"prime numbers formula" crankery

[Mini-Geek]

http://www.primenumbersformula.com/

In classic crank fashion, it's hard to understand what he's trying to say, but I'm pretty sure he claims to have formulas for generating primes and Mersenne primes, has proved the infinitude of twin primes, and has solved the Riemann hypothesis.

[cheesehead]

Originally Posted by Mini-Geek

http://www.primenumbersformula.com/

In classic crank fashion, it's hard to understand what he's trying to say,

But let's be careful to separate the difficulty of understanding his noticeably-flawed English from the actual "crankness" of ideas/claims he presents.

but I'm pretty sure he claims to have formulas for generating primes and Mersenne primes, has proved the infinitude of twin primes, and has solved the Riemann hypothesis.

I don't see any claim of his to have proven the Riemann Hypothesis.

I do see references to "the solution of Riemann Zeta equation" and "solution to Riemann zeta equation (http://www.primenumbersformula.com/a...s/image038.gif)", but those are not at all the same as claiming a proof of the Riemann Hypothesis. (The Riemann Hypothesis is a conjecture about a common property of all nontrivial zeros (solutions) of the zeta function.)

At least he credits GIMPS properly, though without a single link (even in his "Favorite Links" section!) to us:

GIMPS, the Great Internet Mersenne Prime Search, was formed in January 1996 to discover new world-record-size Mersenne primes. GIMPS harnesses the power of thousands of small computers like yours to search for these "needles in a haystack".

Most GIMPS members join the search for the thrill of possibly discovering a record-setting, rare, and historic new Mersenne prime. Of course, there are many other reasons.

He does have multiple links to Chris Caldwell's pages. His section "Why do people find these primes?" is adapted from Caldwell's page with the same title, and credited properly thereto.

[CRGreathouse]

His claim that generating a formula for the prime is a "2300-years old unsolvable problem" is a little wacky. It's been solved... over and over and over.

[retina]

But the formula is posted there on the page in plain view. I would think it would by easy to find a non-prime generated by the formula.

Although strange how it says "unsolvable problem" and then goes on to give a solution!

[Uncwilly]

Correct me if I am wrong, but, doesn't this simplify to:

H(m)=(2m+1)¹

?

[retina]

Originally Posted by Uncwilly

Correct me if I am wrong, but, doesn't this simplify to:

H(m)=(2m+1)¹

?

Well, at this stage I am too lazy to program anything up to check it, but in the website it shows this sequence "3,5,7,2,11,13,2,17,19, ..." So assuming they applied their formula correctly (I Haven't checked), then it can't be a simple 2m+1.

[bsquared]

Originally Posted by Uncwilly

Correct me if I am wrong, but, doesn't this simplify to:

H(m)=(2m+1)¹

?

Not with those floor functions...

Here's excel code:

=2*((2*B16+1)/2)^(FLOOR((2*B16+1)/(FACT(2*B16)+1)*FLOOR((FACT(2*B16)+1)/(2*B16+1),1),1))

The first counterexample I find is at m=12.

[Jens K Andersen]

Originally Posted by bsquared

Here's excel code:

You probably have rounding errors. In PARI/GP the formula is:
H(m) = 2*((2*m+1)/2)^floor((2*m+1)/((2*m)!+1)*floor(((2*m)!+1)/(2*m+1)))

The formula is correct but useless. It uses Wilson's theorem and the floor function to give:
H(m) = 2m+1, if 2m+1 is prime
= 2, otherwise

Wilson's theorem says 2m+1 is prime iff (2m)!+1 is divisible by 2m+1.
Then floor((2*m+1)/((2*m)!+1)*floor(((2*m)!+1)/(2*m+1))) becomes 1 when 2m+1 is prime, and 0 when it's composite.

[CRGreathouse]

The formula looks fine to me -- it should generate the odd primes in order, with 2 replacing each odd composite.

Edit: Jens Anderson beat me to it.

[cheesehead]

Originally Posted by Jens K Andersen

The formula is correct but useless. It uses Wilson's theorem and the floor function to give:
H(m) = 2m+1, if 2m+1 is prime
= 2, otherwise

Wilson's theorem says 2m+1 is prime iff (2m)!+1 is divisible by 2m+1.
Then floor((2*m+1)/((2*m)!+1)*floor(((2*m)!+1)/(2*m+1))) becomes 1 when 2m+1 is prime, and 0 when it's composite.

Hmmm... Makes me wonder how:

In Year of 2007 (AAAS) " National Association Of Academies Of Science " (USA) Awarded an A++ = Excellent grade to prime numbers formula and its results by prof.S.M.R.Hashemi Moosavi.

[retina]

It seems to me that this is more of prime testing formula than a function. They have taken a prime testing formula and manipulated the algebra to give you back the original prime you tested if it passes or 2 if it fails. It would be easy to change the '2' to any other number (like pi or e or i) to give a fixed value when the test fails.

Hmm, that has given me an idea ...