Mathematics Problem Of the Week

Spring 2008

POW #11

Cutting Primes

While hobby-logging last weekend, Dr. Hardwood noticed a strange log with the prime number 3739 inscribed on it. Following the number was this rather mysterious message “dare you to unprime me".

Rising to the challenge (logging is not as exciting as one might think) Dr. Hardwood bravely chainsawed the 9 off of the right end of the log. Unfortunately, the resulting number (373) was also prime. Trying again, he sliced another digit from the right (the 3) which yielded 37 (also prime). Sadly, trimming the last 7 resulted in a prime digit of 3.

It seems Dr. Hardwood encountered a prime number that retained its primality no matter how many digits were cut from the right. All he had left were a few bits of wood, a single digit prime on the log, and broken dreams.

To recap, the progression of cutting this prime number was 3739, 373, 37, 3.

The problem(s) for this week:

1. What is the largest prime number you can find with the right-cutting property described above?

2. If you believe you have found the largest prime number with this property, prove it.

Due Friday, April 18^th at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math/CS/Stat office or sent via e-mail to rlock@stlawu.edu.