Mathematics is really changing with the use of computers and the internet. WOW!
We are able to research very big numbers that were simply beyond reach 100 years ago.
For example: consider the 7,669 digit number that starts with a 1, and ends with a 3, and has 7,667 zeros between the 1 and the 3.
OK, I don't think you will see this number in the SAT or ACT tests. I probably won't help us get to Mars or cure any diseases. But this number does have a story to tell.
We could talk about how big this number is and compare it to something so we could grasp the concept - like 7,667 minutes is a bit more than 5 days. (This won't be on the SAT or ACT test either.)
But without computers we would not know that this is a prime number. The next smaller prime that starts with a 1, ends with a 3, and only has zeros between has 2,606 zeros.
This prime number is also a "Naughty" prime because is composed mostly of naughts (zeros). It is also a "Repubican" prime, because the right half of this number is a prime number, but the left half is not a prime. And, oh yeah, it's an odd number too!
I also know that the number two less than this number is not a prime, and the number two more that this number is not a prime. So this prime number is not part of a twin prime pair. With a little more work I could determine if it is part of a cousin prime pair or a sexy prime pair.
One hundred years ago if you had asked a mathematician about this number, and what properties it my or may not have he or she would only be able to tell you that it is a really big number that happens to be an odd number.
Because of computers I have know for a while that in August of next year my house will be in an area to experience a total solar eclipse. And on that day I will pause for a few minutes to observe the eclipse. And then I will return to my work of searching for an uninteresting number (which I think is impossible because I think that every number has something interesting.
Well, I better get back to my therapy.