examday

/TMUA

Consider the following conjecture:

If $N$ is a positive integer that consists of the digit 1 followed by an odd number of 0 digits and then a final digit 1, then $N$ is a prime number.

Here are three numbers:

• I $N=101$ (which is a prime number)
• II $N=1001$ (which equals $7\times11\times13$)
• III $N=10001$ (which equals $73\times137$)

Which of these provide(s) a counterexample to the conjecture?