document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619418>Question 619418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please explain this problem to me. I have given some of the solutions I have tried but do not know if I am doing it right.\r<BR>\n" );
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document.write( "To prove or disprove the following: The expression n2 - n + 41 produces a prime number for every positive integer n. (Hint: try the following numbers 1, 10, and 41).  \r<BR>\n" );
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document.write( "I have tried this in two seperate ways-The first reading the 2 as a power of. Therefore making the problem n^2 -n + 41.  The second attempt was n(2) -n +41.  \r<BR>\n" );
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document.write( "n^2 - n + 41 = 1^2 - 1 + 41 = 1 - 1 + 41 = n=41\r<BR>\n" );
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document.write( "n(2) - n + 41 = 1(2) - 1 + 41 = 2 - 1 + 41 = 1 + 41 = 41 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389652 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=389652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Try n = 1\r<BR>\n" );
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document.write( "n^2 - n + 41\r<BR>\n" );
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document.write( "1^2 - 1 + 41\r<BR>\n" );
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document.write( "1 - 1 + 41\r<BR>\n" );
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document.write( "41\r<BR>\n" );
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document.write( "Which is prime. So it works so far.\r<BR>\n" );
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document.write( "Try n = 2\r<BR>\n" );
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document.write( "n^2 - n + 41\r<BR>\n" );
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document.write( "2^2 - 2 + 41\r<BR>\n" );
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document.write( "4 - 2 + 41\r<BR>\n" );
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document.write( "43\r<BR>\n" );
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document.write( "Which is prime. So it works so far.\r<BR>\n" );
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document.write( "Try n = 41\r<BR>\n" );
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document.write( "n^2 - n + 41\r<BR>\n" );
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document.write( "41^2 - 41 + 41\r<BR>\n" );
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document.write( "41(41 - 1 + 1)\r<BR>\n" );
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document.write( "41(41)\r<BR>\n" );
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document.write( "Which is NOT prime since we can write the final expression as a product of two primes. So this is where the formula breaks down.<BR>\n" );
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