User:Julzes/365.25

365.25 is the approximation most natural for people living today to make to the average number of days in a year of the Gregorian calendar most commonly used around the world, and therefore is of strong significance. Written with a fraction rather than a decimal number, it is the same as 365+1/4. This is a way to write a simple expression made from the digits 1 through 6, excluding 2, and squaring it and taking the prime factorization of the whole part generates the esthetically appealing and suggestive equation (365+1/4)^2=3^7*61+9/16. Its square with instead the fractional part factored is equally appealing and suggestive, though it uses two 4s and no 2s. It is (365+1/4)^4=17797577732+7^2/2^8. Note that the right-hand side uses seven 7s, which is far out of the norm for an expression of this length. A final observation is that, using also zero 0s and one 1, the three such digits may be concatenated to form the prime 107, which is the largest factor of 642, with this latter being the concatenation of the digits used in the observation that the first 6 digits are each used once except for an extra 4 replacing 2.