Is it true that the book 'Calculate Primes' has found the pattern? 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. 
 A: 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
A: 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.
A: 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.
A: 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!
