## 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.