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I happened to stumble upon this page. Does anyone know about the validity of this claim?

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In principle it looks OK, the summation tests for divisibility by odd numbers between $3$ and $\sqrt{N}$. The claims about Riemann hypothesis, Goldbach Conjecture, and so on are, to put it nicely, ambitious. – André Nicolas Dec 3 '11 at 16:57
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@AndréNicolas What claims do you refer to? Note that these formulas are simply well-known algorithms encoded into a more arithmetical programming language. This is clearer when it is made explicit, e.g. see Conway's Fractran language. – Gone Dec 3 '11 at 18:52
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@Bill Dubuque: It is best not to attempt to summarize. One need only travel to the web site linked to in the main post. – André Nicolas Dec 3 '11 at 19:21
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Note that "a formula for the n-th prime" has never been considered an open problem. I honestly don't know why so many cranks think it is... – Charles Dec 4 '11 at 17:16

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His equations seem correct after skimming, but they are trivial and do not solve any open problem, they just an extremely roundabout and unhelpful way of stating the definitions. Stating Riemann hypothesis or twin prime conjecture is very far from proving it. He claims he proved them on "about discovery page". See Ten Signs a Claimed Mathematical Breakthrough is Wrong.

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We're in no position to judge, I saw this on the website: "NAAS (USA) Awarded A++ = Excellent Grade to article of prime numbers formula by Prof. S.M.R.Hashemi Moosavi" – Gigili Jan 3 '12 at 15:57
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Awards prove nothing. They are mostly given for political reasons. Further, we are in a position to judge since we have the ability to think. – user16697 Jan 3 '12 at 16:20

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