New pattern found in prime numbers
Posted by Science Oxford on October 1, 2009 | comments
Are you a math junkie? Or a big fan of prime numbers? The below article from AlphaGalileo outlines new research into the patterns found in prime numbers.
Visit this page »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 prime numbers: the distribution of the leading digit in the prime number sequence can be described by a generalization of Benford’s law. Benford’s law describes the logarithmic distribution of the first digit of a set of numbers in a wide variety of data sets, where 1 appears much more frequently than 9.
Although researchers have known that prime numbers in general do not follow Benford’s law, Luque and Lacasa noticed that smaller sets of primes exhibit a bias in the first digit distribution. But as data sets of primes increase, the first digit distribution tends to uniformity. The researchers discovered that, as the data sets of primes increase to infinity, the trend toward uniformity follows a generalized Benford’s law. This law describes the first digit distribution of numbers in a series that are generated by power law distributions, as in the case of the prime sequences studied here.
Most significantly, Luque and Lacasa showed that a generalized Benford’s law can be explained by the prime number theorem, and also developed a mathematical framework that provides conditions for any distribution to conform to the law. The researchers hope that this work could help identify other sequences that aren’t Benford distributed, but follow a generalized Benford’s law. Besides providing insight into the nature of primes, the finding could also have applications in areas such as fraud detection and stock market analysis.
Article Credit: AlphaGalileo
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