document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198533>Question 1198533</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cut-tail prime is a prime number that keeps giving prime numbers as its last digit is continually removed. For example, 37397 is a cut-tail prime because 37397 and 3739 and 373 and 37 and 3 are all primes. The number of three-digit cut-tail primes is __ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832155 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let a,b,c be the digits of the number abc.<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( "c = 5<BR>\n" );
document.write( "abc = 125<BR>\n" );
document.write( "I'm not multiplying the digits but rather I'm concatenating them.\r<BR>\n" );
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document.write( "'a' must be prime so it must be from the set {2,3,5,7}<BR>\n" );
document.write( "The value 1 is NOT prime.<BR>\n" );
document.write( "ab must also be prime, and same goes for abc.\r<BR>\n" );
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document.write( "If a = 2, then here are all the possibilities for b<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "b = 9<BR>\n" );
document.write( "We form the numbers ab = 23 and ab = 29 respectively.\r<BR>\n" );
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document.write( "If a = 3, then,<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "b = 7<BR>\n" );
document.write( "Giving us ab = 31 and ab = 37 in that order\r<BR>\n" );
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document.write( "If a = 5, then<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "b = 9<BR>\n" );
document.write( "Giving ab = 53 and ab = 59\r<BR>\n" );
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document.write( "If a = 7, then<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "b = 9<BR>\n" );
document.write( "Giving ab = 71, ab = 73, and ab = 79\r<BR>\n" );
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document.write( "Refer to a list/chart of two digit prime numbers to determine those a,b values.\r<BR>\n" );
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document.write( "Summary so far<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
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document.write( "<tr><TD >Value of 'a'</TD><TD >Value of 'b'</TD><TD >ab</TD><TD >count</TD></tr>\r\n" );
document.write( "<tr><TD  rowspan=2>2</TD><TD >3</TD><TD >23</TD><TD  rowspan=2>2</TD></tr>\r\n" );
document.write( "<tr> <TD >9</TD><TD >29</TD> </tr>\r\n" );
document.write( "<tr><TD  rowspan=2>3</TD><TD >1</TD><TD >31</TD><TD  rowspan=2>2</TD></tr>\r\n" );
document.write( "<tr> <TD >7</TD><TD >37</TD> </tr>\r\n" );
document.write( "<tr><TD  rowspan=2>5</TD><TD >3</TD><TD >53</TD><TD  rowspan=2>2</TD></tr>\r\n" );
document.write( "<tr> <TD >9</TD><TD >59</TD> </tr>\r\n" );
document.write( "<tr><TD  rowspan=3>7</TD><TD >1</TD><TD >71</TD><TD  rowspan=3>3</TD></tr>\r\n" );
document.write( "<tr> <TD >3</TD><TD >73</TD> </tr>\r\n" );
document.write( "<tr> <TD >9</TD><TD >79</TD> </tr>\r\n" );
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document.write( "Adding the values in the \"count\" column gets us 2+2+2+3 = 9 two digit cut-tail primes.<BR>\n" );
document.write( "They are primes in the form ab where ab itself is prime, and so is 'a'. <BR>\n" );
document.write( "The b value doesn't need to be prime.\r<BR>\n" );
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document.write( "Here's a list of those two digit cut-tail primes: <BR>\n" );
document.write( "23, 29, <BR>\n" );
document.write( "31, 37, <BR>\n" );
document.write( "53, 59, <BR>\n" );
document.write( "71, 73, 79<BR>\n" );
document.write( "Refer to <a  rel=nofollow HREF= \"https://en.wikipedia.org/wiki/Truncatable_prime\">this article</a> for more details<BR>\n" );
document.write( "The specific section to focus on has the phrasing \"right-truncatable primes\".\r<BR>\n" );
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document.write( "You'll follow the same basic outline I mentioned above to form the three digit cut-tail primes.<BR>\n" );
document.write( "Those primes are: <BR>\n" );
document.write( "233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797<BR>\n" );
document.write( "in which there are 14 of them.\r<BR>\n" );
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document.write( "Answer: <font color=red>14</font><BR>\n" );
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