On December 22, 2009 my book was published!
On June 3, 2010 the Mathematical Association of America (MAA) completed their review (click on Links and scroll down until you see “MAA Review” ).
SOME OF MY BOOK’S HIGHLIGHTS
I prove that the distribution of the prime numbers follows a fractal binary pattern.
I show that every positive integer starting from one has a distinct physical equivalent (click on Game and read the instructions).
I demonstrate that every twin prime is either a pair of an ordinary prime and a Gaussian prime or vice-versa. How can we achieve this? It is very simple. Let OP represent an ordinary prime and GP stand for a Gaussian prime, then every twin prime (p, p + 2) must be any of the following possibilities: (OP, OP) or (GP, GP) or (OP, GP) or (GP, OP). Hence, if OP = 4n + 1 and GP = 4m + 3 where both n and m are positive integers it is easy to show that every twin prime must be either of the type (OP, GP) or (GP, OP). To achieve our objective just equate each possibility with the respective formula. Please, try it yourself! For example, the first case is (OP, OP) which is equivalent to (4n + 1, 4m + 1) = (p, p + 2). In order for the previous equation to be valid both p = 4n + 1 and p + 2 = 4m + 1 must be true. But that is not possible since m = n + ½ and consequently m is not an integer as it should be. Repeating this procedure for the remaining cases you will realize that m and n are both positive integers only for (OP, GP) and (GP, OP) as mentioned previously.
I conjecture that 3x + 1 is not the only solution for the well-known Collatz problem. But what is the Collatz problem? This famous mathematical enigma states the following: pick any positive integer; if it is even divide it by two and if it is odd multiply the given number by three and add one to the result. If you repeat this process over and over again, the final answer will always be one independent of the integer picked. For example, pick 5 which is odd then 5 times three plus one is 16 which is even. Then, 16 divided by two is 8 which is even and when divided by two becomes 4 which is even. Finally, 4 divided by two is 2 which divided by two is one as expected. Try it with 7 and see if you get as a final result a one. Amazingly, nobody in this world is able to explain why this happens for every single positive integer that has been tested until today!
AND MUCH MORE…