Anita Calculations about prime numbers
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The principal role in all efforts in the discrete mathematic is played by the prime numbers always present with their beautiful, powerful, necessary and mysterious irregularity. This application was developed to be a small tool that works with prime numbers. In this program you will find: 1) Prime Calculations about prime numbers: How many primes up to N(Phi(N)),lists of prime with index, list of twins, lists of gaps, factorisation 2) Divisors Obtain a Vector indicating for any N < 2147483000 how many numbers there are with 2,3,4,5,6 ....divisors. Obtain lists of numbers characterized by the same number of their divisors. Information on other arithmetical functions and combinatory. 3) Methods of inclusion-exclusion and reverse. Calculate Phi (N) with these two methods. 4)Goldbach conjecture calculate pairs of prime, mixed and composites 5) Study and examine not formal elementary proofs of the Theorem of Fermat and the problem of 2N as well as the Goldbach conjecture. In particular to understand the proofs one has to read carefully the inclusion-exclusion and reverse methods and some part of the source file. 6) By using options 6 and 7 of the main menu there is the possibility to change the data of the 2 main arrays containing primes and composites. In these cases the program will produce many wrong data. On the base of these errors and absurd results it is possible sometime to arrive to some logical conclusion. Some examples of this usage are given in the next chapters. After these usages it is recommended to restore the arrays with option 8. All calculations are printed in a file called session 7.dat. If you close the program and run it again the old data are cancelled and the new one are printed in the file session7.dat. If you want to save some data you have to copy them in a new file. The use of the program to obtain lists and data is easy. Follow the instruction given on the screen.

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