The following are all of the 2-digit primes: \[11,\ 13,\ 17,\ 19,\ 23,\ 29,\ 31,\ 37,\ 41,\ 43,\ 47,\ 53,\ 59,\ 61,\ 67,\ 71,\ 73,\ 79,\ 83,\ 89,\ 97.\] Concatenating 17 and 79 in such a way that the common digit 7 collapses on each other, we can make 179.

In the same fashion, we can construct 613, where 61 and 13 were used with 1 appearing only once.

A much bigger example would be 4731979, where six 2-digit primes 47, 73, 31, 19, 97, 79 were used in that order.

What is the largest number that can be constructed this way, using each 2-digit prime at most once?

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