(no subject)
My grandson asked me recently what my favourite number is. I told him 510510.
It's easy to impress little kids.
The most obvious thing about the number is that it is a sequence of three digits, which repeats. This simply means that it is a product of a three digit number and 1001, whose prime factors (this is important) are 7, 11 and 13.
More interesting is the fact that it equals 714 x 715, and is therefore the sum of the first 714 even numbers, from 2 to 1428. This makes it a double triangular number.
It is the combination of the next two interesting facts that make it my favourite number:
It is the product of the first 7 prime numbers: 2 x 3 x 5 x 7 x 11 x 13 x 17.
It is also the product of 4 successive Fibonacci numbers: 13 x 21 x 34 x 55.
Another number I am very fond of is 0.88622692545275801364908374167057. It is a number which I found for myself, in its first 15 decimal places. It is ½! - the factorial of ½. With a tip from my son-in-law
sambarham, I discovered what you get when you double the number and square the result...