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

(Solution)
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== Solution ==
 
== Solution ==
  
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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.
  
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''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
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'''Add 3 to get 93, the largest prime less than 97'''
  
 
9793
 
9793

Revision as of 17:18, 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 $93$ 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