Randomness

[*NOTE*: The following paragraph could be a sidebar. May also need to cut this down if it is too much of an aside. Need to fact-check the assertion that /W instruction relates to Mersenne research, perhaps in: Lavington, Simon (1998), A History of Manchester Computers (2 ed.), Swindon: The British Computer Society. See also Brian Napper, The Mathematics Department and the Mark 1. http://www.computer50.org/mark1/maths.html]

[*NOTE*: The following paragraph could be a sidebar. May also need to cut this down if it is too much of an aside. Need to fact-check the assertion that /W instruction relates to Mersenne research, perhaps in: Lavington, Simon (1998), A History of Manchester Computers (2 ed.), Swindon: The British Computer Society. See also Brian Napper, The Mathematics Department and the Mark 1. http://www.computer50.org/mark1/maths.html]

Turing's addition of a built-in random function (not present in the Manchester prototype) may have been specifically motivated by his research interests in the search for large prime numbers, in particular his early work with Newman on using the early Manchester machines to search for Mersenne primes (i.e. primes amounting to one less than a power of two). Turing's 1949 prime search was implemented following the approach of Derrick Lehmer, who had developed the Lucas–Lehmer primality test. Turing's computational application of Lehmer's approach was later successfully applied by Lehmer's colleague Raphael Mitchel Robinson in 1952 in discovering the next five Mersenne primes (521, 607, 1279, 2203, 2281), and indeed has been used in all 30 discoveries of Mersenne primes since then, and is still used today in the distributed computing efforts of the Great Internet Prime Search. Lehmer, in turn, proposed in 1949 the linear congruential model for random number generation, and both linear congruential generators (LCGs) in general and Lehmer random number generators (LRNGs) specifically would later be used in a variety of programming languages and computing platforms, including Dartmouth BASIC, the ZX Spectrum, and (in modified form) in the 6502 Microsoft BASIC that became the core of Commodore BASIC in the Commodore PET, VIC-20, and 64.

Turing's addition of a built-in random function (not present in the Manchester prototype) may have been specifically motivated by his research interests in the search for large prime numbers, in particular his early work with Newman on using the early Manchester machines to search for Mersenne primes (i.e. primes amounting to one less than a power of two). Turing's 1949 prime search was implemented following the approach of Derrick Lehmer, who had developed the Lucas–Lehmer primality test. Turing's computational application of Lehmer's approach was later successfully applied by Lehmer's colleague Raphael Mitchel Robinson in 1952 in discovering the next five Mersenne primes (521, 607, 1279, 2203, 2281), and indeed has been used in all 30 discoveries of Mersenne primes since then, and is still used today in the distributed computing efforts of the Great Internet Prime Search. Lehmer, in turn, proposed in 1949 the linear congruential model for random number generation, and both linear congruential generators (LCGs) in general and Lehmer random number generators (LRNGs) specifically would later be used in a variety of programming languages and computing platforms, including Dartmouth BASIC, the ZX Spectrum, and (in modified form) in the 6502 Microsoft BASIC that became the core of Commodore BASIC in the Commodore PET, VIC-20, and 64.

http://www.alpha60.de/research/muc/

http://www.alpha60.de/research/muc/

http://www.alpha60.de/research/muc/Link_MustBeAnAngel_2006.pdf

http://www.alpha60.de/research/muc/Link_MustBeAnAngel_2006.pdf

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