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CITC
Fri Jan 09, 2004 9:28 pm
Program to Determine Perfect Numbers
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Unfortunately this program takes really long to determine the perfect numbers after 1700 something... I don't think theres any better way to do it though, or it hasn't been discovered yet.. this is brute force!! :wink:
for any who don't know: Perfect Numbers are numbers that their factors (excluding the number itself) add up to the number... wow explained that bad, here's an example.
6 is a perfect number.. factors of 6 = 1,2,3,6.. exclude 6... 1+2+3 = 6
var num : int := 0
var key : string (1)
loop
cls
num += 1
var keep : array 1 .. num of int
var total : int := 0
for k : 1 .. num
keep (k) := 0
end for
for i : 1 .. num
if num rem i = 0 then
keep (i) := i
end if
end for
for p : 1 .. num
if keep (p) not= 0 then
total += keep (p)
end if
end for
if (total div num = 2) and (total rem num = 0) then
put num
for o : 1 .. num
if keep (o) not= 0 then
put keep (o), ", " ..
end if
end for
getch (key)
end if
end loop
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McKenzie
Fri Jan 09, 2004 10:49 pm
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A bit faster:
function isPerfect (n : int) : boolean
var sum := 0
for i : 1 .. n div 2
if n mod i = 0 then
sum := sum + i
end if
end for
if sum = n then
result true
else
result false
end if
end isPerfect
var now:int
for i:1..10000
if isPerfect(i) then
put i
clock(now)
put "time ",now/1000 :0:2, " Seconds"
end if
end for
The timer stuff is there because I was comparing with yours to make sure mine was worth posting.
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AsianSensation
Fri Jan 09, 2004 10:50 pm
Re: Program to Determine Perfect Numbers
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I don't think theres any better way to do it though, or it hasn't been discovered yet..
yeah, actually there is a better way, there is a formula that let you derive any perfect number, google it up, I sure it's on the web somewhere.
or you can prove it yourself?
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Andy
Sat Jan 10, 2004 10:41 am
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LOL.... formulas... the reason why we use compsci is cuz we dont like formulas.... its actually the same speed for a computer to use a for loop to add one to a number than to multiply the number
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CITC
Sat Jan 10, 2004 11:40 am
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Your right there is a formula for it. I'll post the program in a day or two probably.
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santabruzer
Sat Jan 10, 2004 4:18 pm
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i've always wondered if there was a formula for prime numbers.. so that you wouldn't have to devide by every number halfway up to that number... and for perfect ones.. iyea.. it's cool.. there's a formula...
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AsianSensation
Sat Jan 10, 2004 5:47 pm
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there is no formula for prime numbers, that's why really really large prime numbers are used to encrypt many many things.
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Andy
Sat Jan 10, 2004 8:04 pm
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but u can get a program that generates prime numbers... me and shaun are making one, one of these days
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AsianSensation
Sat Jan 10, 2004 9:55 pm
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sure, there are many many ways of generating a prime number, but starting with the Mersenne (did I spell that right?) prime is what they do now to find a really large prime number. Mersenne primes are number in the form of 2^n - 1. The other day, we were told that the largest prime known was updated again, and they found that number by passing parts of the prime finding program to alot of computers, so if you want to be part of the finding team, all you have to do was download their program, and it runs in the background. Then they take all the info generated at different computer and come up with the number.
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CITC
Sat Jan 10, 2004 11:37 pm
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I heard about 1 year and a half ago (i think) that an Indian mathemetician who was amazing with numbers and patterns had discovered a formula to get prime numbers... read it in some magazine, dunno which. I'm not too sure though, I could be wrong.
btw, that bit about the mersenne prime formula being 2^n - 1 is half of the perfect number formula.
its 2^(n - 1) * (2^n - 1)
I'm overwhelmed with trying to get the slime volleyball bouncing thing working though, if no one else makes this program and posts it, I'll make it when I can.
Cheers