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Summary: Physica A 360 (2006) 285296
Hidden structure in the randomness
of the prime number sequence?
S. Aresa,b,Ć, M. Castroa,c
a
Grupo Interdisciplinar de Sistemas Complejos (GISC)
b
Departamento de Matema“ticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30,
28911 Legane“s, Madrid, Spain
c
Grupo de Dina“mica No Lineal (DNL), Escuela Te“cnica Superior de Ingenieri“a (ICAI),
Universidad Pontificia Comillas, 28015 Madrid, Spain
Received 9 March 2005; received in revised form 31 May 2005
Available online 21 July 2005
Abstract
We report a rigorous theory to show the origin of the unexpected periodic behavior seen in
the consecutive differences between prime numbers. We also check numerically our findings to
ensure that they hold for finite sequences of primes, that would eventually appear in
applications. Finally, our theory allows us to link with three different but important topics: the
HardyLittlewood conjecture, the statistical mechanics of spin systems, and the celebrated
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