It’s probably a long shot, but is there a way around this error? It’s highly annoying. I’ve ran into it twixe so far. Once when trying to do RSA encryption, and now again while testing Carmichael numbers. I don’t want to break my simple equations down into smaller ones…
Aren’t Carmichael Numbers the pseudo primes? I vaguely recall that they get large pretty quickly, so you’d need multiple precision arithmetic to calculate them. AppleScript doesn’t support more than single precision (unless someone has written an OSAX for higher precision).
Yes, they’re numbers that pass the Fermat test, but are not prime.
They start at 561.
My script is theoretically sound. It works in terms of testing Prime, and testing Carmichael, yet I can’t see if Carmichael works properly because it get this error. I suppose i could just go on not knowing, and I’m pretty sure it works, I’m just one of those people who “have to know”.
I am a bit out of my league here, but could you use the shell and pipe your equations to ‘bc’ ?
I believe that bc can handle quite large integers without modification.
Andy
I <3 you. I mean that in the most non-weird way. 
code!
global buttonPressed
property carmichaelness : false
property primeness : false
property isPrime : false
main()
on main()
set buttonPressed to "x"
display dialog "Enter a number:" default answer "" buttons {"Cancel", "OK"} default button "OK"
try
set theNumber to text returned of result as number
on error
display dialog "I said enter a number." buttons {"OK"} default button "OK" with icon stop
restartScript()
end try
my testCarmichael(theNumber)
my testPrimeness(theNumber)
if carmichaelness and not primeness then
display dialog theNumber & " is a Carmichael number." as string buttons {"OK"} default button "OK" with icon 1
restartScript()
else
display dialog theNumber & " is normal." as string buttons {"OK"} default button "OK" with icon 1
restartScript()
end if
end main
on testCarmichael(testCar)
if testCar ≠1 then
set testCar2 to testCar - 1
set randomNumber to random number from 2 to testCar2
set theResult to "echo '" & randomNumber & " ^ " & testCar & " % " & testCar & "' | bc" as string
set theResult to do shell script theResult
set theResult to theResult as number
if theResult is equal to randomNumber then
set carmichaelness to true
else
set carmichaelness to false
end if
else
set carmichaelness to false
end if
end testCarmichael
on testPrimeness(testPrime)
if class of testPrime is real then
display dialog "Real numbers cannot be prime." buttons {"OK"} default button "OK" with icon stop
copy the result as list to {buttonPressed}
end if
if testPrime < 0 then
set theFlag to -1
else
set theFlag to 1
end if
if testPrime is in {2, -2} then
set testPrime to testPrime as string
display dialog testPrime & " is a prime number, but not a Carmichael number." buttons {"OK"} default button "OK"
restartScript()
else if testPrime is in {1, 0, -1} then
set testPrime to testPrime as string
display dialog testPrime & " is not a prime, or Carmichael number." buttons {"OK"} default button "OK"
restartScript()
end if
if (testPrime mod 2) = 0 then
if testPrime ≠"2" then
display dialog "Even numbers whos magnitude are greater than 2 are never prime." buttons {"OK"} default button "OK" with icon stop
copy the result as list to {buttonPressed}
end if
end if
repeat with inc from 3 to (2 * (((testPrime * theFlag) ^ (1 / 2)) div 2) + 3) by 2
if (testPrime mod inc) = 0 then
set testPrime to testPrime as string
set primeness to false
display dialog testPrime & " is not a prime number as it has a divisor of " & inc buttons {"OK"} default button "OK"
copy the result as list to {buttonPressed}
end if
end repeat
if buttonPressed = "OK" then
set isPrime to false
else
set isPrime to true
end if
if isPrime = true then
set testPrime to testPrime as string
set primeness to true
display dialog testPrime & " is a prime number." buttons {"OK"} default button "OK"
end if
end testPrimeness
on restartScript()
display dialog "Do you want to go again?"
main()
end restartScript
This is pretty cool. On my dual 2.7 GHz G5 it took about 4 minutes to do 825265. I didn’t try any higher. How high are you trying to go?
I did not try:
999987515379253441
Andy
Browser: Safari 412
Operating System: Mac OS X (10.4)
Slick, but requires patience. I’ve had 1234567 running for a long time now and it’s eating cpu cycles in bc without a result so I can’t tell if it’s stuck, or just munching away. There is another calculator in Darwin calle dc; “a reverse-polish desk calculator which supports unlimited precision arithmetic”. Maybe it’s faster (haven’t used it).
Honestly I was just doing the first few numbers as part of a challenge. As for dc, it’s stack based. So it looks like “3 4 *” to get 3 * 4. It’s just too weird for me.