 To 9
num = CLng(nine)
result = result & vbCrLf & Format$(num) & " = " & Factors(num)
nine = "9" & nine
Next i
result = Mid$(result, Len(vbCrLf) + 1)
txtResult.Text = result
txtResult.SelStart = 0
txtResult.SelLength = 0
End Sub
The Factors function is the only part of this program that is really
generally useful. It returns a string listing a number's prime factors.
The function starts by pulling factors of 2 out of the number. As long
as the number is divisible by 2, the program adds a 2 to the output and
divides the number by 2.
Eventually the number becomes odd (there may be remaining odd factors
or, if the number is a power of two, then this step reduces the number
to 1). At that point, the program starts pulling out odd factors.
Starting with the test factor value 3, if the test factor value divides
the number evenly, then the program adds it to the output and divides
the test factor from the number. If the test factor doesn't divide the
number evenly, then the program adds 2 to the test factor to consider
the next odd number.
The program repeats this step until the test factor is greater than the
square root of the remaining number. At that point, whatever is left of
the number is prime.
' Return the number's prime factors.
Private Function Factors(ByVal num As Long) As String
Dim result As String
result = ""
' Take out the 2s.
Do While num Mod 2 = 0
' This is a factor.
result = result & " x 2"
num = num \ 2
Loop
' Take out other primes.
Dim factor As Long
factor = 3
Do While factor * factor <= num
If num Mod factor = 0 Then
' This is a factor.
result = result & " x " & Format$(factor)
num = num \ factor
Else
factor = factor + 1
End If
Loop
If num > 1 Then result = result & " x " & Format$(num)
If Len(result) = 0 Then
result = "1"
Else
result = Mid$(result, 3)
End If
Factors = result
End Function
Incidentally, the very next number with this format (the first one
that's hard to verify in your head) is non-prime:
9997 = 13 x 769
Nice try, kids!
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<Both>
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http://www.vb-helper.com/links.html
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