document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=319408>Question 319408</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Find a counterexample to the statement: The cube of a number added to the sum of three times the number and 3 is a prime number. Justify your solution by supporting it with step by step work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #228904 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=228904\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find a counterexample to the statement:<BR>\n" );
document.write( " The cube of a number added to the sum of three times the number and 3 is a prime number. <BR>\n" );
document.write( ":<BR>\n" );
document.write( "x = \"number\"<BR>\n" );
document.write( "the equation<BR>\n" );
document.write( "y = x^3 + 3x + 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Substituting:<BR>\n" );
document.write( "x = 1, then y = 7, a prime number<BR>\n" );
document.write( "x = 2, then y = 17, a prime number<BR>\n" );
document.write( "however,<BR>\n" );
document.write( "x = 3, then y = 39, not a prime number<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );