*"... upon looking at prime numbers one has
the feeling of being in the presence of one
of the inexplicable secrets of creation."
*D.Zagier in

I am a physicist at the Faculty of Mathematics and Natural Sciences.College of Sciences . In the late seventies I started working on strings and supersymmetry. This was my major field of interest until 1984, when I bought the famous ZX Spectrum computer (for less than 200$ !!!). Only then did I understand what good physics was. Immediately I turned from quantum field theory to fractals and chaos. Since Summer 1995 I am also interested in prime numbers, but I still believe that:

*Physics is Fun ! *

e-mail: m.wolf at uksw.edu.pl

Curriculum
vitae (for pdf
click here)
(look also here )

I am a member of the Editorial Board of the Computational Methods in Science and Technology and Waves, Wavelets and Fractals. Advanced Analysis

Below you can find my papers on the prime numbers:

This figure presents the main results reported in the paper:

Some Conjectures on the Gaps between Consecutive Primes (1.4 MB)

Here is gzip-ed file: Download "conjectures.ps.gz" (420 kB)

The more popular exposition of the above results is here:

Unexpected Regularities in the Distribution of Prime Numbers (840 kB)

Here is gzip-ed file: Download "primes.ps.gz" (260 kB)

In the paper "Generalized Brun's constants" it is argued, that the sum of reciprocals of all consecutive primes separated by distance d is equal to 4c_2/d \prod_{p\mid d} {p-1\over p-2}.

M.Wolf, Generalized Brun's constants (580 kB)

Here is gzip-ed file: "brun_gen.ps.gz"
(180 kB)

In the paper "First Occurrence of a given gap between consecutive primes" the formula for the smallest prime such, that the next prime will be in the distance d is conjectured and compared with the results of the computer search:

First Occurrence of a given gap between consecutive primes (200kB)

Here is gzip-ed file: "firstocc.ps.gz"
(68kB)

On the similar subject you can read the paper by Thomas Nicely.

In this paper the fractal structure on the set of prime numbers is described:

Download On the Twin and Cousin Primes (0.5 MB)

Here is gzip-ed file: "twins_ps.ps.gz"
(110 kB)

Download fig.1b (770 kB)

Download fig.1c (1.3 MB)

In this paper the analog of the Skewes number for twins is considered:

An Analog of the Skewes Number for Twins
(100 kB)

The conjectures and results contained in the above papers are cited in the famous Mathworld maintained by Eric Weisstein :

http://mathworld.wolfram.com/TwinPrimes.html

http://mathworld.wolfram.com/PrimeGaps.html

http://mathworld.wolfram.com/PrimeCountingFunction.html

http://mathworld.wolfram.com/PrimeDifferenceFunction.html

http://mathworld.wolfram.com/k-TupleConjecture.html

http://mathworld.wolfram.com/BrunsConstant.html

http://mathworld.wolfram.com/ShanksConjecture.html

http://mathworld.wolfram.com/CousinPrimes.html

There is a printed version of this website CRC Concise Encyclopedia of Mathematics.

My papers are cited on the Wikipedia:

http://en.wikipedia.org/wiki/Brun's_constant

http://en.wikipedia.org/wiki/Cousin_prime

http://en.wikipedia.org/wiki/Riesz_function

My results are also cited at the famous The On-Line Encyclopedia of Integer Sequences

maintained by N. J. A. Sloane:

http://oeis.org/A002496

http://oeis.org/A083844

http://oeis.org/A000101

http://oeis.org/A001912

http://oeis.org/A052291

http://oeis.org/A079296

http://oeis.org/A084255

http://oeis.org/A066081

http://oeis.org/A005250

and also here:

http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/surprising.htm

http://empslocal.ex.ac.uk/people/staff/mrwatkin/zeta/NTfractality.htm

http://www.secamlocal.ex.ac.uk/people/staff/mrwatkin/isoc/evolutionnotes.htm

www.secamlocal.ex.ac.uk/people/staff/mrwatkin/isoc/fractality.htm

www.secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/1fnoisesigprocNT.htm

www.secamlocal.ex.ac.uk/people/staff/mrwatkin/zeta/physics6.htm

http://empslocal.ex.ac.uk/people/staff/mrwatkin/isoc/psizoom.htm

Here (server in USA) you can find the paper "Jumping Champions" (at this web site in Poland) written by Andrew Odlyzko, Michael Rubinstein and me. It is about champions - the most often occuring gaps between consecutive primes. The most often occuring gaps are "primorials", i.e. products of consecutive primes. For example 6=2x3, 30=2x3x5, 210=2x3x5x7. If

* *

My papers are reviewed here by Matthew Watkins. I recommend his web page as a source of many very interesting articles about primes, zeta function etc.

I was astonished by the Riemann Series Theorem and I have written the program asking for a number and rearranging the alternating harmonic series to reach an accuracy epsilon and creating the Latex file with the output. By default the number is the Golden Ratio (approx 1,618033989) and epsilon is 0,001.

Here is a link to the weekly newspaper
KURIER PLUS , where the interview * Czy Bóg gra w koci * with
me
can be found. It is in Polish and deals with chaos, determinism, Plato,
nature of mathematical theorems etc and was conducted by Elzbieta
Kolakowska.
** **