For k=2,3,4,5,6 find an example (or prove absence) of a circular prime of k digits (i.e. a prime number that remains prime as its leftmost digit (Most Significant Digit) is moved in turn to the right hand side).

This link provided some interesting information, including the tries below:  http://www.worldofnumbers.com/circular.htm

For k=8

     71777393 prime
     17773937 prime
     77739371 prime
     77393717 prime
     73937177 prime
     39371777 prime
     93717773 prime
but 37177739 = 29 * 683 * 1877

For k=7

a)   9197777 prime
     1977779 prime
     9777791 prime
     7777919 prime
     7779197 prime
     7791977 prime
but 7919777 = 83 * 95419

b)   9991313 prime
     9913139 prime
     9131399 prime
     1313999 prime
     3139991 prime
     1399913 prime
but 39991313= 17 * 235243

 

Posted by xdog on 2012-02-07 20:02:26