I'll have to admit that I even tried to implement Mr. Brown's

algorithm, to torture-test the primality-checking routines in my

programming language "Frink",

http://futureboy.homeip.net/frinkdocs/
(although I'll certainly admit that the description given in his

PowerPoint presentation does not give enough information to be usable to

anyone. The mention of the "Nyquist Criterion" is, I believe,

intentionally vague. I understand both the Nyquist stability criteria,

and the Nyquist sampling criteria, and those who understand them will

see, readily, that this mention is insufficient and inappropriate.)

He also sent me a spreadsheet that just had unexplained numbers in

it, all entered by hand; there was no equation in the entire thing, and

was thus useless.

In any case, even though the description was clearly insufficient, I

gave him the benefit of the doubt and tried many different

interpretations of the vague bits.

For example, it's unclear what "minimums of R" means, so I tried all

of the following:

* Minimum value of R found in a range

* Minimum absolute value of R

* Minimum sum of values of R

* Minimum sum of absolute values of R

* Minimum RMS sum of values of R

In addition, since this is obvious *incredibly* sensitive to the

exact numbers you sample, I tried lots of sampling rates and sampling

offsets, including very high sampling rates which should exceed any

interpretation of the Nyquist sampling criterion, if indeed that is what

was meant. I tried lots of "bin" sizes for the sums and averages. I

also tried scaling the minima along with their magnitudes (the values of

R tend to get larger as you sample larger numbers, of course.)

I worked with numbers of which I knew the factors, and, to make a

long story short, I see absolutely no evidence that the algorithm, as

presented, has any utility. Even if you know the exact factors, and try

really hard to make it fit, you can't even force the algorithm to point

to the right places, other than what would be expected by pure

probabilities. If you have 10 bins, 1/10 of the time you'll sample

numbers that drop it in the right bin. I don't see that as strong evidence.

Rather, it became quite clear that the minima found, even with the

smoothing produced by summing, has a lot of stochastic variation which

is directly due to the particular sample points that you chose.

It is easy to see, therefore, that _post facto_, one could choose a

set of sample points that "proved" this algorithm true if you already

knew the factors of a number. I will absolutely not accept any post

facto evidence as evidence that this algorithm works, especially when

work is not shown.

I agree that Décio's test is fair, acceptable, and should well be

within the reach of Mr. Brown's algorithm if it works as claimed. So,

please, either provide the digits, or go back to the drawing board, and

stop making further unsubstantiated claims. I would suggest that it is

not a worthwhile use of one's time to attempt to reproduce this

algorithm unless Mr. Brown provides the digits requested (unless you're

writing a programming language that you're torture-testing. :) )

If, indeed, he provides the factors, I will gladly help code the

algorithms. Seems like pretty safe money.

--

Alan Eliasen | "You cannot reason a person out of a

eliasen@... | position he did not reason himself

http://futureboy.homeip.net/ | into in the first place."

| --Jonathan Swift