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I read about a book called 'Calculate Primes' by James McCanney. It claims to have cracked the pattern for generating families of primes, and also the ability to factorize large numbers. http://www.jmccanneyscience.com/CalculatePrimesCoversandTableofContents.HTM Is this true ? I am a math newbie, so asking out of curiosity.

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I would want to see them solve the RSA Factoring problem before I even get interested. Show me the factors! –  Amzoti Feb 20 '13 at 16:56
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An unusual book. Goes against convention by listing $1$ as a prime. –  André Nicolas Feb 20 '13 at 17:13
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I compute 240 points on the prime number crackpot index. Here's a gem from his page: "His second great discovery, which was published almost 2 decades before its discovery..." (Was this discovery time travel?) –  Douglas S. Stones Feb 20 '13 at 18:52
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Looks like it's a version of the sieve: tysondw.blogspot.co.uk/2009/01/… –  Jack Aidley Feb 20 '13 at 20:55
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In law, there's 'innocent until proven guilty'. In math, it's 'suspicious until proven correct'. –  Quinn Culver Feb 20 '13 at 22:19

4 Answers 4

It is true that the author claims to have cracked "the" prime number problem. It is however very hardly true that he has. If the finding were as correct an valuable as claimed and the author were as truely a mathematician as claimed, then probably,

  • the title page would not contain such a blatant typo RANDON for RANDOM
  • the result would have been published in a peer-reviewed journal before such a popularizing all-round monograph covering also galaxies and snowflakes
  • the result would probably not be trademakred and patented

Then again, his claim that "the Prime numbers are a unique set of numbers. They can be calculated using only the operations of addirion and subtraction, starting with just the numbers $0$ and $1$" can hardly be defeated.

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The guy also writes a preface, but doesn't capitalize the first letters in his first and last name when signing it. –  krikara Feb 21 '13 at 1:44

Almost certainly not, and I can guarantee it's not worth \$24.95 for the privilege of checking.

Some helpful links include here and here.

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A mathematician Underwood Dudley, had written on how to deal with such "ground breaking" claims which don't have a leg of their own to stand on, in his paper "What to do when the Trisector Comes" (A trisector being someone who claims to have found a way to trisect an angle using only ruler and pair of compasses). I'm providing the link here, and also quoting part of the conclusion:

Then what is the right thing to do when the trisector comes? To the first letter from a trisector respond politely, being sure to congratulate him for the goodness of his approximation, or its simplicity, or his cleverness in finding a new approximation. Include a computer printout giving the errors in the construction for angles of various sizes--I go from 0 to 180 degrees in steps of three. This is important because the computer still has the power to inspire respect and awe. Also, enclose some other approximate trisections with some remark like, "I thought you might be interested in seeing how other people have gotten approximate trisections."

Applying this technique, one might ask the author of this book to try to use his method to factor 2048 bit RSA keys, or even better, beat the current world record in computing the highest prime number!

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Nice response! One thing that's worth pointing out for those who didn't spot it is that the angles that he uses are not chosen at random. An angle of 3 degrees (and hence any integer multiple thereof) is constructible by straightedge and compass, but an angle of 1 degree is not. –  Pseudonym Feb 20 '13 at 22:55
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Underwood Dudley has actually published a few books on this sort of behavior. I rather enjoyed "Mathematical Cranks", which is a collections of some of the more interesting cases he's collected. –  MartianInvader Feb 20 '13 at 23:26

His method is a "Fast Eratosthenes Sieve": he combines Erathostene's sieving (excluding multiples) with enriching the remaining integers by adding the primorials, obtaining numbers with higher primes content a la Euclid p1...pk+1, and its generalizations N=p1.p2....pk + integer not divisible by the previous pk's; these are again used to remove composite numbers. Lucian

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