Question 1198533
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Let a,b,c be the digits of the number abc.
Example:
a = 1
b = 2
c = 5
abc = 125
I'm not multiplying the digits but rather I'm concatenating them.


'a' must be prime so it must be from the set {2,3,5,7}
The value 1 is NOT prime.
ab must also be prime, and same goes for abc.


If a = 2, then here are all the possibilities for b
b = 3
b = 9
We form the numbers ab = 23 and ab = 29 respectively.


If a = 3, then,
b = 1
b = 7
Giving us ab = 31 and ab = 37 in that order


If a = 5, then
b = 3
b = 9
Giving ab = 53 and ab = 59


If a = 7, then
b = 1
b = 3
b = 9
Giving ab = 71, ab = 73, and ab = 79


Refer to a list/chart of two digit prime numbers to determine those a,b values.


Summary so far
<table border = "1" cellpadding = "5">
<tr><td>Value of 'a'</td><td>Value of 'b'</td><td>ab</td><td>count</td></tr>
<tr><td rowspan=2>2</td><td>3</td><td>23</td><td rowspan=2>2</td></tr>
<tr> <td>9</td><td>29</td> </tr>
<tr><td rowspan=2>3</td><td>1</td><td>31</td><td rowspan=2>2</td></tr>
<tr> <td>7</td><td>37</td> </tr>
<tr><td rowspan=2>5</td><td>3</td><td>53</td><td rowspan=2>2</td></tr>
<tr> <td>9</td><td>59</td> </tr>
<tr><td rowspan=3>7</td><td>1</td><td>71</td><td rowspan=3>3</td></tr>
<tr> <td>3</td><td>73</td> </tr>
<tr> <td>9</td><td>79</td> </tr>
</table>
Adding the values in the "count" column gets us 2+2+2+3 = 9 two digit cut-tail primes.
They are primes in the form ab where ab itself is prime, and so is 'a'. 
The b value doesn't need to be prime.


Here's a list of those two digit cut-tail primes: 
23, 29, 
31, 37, 
53, 59, 
71, 73, 79
Refer to <a href = "https://en.wikipedia.org/wiki/Truncatable_prime">this article</a> for more details
The specific section to focus on has the phrasing "right-truncatable primes".


You'll follow the same basic outline I mentioned above to form the three digit cut-tail primes.
Those primes are: 
233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797
in which there are 14 of them.


Answer: <font color=red>14</font>
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