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

Revision as of 18:24, 19 September 2008

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

We list all 2 digit primes:

11, 13, 17, 19

23, 29

31, 37

41, 43, 47

53, 59

61, 67

71, 73, 79

83, 89

97

Picking a 9 would get us:

97371311

So we pick an 8.

837319737131

That's the greatest.

@@ Line 2: / Line 2: @@
 Find the largest 12-digit number for which every two consecutive digits form a distinct 2-digit prime number.
-== Solution ==
+== Solutions ==
+We list all 2 digit primes:
-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.
+, 13, 17, 19
-''Original Solution:''
+, 29
-We start with 97, which is the largest 2 digit prime.
+, 37
+, 43, 47
+, 59
-Then we add 9 to get 79, the largest 2 digit prime with tens digit 7.
+, 67
+, 73, 79
-'''Add 3 to get 93, the largest prime less than 97'''
+, 89
-Now the largest two digit prime with tens digit 3 is 37. So we add a 7
+Picking a 9 would get us:
-Now we add another 3 as 79 already exists.
+97371311
+So we pick an 8.
-And proceeding like this will get us
+837319737131
-979373191713
+That's the greatest.
 == See also ==