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From: Dave L. Renfro on 12 Jul 2006 18:35
Colin wrote:

>> What's everyone's opinion of the site
>> www.primenumbersformula.com? Is the
>> author for real, or just a crank?

Phil Carmody wrote:

> At least a non-negligible proportion of crank.
> The only sensible material on that page is vast
> swathes of copyrighted material lifted from
> Professor Caldwell's Prime Pages, such as
> http://primepages.org/notes/faq/why.html

Heh, he didn't even bother to correct the grammar
error when he lifted the material!

"... numbers like 6 and 28 who are equal to the sum
of their aliquot divisors ..."

Dave L. Renfro

From: Ioannis on 12 Jul 2006 18:46
"Phil Carmody" <thefatphil_demunged(a)yahoo.co.uk> wrote in message
news:87u05mo5s5.fsf(a)nonospaz.fatphil.org...
>
> "Colin" <colinpoakes(a)hotmail.com> writes:
>
> > What's everyone's opinion of the site www.primenumbersformula.com? Is
> > the author for real, or just a crank?
>
> At least a non-negligible proportion of crank. The only sensible
> material on that page is vast swathes of copyrighted material
> lifted from Professor Caldwell's Prime Pages, such as
> http://primepages.org/notes/faq/why.html

Also, a researcher of high caliber must be REALLY careful about what one
writes on one's webpage:

Two quotes:

1) I have discovered the formula of the prime numbers after 20 years of
research and injury.

2) I am Seyyed Mohammad Reza Hashemi Moosavi and university professor that I
chosen as a superior investigator in superiors and initiators festival in
1383.

What's 1) supposed to mean? That he got injured after finding the formula or
that he was continuously injured during those 20 years as a result of his
research?

According to 2) this guy is at least 623 years old. Perhaps his formula was
the elixir for eternal life.

> Phil
--
Ioannis

From: Tim Peters on 12 Jul 2006 20:20
[amzoti, on www.primenumbersformula.com]
> Hi Phil,
>
> do you actually know how to interpret this function?
>
> I was trying to read it and not sure what the floor like functions
> mean.

I'm sure they mean the floor.

> I must also be misinterpreting something because it looks like
> most stuff cancels out.

I expect that's intentional ;-)

> Any ideas as this would be easy to test?

Well, let's look at it top down. It has the structure:

H(m) = 2*((2m+1)/2)^e(m)

for a messy function e(m), which we'll get to later. _Assume_ for the
moment that:

e(m) = 1 if 2m+1 is prime
= 0 if 2m+1 is not prime

If that's true, then:

H(m) = 2*((2m+1)/2)^1 = 2m+1 if 2m+1 is prime
= 2*((2m+1)/2)^0 = 2 if 2m+1 is not prime

So, if that's true, H(m) _obviously_ generates all and only the primes as m
goes from 1 to infinity, and generates each prime exactly once except for 2.
2 is generated for each m s.t. 2m+1 is not prime. If you look at the
sequence he gives below it:

it generates all the prime numbers (3,5,7,2,11,13,2,17,19, ...)

that matches the above. At m=1, 2m+1=3 and is prime. Likewise for 5 and 7
at m=2 and m=3. At m=4, 2m+1=9 is not prime, and that's the first 2 in his
sequence. m=5 gives 11 and m=6 gives 13, then at m=7 2m+1=15 is not prime
and another 2 shows up in his sequence. Etc.

So it just boils down to finding a function e(m) s.t.

e(m) = 1 if 2m+1 is prime
= 0 if 2m+1 is not prime

His e(m) works, and is really a pretty standard kind of trick if you're
attracted to silly ;-) functions like this:

e(m) = floor(a * floor(b/a) / b)

where:

a = 2m+1
b = (2m)!+1

Remember that Wilson's theorem says p is prime if and only if p divides
(p-1)!+1. Substitute 2m+1 for p to get:

2m+1 is prime if and only if 2m+1 divides (2m!)+1

or, using the variable names just above,

2m+1 is prime if and only if a divides b

Suppose a does divide b (2m+1 is prime). Then b = q*a for some integer q,
and

floor(a * floor(b/a) / b) =
floor(a * floor(q*a/a) / (q*a)) =
floor(a * q / (q*a)) =
floor(1) =
1

So e(m) is 1 if 2m+1 is prime. OTOH, if a does not divide b (2m+1 is not
prime), then b = q*a + r for some integers q and r with 0 < r < a, and

floor(b/a) = floor((q*a + r)/a) = floor(q + r/a) =
since 0 < r/a < 1
q

so

floor(a * floor(b/a) / b) =
floor(a * q / (q*a + r)) =
since r > 0, q*a+r > q*a
0

So e(m) is 0 if 2m+1 is not prime, and we're done.

> However, right now it looks like crank/troll work!

It does seem overly impressed with itself. As an exercise, now figure out
why this function (found on Wikipedia) works:

f(n) = 2 + mod(2*n!, n+1)

That also generates all and only the primes as n goes from 1 to infinity,
and also generates each prime exactly once except for 2 (which is generated
infinitely often). IMO, that's more elegant.


From: Phil Carmody on 12 Jul 2006 21:07
"amzoti" <amzoti(a)yahoo.com> writes:
> Phil Carmody wrote:
> > mathman <mathnucl(a)optonline.net> writes:
> > > If the author is correct, his work would be publicized widely in the mathematics community. So far it hasn't happened, so I am skeptical.
> >
> > Anyone who's learned computability knows how to create an
> > almost unending stream of prime number generation functions.
> > There is no novel 'discovery' in that direction any more.
>
> Hi Phil,
>
> do you actually know how to interpret this function?
>
> I was trying to read it and not sure what the floor like functions
> mean. I must also be misinterpreting something because it looks like
> most stuff cancels out.
>
> Any ideas as this would be easy to test?
>
> However, right now it looks like crank/troll work!

I didn't look closely - I'd be surprised if there was anything
pithy in the first equation I saw. However, I do know that
floor is a 'cheat' used when counting things, such as factors.
If you take floor(x/a)-floor((x-1)/a) for example you get the
predicate 'x is divisibly by a' evaluated as 1 (true) or 0 (false).
Thus 'sieves' can be built by summing such expressions, and
the result 0 would imply passing the sieve - i.e. primeness.
Counting the number of values that pass that test gives you
the Pi function.

It's all fairly trivial. Fun when you first see it, but not deep.

Phil
--
The man who is always worrying about whether or not his soul would be
damned generally has a soul that isn't worth a damn.
-- Oliver Wendell Holmes, Sr. (1809-1894), American physician and writer
From: Phil Carmody on 12 Jul 2006 21:11
"Dave L. Renfro" <renfr1dl(a)cmich.edu> writes:
> Heh, he didn't even bother to correct the grammar
> error when he lifted the material!

The editors have been informed...

Phil
--
The man who is always worrying about whether or not his soul would be
damned generally has a soul that isn't worth a damn.
-- Oliver Wendell Holmes, Sr. (1809-1894), American physician and writer
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