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Saturday, January 01, 2011

Happy Binary Day !

Today is 010111 which is 23 in decimal.

According to Wikipedia:

Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. Twenty-three is also the fifth factorial prime, the third Woodall prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. 23 is a number.

I'm glad someone put that last sentence in.

The fifth Sophie Germain prime and the fourth safe prime, 23 is the next to last member of the first Cunningham chain of the first kind to have five terms (2, 5, 11, 23, 47). Since 14! + 1 is a multiple of 23 but 23 is not one more than a multiple 14, 23 is a Pillai prime. 23 is the smallest odd prime to be a highly cototient number, as the solution to x − φ(x) for the integers 95, 119, 143, 529.

Twenty-three is the aliquot sum of two integers; the discrete semiprimes 57 and 85 and is the base of the 23-aliquot tree.

23 is the first prime P for which unique factorization of cyclotomic integers based on the Pth root of unity breaks down.

The sum of the first 23 primes is 874, which is divisible by 23, a property shared by few other numbers.

In the list of fortunate numbers, 23 occurs twice, since adding 23 to either the fifth or eighth primorial gives a prime number (namely 2333 and 9699713).

23 also has the distinction of being one of two integers that cannot be expressed as the sum of fewer than 9 cubes of integers (the other is 239). See Waring's problem.

23 is a Wedderburn–Etherington number. The codewords in the perfect (non-extended) binary Golay code are of size 23.

I have no idea what any of that meant.

Oh, Happy New Year !

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