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surprising connections between number theory and
physics
Matthew R. Watkins http//www.maths.ex.ac.uk/mwa
tkins/zeta/physics.htm
Still, as T. Gowers has observed in Go
"Although the prime numbers are rigidly
determined, they somehow feel like experimental
data."
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The key to this method is the following
hypothesis if the prime numbers are truly
random then, for an infinite amount of them, the
distribution of their first digits (1,2,39)
should all be equal to 100/9 11,1111111111.
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If you want to falsify the null-hypothesis (H0
the prime numbers are truly randomly distributed)
for 8 degrees of freedom with a confidence level
lt 10-10 then Chi-square has to be gt 56,4586.6
As one can clearly see from Fig. 2 and Table 1
that with an increasing N, with N gt 106 above
the critical point, Chi-square goes far beyond
56,4586. This can only mean that for N gt 106 H0
is falsified with a confidence level of ltlt 10-10.
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R. C. Vaughan (February 1990) "It is evident
that the prime numbers are randomly distributed
but, unfortunately, we don't know what 'random'
means."
the connection between the Riemann Zeta function
and random matrix theory 'A Prime Case of Chaos'
webpage.
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Ley de Benford
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Las barras representan las frecuencias de
aparición como primer dígito de los números 10 a
99 en los N 1295777 ficheros medidos. La línea
continua representa la ley de Benford
generalizada para dos dígitos.
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Las barras negras representan las frecuencias de
aparición como primer dígito significativo de los
números 1 a 9 en una lista de N 201 constantes
físicas. La línea roja continua representa la
ley de Benford.
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En barras blancas aparecen las frecuencias de
aparición como primer dígito de los números 1 a 9
en los N 1295777 ficheros medidos. En barras
negras se muestran las frecuencias predichas por
la ley de Benford.
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