*Wissenschaftliches Programm*   *Liste der Vortragenden*

Sektion 10
Dienstag, 19.09.2000, 14.30–14.50 Uhr, PHY C 213

## A General Formula for Primes and a Solution for Goldbachsche Vermutung

#### Shahram Shafii,

A special configuration of natural numbers in the form of triangle can produce a subset of prime numbers, which in turn leads to a general formula for prime numbers.Then a number of limiting conditions will be represented in order to enable the formula produce only the prime numbers and sieve the compound numbers. A parallel and similar study on ”Count Suano’s Table” of natural numbers leads to a general formula also for the compound numbers located in the first and the fifth columns,which in turn enables us to check the whole numbers situated in the above mentioned columns for primarity with the help of computers. Also a sery will be represented which could produce big primes.

The correctness of a part of this study has been based on Fermats formula for prime numbers which is: ( A power(P - 1) )-1 = P . Q, in which A is an integer number, P is a prime , and A&P are not dividable to each other. Example: A = 2, P = 5. This study has also lead to a solution for ”Riemannsche Vermutung” (Riemann’s Zeta function) and proves that for (s) = 0 the real part of the s, just as Bernhard Riemann himself had only guessed, should be equal to 1/2.