Alice, Betty and Carol each chose two 2-digit semiprimes (products of exactly two primes each) whose difference was also a semiprime. In each of the three cases, the six primes going into the three semiprimes involved were all different. Also in each case, the sum of the two semiprimes was a perfect square.

Alice, Betty and Carol had different pairs of semiprimes, though there may have been repetition of any given semiprime. Alice and Betty had the same sum for their semiprimes, but Carol's sum was different.

What were Carol's two semiprimes?

(In reply to Solution by Dej Mar)

Up until this morning my spreadsheet was written as headings/labels;  SPx = semiprime  Px = Prime.

While I had begun to build a table of Primes and semiprimes I had not completed my determinations.

My concern is about the meaning of this sentence: "In each of the three cases, the six primes going into the three semiprimes involved were all different."  Using the labels from the table below my understanding is that the three semiprimes to which that refers are P11, P12 and P13.  If that is the case then only 4 primes are used not 6.

The values within the following table are those determined by Dej Mar in the prior comment. 

Alice  SP1 SP2  ABS(SP1-SP2)=SP11   P1  P2  SP1+SP2=SQ1
         35   86           51                        3  17       121  
                
Betty SP3 SP4  ABS(SP3-SP4)=SP12   P3  P4  SP3+SP4=SQ2
          26  95           69                        3  23       121                                                                                                  SQ1=SQ2
Carol SP5 SP6 ABS(SP5-SP6)=SP13  P5 P6  SP5+SP6=SQ3
          74  95           21                        3   7       169 
                                                               SQ3(!=)SQ1&&(!=)SQ2  

Posted by brianjn on 2011-04-13 03:51:59