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Ron Rivest used pi to generate the S-box of the MD2 hash. [4]Ron Rivest used the trigonometric sine function to generate constants for the widely used MD5 hash. [5]The U.S. National Security Agency used the square roots of the first eight prime integers to produce the hash constants in their "Secure Hash Algorithm" functions, SHA-1 and SHA-2. [6]
It was used in the world record calculations of 2.7 trillion digits of π in December 2009, [3] 10 trillion digits in October 2011, [4] [5] 22.4 trillion digits in November 2016, [6] 31.4 trillion digits in September 2018–January 2019, [7] 50 trillion digits on January 29, 2020, [8] 62.8 trillion digits on August 14, 2021, [9] 100 trillion ...
A modification of Lagged-Fibonacci generators. A SWB generator is the basis for the RANLUX generator, [19] widely used e.g. for particle physics simulations. Maximally periodic reciprocals: 1992 R. A. J. Matthews [20] A method with roots in number theory, although never used in practical applications. KISS: 1993 G. Marsaglia [21]
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A sequence of six consecutive nines occurs in the decimal representation of the number pi (π), starting at the 762nd decimal place. [1] [2] It has become famous because of the mathematical coincidence, and because of the idea that one could memorize the digits of π up to that point, and then suggest that π is rational.
Later computers calculated pi to extraordinary numbers of digits (2.7 trillion as of August 2010), [4] and people began memorizing more and more of the output. The world record for the number of digits memorized has exploded since the mid-1990s, and it stood at 100,000 as of October 2006. [ 6 ]
The decay time for a supermassive black hole of roughly 1 galaxy-mass (10 11 solar masses) due to Hawking radiation is on the order of 10 100 years. [7] Therefore, the heat death of an expanding universe is lower-bounded to occur at least one googol years in the future.
Alternatively, the quick approximation 99/70 (≈ 1.41429) for the square root of two was frequently used before the common use of electronic calculators and computers. Despite having a denominator of only 70, it differs from the correct value by less than 1/10,000 (approx. 7.2 × 10 −5). Its simple continued fraction is periodic and given by: