Sunday 29 January 2012

Sunday, 29 January 2012

Today is 29 day of the year.
29 is prime.
29 is the maximum number of pieces of pizza one can create from 7 cuts, 29 is a lazy caterer number.
29 is a member of two primitive, Pythagorean triples (20, 21, 29) and (29, 420, 421).
29 is part of Cunningham chain of length 2, e.g. 29, 59 because 29 is a Sophie Germain prime.
29 is a Lucas number.
29 is a Pillai prime because 18! + 1 = 29 * 220,771,507,094,069 but 29 is not one greater than 18.

29 is a primorial prime.
Primorials are analogous to factorials. The nth  factorial is the product of the first n natural numbers
e.g. 5! = 5 x 4 x 3 x 2 x 1 = 120.
The nth primorial is the product of the first n primes
e.g. p5# = p1 x p2 x p3 x p4 x p5 = 2 x 3 x 5 x 7 x 11 = 2,310
A primorial prime is a prime that differs from a primorial by 1.
2 x 3 x 5 = 30 = 29 + 1

The 29 digit, palindromic number 20,431,106,772,402,320,427,760,113,402 can be expressed as the product of three pandigital numbers 2,067,945,831, 2,758,436,091 and 3,581,704,962. This was discovered by Frank Rubin in early January 2012.

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