document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189399>Question 1189399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When the digits in the number 2005 are reversed we obtain the number 5002, and 5002 = a * b * c, such that a, b and c are three distinct primes. How many other positive integers are the products of exactly three distinct primes prime1, prime2 and prime3 such that prime1 + prime2 + prime3 = a+b+c? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820762 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "5002 = 2*41*61 = a*b*c<br><BR>\n" );
document.write( "a+b+c=104<br><BR>\n" );
document.write( "The question asks how many other positive integers are the products of exactly three distinct primes whose sum is also 104.<br><BR>\n" );
document.write( "For the sum of three distinct primes to be 104, one of them has to be 2, so the sum of the other two has to be 102.<br><BR>\n" );
document.write( "So you need to find the number of pairs of primes other than 41 and 61 that also have a sum of 102.<br><BR>\n" );
document.write( "You will learn nothing from this question if we work the whole problem for you, so I leave it to you to finish the problem.<br><BR>\n" );
document.write( "(my answer was 7....)<br><BR>\n" );
document.write( " </SPAN>\n" );
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