document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006479>Question 1006479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many three digit primes have all three digits as different primes? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622603 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=622603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The single digit prime numbers are: 2,3,5,7\r<BR>\n" );
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document.write( "There are 4*3*2 = 12*2 = 24 different ways to select 3 numbers from the list of 4 primes shown above.\r<BR>\n" );
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document.write( "Here is the list of all of the possible 3 digit numbers we can form\r<BR>\n" );
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document.write( "235<BR>\n" );
document.write( "237<BR>\n" );
document.write( "253<BR>\n" );
document.write( "257<BR>\n" );
document.write( "273<BR>\n" );
document.write( "275<BR>\n" );
document.write( "325<BR>\n" );
document.write( "327<BR>\n" );
document.write( "352<BR>\n" );
document.write( "357<BR>\n" );
document.write( "372<BR>\n" );
document.write( "375<BR>\n" );
document.write( "523<BR>\n" );
document.write( "527<BR>\n" );
document.write( "532<BR>\n" );
document.write( "537<BR>\n" );
document.write( "572<BR>\n" );
document.write( "573<BR>\n" );
document.write( "723<BR>\n" );
document.write( "725<BR>\n" );
document.write( "732<BR>\n" );
document.write( "735<BR>\n" );
document.write( "752<BR>\n" );
document.write( "753\r<BR>\n" );
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document.write( "Notice there are 24 numbers in the list above.\r<BR>\n" );
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document.write( "Now let's toss out the composite (aka non-prime) numbers\r<BR>\n" );
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document.write( "235 is not prime because 5 is a factor ( 5*47 = 235)<BR>\n" );
document.write( "237 is not prime because 3 is a factor ( 3*79 = 237)<BR>\n" );
document.write( "253 is not prime because 11 is a factor ( 11*23 = 253)<BR>\n" );
document.write( "273 is not prime because 3 is a factor ( 3*91 = 273)<BR>\n" );
document.write( "275 is not prime because 5 is a factor ( 5*55 = 275)<BR>\n" );
document.write( "325 is not prime because 5 is a factor ( 5*65 = 325)<BR>\n" );
document.write( "327 is not prime because 3 is a factor ( 3*109 = 327)<BR>\n" );
document.write( "352 is not prime because 2 is a factor ( 2*176 = 352)<BR>\n" );
document.write( "357 is not prime because 3 is a factor ( 3*119 = 357)<BR>\n" );
document.write( "372 is not prime because 2 is a factor ( 2*186 = 372)<BR>\n" );
document.write( "375 is not prime because 3 is a factor ( 3*125 = 375)<BR>\n" );
document.write( "527 is not prime because 17 is a factor ( 17*31 = 527)<BR>\n" );
document.write( "532 is not prime because 2 is a factor ( 2*266 = 532)<BR>\n" );
document.write( "537 is not prime because 3 is a factor ( 3*179 = 537)<BR>\n" );
document.write( "572 is not prime because 2 is a factor ( 2*286 = 572)<BR>\n" );
document.write( "573 is not prime because 3 is a factor ( 3*191 = 573)<BR>\n" );
document.write( "723 is not prime because 3 is a factor ( 3*241 = 723)<BR>\n" );
document.write( "725 is not prime because 5 is a factor ( 5*145 = 725)<BR>\n" );
document.write( "732 is not prime because 2 is a factor ( 2*366 = 732)<BR>\n" );
document.write( "735 is not prime because 3 is a factor ( 3*245 = 735)<BR>\n" );
document.write( "752 is not prime because 2 is a factor ( 2*376 = 752)<BR>\n" );
document.write( "753 is not prime because 3 is a factor ( 3*251 = 753)\r<BR>\n" );
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document.write( "Those numbers listed above are tossed out of the list. The only numbers left are 257 and 523\r<BR>\n" );
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document.write( "The only prime numbers of that 24 item list are<BR>\n" );
document.write( "257<BR>\n" );
document.write( "523\r<BR>\n" );
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document.write( "There are only 2 such numbers that have these characteristics<BR>\n" );
document.write( "a) the number is 3 digits<BR>\n" );
document.write( "b) each digit is a prime number<BR>\n" );
document.write( "c) each digit is unique/different<BR>\n" );
document.write( "d) the number is prime\r<BR>\n" );
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document.write( "Question: How many three digit primes have all three digits as different primes?\r<BR>\n" );
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document.write( "Answer: 2 </SPAN>\n" );
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