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Abstract.
Prime numbers play the role of ''atoms'' from which
all natural numbers can be obtained via multiplication.
Already Euclid knew that there are infinitely primes
but many more subtle questions about distributions
of prime numbers among all natural numbers remain
open up to now.
One of such open questions is the
validity of the Riemann Hypothesis about
zeroes of the zeta function. The Hypothesis was stated
in 1859 but still resists all attacks to prove or
disprove it. In 2000 the Hypothesis got the
status of one of the seven Millennium Prize Problems.
Taking its origin in number theory, the Riemann
Hypothesis has many connections with other
sciences, including theoretical physics and
computer science (in the latter case the
Hypothesis allows one to construct more
efficient algorithms).
The talk will include
short history of studies of prime numbers and
the Riemann Hypothesis, and then the speaker
will present his resent discovery of new
relationship between prime numbers and
the zeta function found by intensive
computer calculations. |