Difference between revisions of "2005 PMWC Problems/Problem T10"
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== Solution == | == Solution == | ||
| + | This page needs a solution. The original one, shown below, has an error (denoted by the bolded statement): the number <math>93</math> is certainly not prime; it is divisible by 3. | ||
| + | ''Original Solution:'' | ||
We start with 97, which is the largest 2 digit prime. | We start with 97, which is the largest 2 digit prime. | ||
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979 | 979 | ||
| − | Add 3 to get 93, the largest prime less than 97 | + | '''Add 3 to get 93, the largest prime less than 97''' |
9793 | 9793 | ||
Revision as of 18:18, 20 May 2008
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
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 | ||
