Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Prime numbers and primality tests
Replies: 4   Last Post: Jan 22, 2013 11:18 PM

 Messages: [ Previous | Next ]
 bobbaillie@frii.com Posts: 18 Registered: 11/27/06
Re: Prime numbers and primality tests
Posted: Jan 21, 2013 12:06 AM

I forgot to say: if a composite N passes the usual probable prime
test
b^(N-1) = 1 (mod N)
for one base b, then it is more likely than the average number that
size to pass another test, c^(N-1) = 1 (mod N).

For example, N = 341 is a pseudoprime base 2, which means that 2^3401 (mod 341). There are 100 bases b between 1 and 340 such that b^340
= 1 (mod 341).

On the other hand, if b^(N-1) = 1 (mod N), then this N seems
(empirically and heuristically) to be LESS likely than average to pass
a Lucas probable prime test.

That's why I like to do one or more of EACH type of test, which I
think is what PrimeQ does.

Date Subject Author
1/14/13 John Feth
1/19/13 amzoti
1/20/13 bobbaillie@frii.com
1/21/13 bobbaillie@frii.com
1/22/13 bobbaillie@frii.com