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

Revision as of 08:16, 11 October 2007

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

First Solution:

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.

Second 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.

97937

And proceeding like this will get us

979373191713

Which answer is correct?

@@ 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 ==
+'''First Solution:'''
 We list all 2 digit primes:
@@ Line 33: / Line 35: @@
 That's the greatest.
+'''Second Solution:'''
+We start with 97, which is the largest 2 digit prime.
+Then we add 9 to get 79, the largest 2 digit prime with tens digit 7.
+Add 3 to get 93, the largest prime less than 97
+Now the largest two digit prime with tens digit 3 is 37. So we add a 7
+Now we add another 3 as 79 already exists.
+And proceeding like this will get us
+979373191713
+Which answer is correct?
 == See also ==