Wednesday, May 12, 2010

Number 91

What's wrong with the number 91?

Consider this: With just three exceptions, all of the composite numbers up to 100 have a factor of either 2, 3, or 5. So, for all of those numbers, you can pretty much immediately see that they're composite, via your simple, standard divisibility-identifying tricks.

The three exceptions, things that have a "7" built into them as their smallest factor, are: 49 (7*7), 77 (7*11), and 91 (7*13). Of course, 49 and 77 are pretty obviously composite (knowing one's squares and what divisibility-by-11 looks like).

So 91 is the only composite number up to 100 that I can't immediately identify. I tend to incorrectly conclude that it's prime if I'm just working at it mentally.