Difference between revisions of "2005 PMWC Problems/Problem T10"

Revision as of 10:00, 11 October 2007

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

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

@@ Line 3: / Line 3: @@
 == Solutions ==
-'''First Solution:'''
-We list all 2 digit primes:
-, 13, 17, 19
-, 29
-, 37
-, 43, 47
-, 59
-, 67
-, 73, 79
-, 89
-Picking a 9 would get us:
-97371311
-So we pick an 8.
-837319737131
-That's the greatest.
-[Comment: In this solution the number 837319737131 has many non-distinct two digit subsequences of prime numbers for example 37, 31, 73 all appear more than once. But the question asks for distinct two digit prime numbers.]
-'''Second Solution:'''
 We start with 97, which is the largest 2 digit prime.
@@ Line 64: / Line 28: @@
 979373191713
-Which answer is correct?
 == See also ==