New Pattern Found in Prime Numbers
(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.
May 2009. Luque, Lacasa on Generalised Benford's Law.
“New insights and concepts coming from nonlinear science, such as multiplicative processes, help us to look at prime numbers from a different perspective. According to this focus, it becomes significant that even today it is still possible to discover unnoticed hints of statistical regularity in such sequences, without being an expert in number theory. However, the most significant issue in this work is not to unveil this pattern in primes and Riemann zeros, but to understand the reason and implications of such unexpected structure, not just for number theoretical issues but, interestingly, for other disciplines as well. For instance, these results deepen our understanding of correlations in systems composed of many elements.”
(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 ...
“Imagine that you have $1,000 in your bank account, with an interest rate of 1% per month,” Lacasa said. “The first month, your money will become $1,000*1.01 = $1,010. The next month, $1,010*1.01, and so on. After n months, you will have $1,000*(1.01)^n. Notice that you will need many months to go from $1,000 to $2,000, while to go from $8,000 to $9,000 will be much easier. When you analyze your accounting data, you will realize that the first digit 1 is more represented than 8 or 9, precisely as Benford's law dictates. This is a very basic example of a multiplicative process where 0.01 is the multiplicative constant. “Physicists have shown that many processes in nature can be modeled as stochastic multiplicative processes, where the previously constant value of 0.01 is now a random variable and the data equivalent to the money of our latter example is another random variable with an underlying distribution 1/x. Stochastic processes with such distributions are shown to follow BL....”Why 09/09/09 Is So Special - Yahoo! News
More about 9 than you really wanted to know.
"Not only does the date look good in marketing promotions, but it also represents the last set of repeating, single-digit dates that we'll see for almost a century (until January 1, 2101), or a millennium (mark your calendars for January 1, 3001), depending on how you want to count it." (il ne faut rien exagérer, il y aura le 10/10/2010, puis le 11/11/2011, puis le 12/12/2012 et après, oui, il faudra attendre un bon moment)Prime Numbers and the Benford’s Law | Pyevolve
"Prime Numbers and the Benford's Law | Pyevolve" http://hub.tm/?RHOqX [from http://twitter.com/carreonG/statuses/1747034327]
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NumberQuotes Get a quote and make your point Ever need a good quote to add scale to a number? You know, you’re giving a presentation on sales and you want to give a number some scale.John Graham-Cumming: Squaring two digit numbers in your head