Roger Hui wrote:
> I note that certain statements in
> http://primes.utm.edu/prove/prove2_3.html
> are incorrect.
Roger:
I agree with your analysis. Testing all numbers 73 < n < 9,080,191 gives
the non-primes 946 596926 6376126, and as stated, the bullet point is
false.
To make it true, we have to do the following:
- We only test odd numbers. This is mentioned near the top of the page,
but then ignored.
- We can only test numbers against basis elements smaller than the number.
This point does not arise in most of Jaeschke's paper, since he is
looking at consecutive small primes. The results quoted in the web page
occur almost as an afterthought to main results of the paper.
Despite the flaws in the exposition, I believe this approach can still be
made into a useful primality test. I have not experimented extensively,
but performance may be increased by not evaluating the full expression
(+./c=n-1) +. 1={:c=. a n&|@^ huo n-1
since you can reject a basis element if any element of c is n-1.
Best wishes,
John
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