(PhysOrg.com) -- Prime numbers have intrigued curious thinkers for centuries. On one hand, prime numbers seem to be randomly distributed among the natural numbers with no other law than that of chance. But on the other hand, the global distribution of primes reveals a remarkably smooth regularity. This combination of randomness and regularity has motivated researchers to search for patterns in the distribution of primes that may eventually shed light on their ultimate nature.
In a recent study, Bartolo Luque and Lucas Lacasa of the Universidad Politécnica de Madrid in Spain have discovered a new pattern in primes that has surprisingly gone unnoticed until now. They found that the distribution of the leading digit in the prime number sequence can be described by a generalization of Benford’s law.
Benford's law
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty.
[...] here is the output plot showing an extremely good accuracy claimed by paper authors
- New Pattern Found in Prime Numbers
- Benford's law - Wikipedia, the free encyclopedia
- Prime Numbers and the Benford’s Law | Pyevolve
Related:- Prime Numbers and Benford's Law - Steve Krenzel
- Lucas Lacasa homepage: ABOUT ME
In philosophy, systems theory and the sciences, emergence refers to the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theory of complex systems.
Emergence - Wikipedia, the free encyclopediaTry out this demo:
What’s happening here is that each worm is following two rules: 1) try to move in the same direction as nearby worms (commonly known as the cohesion rule) and 2) move away from other worms if they get too close (known as the separation rule). There is some randomness thrown in so that worms will sporadically move in an arbitrary direction, to give the system a more organic feel. The result is the effect you see: a shifting pattern of motion comprised of groups of individuals, each of which is just moving according to the same two rules.
Christian Cenizal, Designer-Developer (Flocking and emergent behavior)Blogged with Flock
clipped from pyevolve.sourceforge.net
clipped from pyevolve.sourceforge.net
