6,469,693,230

Many of my posts are about travel. As we won’t be visiting new countries for a while, I have been playing around with more technical and computer related stuff. This time however it’s just to tell you something I find interesting. As I write now, this could be titled: My Favourite Number: 6.469.693.230 .

This number is the product of all the prime numbers less than 30.

Specifically, 2 x 3 x 5 x 7 x 11 x 13 x 17 x 19 x 23 x 29

I calculate this in my head. You can too. Here’s my secret recipe.

Ingredients:

1 Algebraic Formula:

(a – b) x (a + b) = a^{2} – b^{2}

2 Squares: 18^{2} = 324 and 26^{2} = 676

Process:

Step 1. Multiply 2 by 5 = 10 and set aside.

Step 2. Multiply 7 by 11 by 13 and be surprised at the result of 1001. Set aside.

Step 3. Multiply 23 by 29 observing that 23 is (26 -3) and 29 is (26 + 3). (26-3) x (26+3) = 26^{2} – 3^{2} or 676 – 9 = 667. Multiply 3 x 667 and be surprised at the result of 2001. Set aside.

Step 4. Multiply the remaining two primes, 17 and 19, by observing that 17 is (18-1) and 19 is (18+1). (18-1) x (18+1) = 18^{2} – 1^{2} or 324 -1 = 323. Set aside.

Now the we start combining the different steps previously set aside.

First, combine Step 2 with Step 3. Multiply 1001 by 2001. The result is 2003001

Next, combine Step 4. Multiply 2003001 by 323 noting that 2 x 323 = 646, 3 x323 = 969. The result is 646969323.

Finally, combine in Step 1. Pop 646969323 in the oven for 10 minutes and out comes: **6,469,693,230**.

When I have trouble getting back to sleep in the middle of the night, one solution is to do tables of squares. 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16. It turns out the table can be built with just addition.

Here’s the formula:

n^{2} + n + (n+1) = (n + 1)^{2}

It means: the current square plus current number plus next number is the next number squared.

Example from above. 16 + 4 + 5 = 25 (that is 5^{2}). 25 + 5 + 6 = 36. And so on. I seldom made it beyond 23. Knowing the squares of 1 to 25 has the additional benefit of knowing the last two digits of every squared number in the universe. Gosh, I’m already sleepy.