Buildingprimes
Most people know what a prime number is: a number (greater than 1) which has only two factors, 1 and itself. "37" is a prime number (37 = 1 * 37); "51" is not (since 51 = 1 * 3 * 17). Consider this algorithm for trying to "build" a prime number:
1. Start with a single digit prime number (2, 3, 5, or 7).
2. To the end of that append another digit.
3. If that new number (one digit longer) is also prime, repeat Step 2.
The largest prime number that exists that can be constructed in this manner is: 73939133.
In other words 73939133 is the largest prime number such that during each reduction in length, when you remove the final digit, what remains is also prime (73939133, 7393913, 739391, 73939, 7393, 739, 73, and 7 are all prime). You might think 73939133 is a pretty large number... but now try to building in the other direction:
Follow the steps above, but instead of appending the new digit to the end of the previous number (in Step 2), add the new digit to the front. What is the largest number that can be built up in this manner (i.e. the largest prime number which, after each "beheading" of its leading digit, is still prime... all the way down to its single digit)?
If you find the answer, you'll see it is much larger than 73939133.