Difference between revisions of "2005 PMWC Problems/Problem T10"
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Find the largest 12-digit number for which every two consecutive digits form a distinct 2-digit prime number. | Find the largest 12-digit number for which every two consecutive digits form a distinct 2-digit prime number. | ||
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Revision as of 09:00, 11 October 2007
Problem
Find the largest 12-digit number for which every two consecutive digits form a distinct 2-digit prime number.
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
See also
| 2005 PMWC (Problems) | ||
| Preceded by Problem T9 |
Followed by Last Question | |
| I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
