Complex Prime Number Test

11112014, 06:09 PM
(This post was last modified: 11132014 01:21 PM by Eddie W. Shore.)
Post: #1




Complex Prime Number Test
Program:
Code: EXPORT cisprime(z) Examples: cisprime(24*i) returns 0 cisprime(2+5*i) returns 1 Source: http://mathworld.wolfram.com/GaussianPrime.html 

11122014, 04:41 PM
Post: #2




RE: Complex Prime Number Test
Wow  never heard of those before. Thanks for teaching us!
I am puzzled  your program tests for 3mod4 of the nonzero component if the other is zero, but doesn't test the nonzero component for primality. So, for example, 0+/ 15i isn't a Gaussian prime as 15 isn't prime. Am I mistaken? 

11122014, 05:31 PM
Post: #3




RE: Complex Prime Number Test
(11122014 04:41 PM)Jim Horn Wrote: I am puzzled  your program tests for 3mod4 of the nonzero component if the other is zero, but doesn't test the nonzero component for primality. So, for example, 0+/ 15i isn't a Gaussian prime as 15 isn't prime. Am I mistaken? Quote:If a=0, then bi is a Gaussian prime iff b is an ordinary prime and b=3 (mod 4). Thus 15i is not a Gaussian prime since 15 is not an ordinary prime. However 5 is not a Gaussian prime though it is an ordinary prime since 5=1 (mod 4). The complex factors of 5 are (2 + i)(2 − i). HTH Thomas 

11132014, 01:23 PM
Post: #4




RE: Complex Prime Number Test
(11122014 05:31 PM)Thomas Klemm Wrote:(11122014 04:41 PM)Jim Horn Wrote: I am puzzled  your program tests for 3mod4 of the nonzero component if the other is zero, but doesn't test the nonzero component for primality. So, for example, 0+/ 15i isn't a Gaussian prime as 15 isn't prime. Am I mistaken? Thomas, Thanks for pointing out the glaring omission  much appreciated. The edited algorithm should be correct now. Eddie 

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