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Random numbers

We can never decide for sure that a number is random, but what we can do is apply an increasing number of tests and treat our sequence of numbers as innocent until proved guilty."

Source Colva Roney-Dougal, Senior Lecturer in Pure Mathematics at the University of St Andrews, speaking in 'Random and Pseudorandom', BBC 'In our time' Jan. 2011.

Although the tests can show that a finite sequence of numbers appears to be random (i.e. it can't be mathematically represented in a shorter form) - there is currently no mathematical method to prove that if it continues, the next numbers in the sequence won't start to repeat.

I can never prove that a sequence of numbers is random, I can only say that it looks and smells random given all the tests I've been able to apply so far."

That's to say it's unknowable if any particular sequence of numbers will remain random if its generation is continued.

A number of 'tests' have been developed to gauge how random a sequence of numbers might be. They include statistical tests, transforms, and measures of complexity - or a mixture of these.

Note : There is currently debate over whether it's possible to distinguish the output of high-quality modern-day pseudo-random number generators (computer algorithms commonly used in cryptography) and truly random sequences. This open question has crucial implications of the security of data encryption.

Also see :Pi (ฯ€) normalityplugin-autotooltip__plain plugin-autotooltip_bigPi (ฯ€) normality

A 'normal' sequence of numbers is one in which no digit occurs more frequently than any other. The mathematical equivalent of White Noise.

'Normality' is usually considered to be one of the tests for randomness.

The ฯ€ sequence has now been computed to

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