There are 43 3-digit prime numbers which, when reversed, also yield a prime number. (Eight of these are actually consecutive primes).

Of the 43, 15 are simply palindromes (e.g. 929), but of the remaining 14 pairs of numbers (called 'emirp's), one pair in particular exhibits two unique characteristics, one of which is rather surprising.

What are the numbers, and what are their unique characteristics?

list
    5   dim P(150)
   10   while N<1000
   20   N=nxtprm(N)
   30   if N>100 and N<1000 then
   40     :S=cutspc(str(N))
   50     :if left(S,1)<>right(S,1) then
   60       :Ct=Ct+1:P(Ct)=cutspc(str(N))
   70   wend
   80   for I=1 to Ct-1
   90   for J=I+1 to Ct
  100   if left(P(I),1)=right(P(J),1) and left(P(J),1)=right(P(I),1) then
  105    :if mid(P(I),2,1)=mid(P(J),2,1) then
  110      :print P(I),P(J)
  120   next
  130   next
OK
run
107     701
113     311
149     941
157     751
167     761
179     971
199     991
337     733
347     743
359     953
389     983
709     907
739     937
769     967
OK

Now, what's special about one of these pairs?

Posted by Charlie on 2009-01-10 14:23:33