2005 PMWC Problems/Problem T10

Problem

Find the largest 12-digit number for which every two consecutive digits form a distinct 2-digit prime number.

Solution

This page needs a solution. The original one, shown below, has an error (denoted by the bolded statement): the number is certainly not prime; it is divisible by 3.

Original Solution: We start with 97, which is the largest 2 digit prime.

97

Then we add 9 to get 79, the largest 2 digit prime with tens digit 7.

979

Add 3 to get 93, the largest prime less than 97

9793

Now the largest two digit prime with tens digit 3 is 37. So we add a 7

97937

Now we add another 3 as 79 already exists.

979373

And proceeding like this will get us

979373191713