document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209417>Question 1209417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Some prime numbers are of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En-1 ALIGN=MIDDLE  ALT=\"2%5En-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. For example, the prime number 7 is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3-1 ALIGN=MIDDLE  ALT=\"2%5E3-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Make a list of the first seven exponents (n<20) that produce prime numbers of this type (include the number 3 as one of the seven in your list).<BR>\n" );
document.write( "CC11F #5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848774 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Some prime numbers are of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En-1 ALIGN=MIDDLE  ALT=\"2%5En-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. For example, the prime number 7 is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3-1 ALIGN=MIDDLE  ALT=\"2%5E3-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Make a list of the first seven exponents (n<20) that produce prime numbers of this type <BR>\n" );
document.write( "(include the number 3 as one of the seven in your list).<BR>\n" );
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document.write( "<U>ANSWER</U>.  The first seven exponents n < 20 that produce prime numbers of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En-1 ALIGN=MIDDLE  ALT=\"2%5En-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > are 2, 3, 5, 7, 13, 17, and 19.\r<BR>\n" );
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document.write( "For the solution, see the link\r<BR>\n" );
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document.write( "https://www.google.com/search?q=.+Some+prime+numbers+are+of+the+form+%7B%7B%7B2%5En-1%7D%7D%7D.+For+example%2C+the+prime+number+7+is+equal+to+%7B%7B%7B2%5E3-1%7D%7D%7D.+Make+a+list+of+the+first+seven+exponents+(n%3C20)+that+produce+prime+numbers+of+this+type+(include+the+number+3+as+one+of+the+seven+in+your+list).+CC11F+%235&rlz=1C1CHBF_enUS1071US1071&oq=.+Some+prime+numbers+are+of+the+form+%7B%7B%7B2%5En-1%7D%7D%7D.+For+example%2C+the+prime+number+7+is+equal+to+%7B%7B%7B2%5E3-1%7D%7D%7D.++Make+a+list+of+the+first+seven+exponents+(n%3C20)+that+produce+prime+numbers+of+this+type++(include+the+number+3+as+one+of+the+seven+in+your+list).+CC11F+%235&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCTQwNjdqMGoxNagCCLACAQ&sourceid=chrome&ie=UTF-8\r<BR>\n" );
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document.write( "This solution is provided by artificial intelligence (AI) by my request.\r<BR>\n" );
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document.write( "Among the obvious facts that are useful to know,  &nbsp;in order for &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En-1 ALIGN=MIDDLE  ALT=\"2%5En-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;be <BR>\n" );
document.write( "a prime integer number, &nbsp;the exponents n must be an odd integer number.\r<BR>\n" );
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document.write( "The even exponents n, higher than 2, produce composite numbers.\r<BR>\n" );
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document.write( "Among other useful facts to know is THIS: \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;if the exponent n is a composite number,\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;then  &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5En-1 ALIGN=MIDDLE  ALT=\"2%5En-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;is a composite number, &nbsp;too.\r<BR>\n" );
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document.write( "So, &nbsp;for such a search as in this problem, &nbsp;you should look among prime exponents n,<BR>\n" );
document.write( "rejecting composite exponents n.\r<BR>\n" );
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document.write( "Enjoy (!)\r<BR>\n" );
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