Question 1198533: 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 __
Answer by math_tutor2020(3817)   (Show Source):
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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
| Value of 'a' | Value of 'b' | ab | count |
| 2 | 3 | 23 | 2 |
| 9 | 29 |
| 3 | 1 | 31 | 2 |
| 7 | 37 |
| 5 | 3 | 53 | 2 |
| 9 | 59 |
| 7 | 1 | 71 | 3 |
| 3 | 73 |
| 9 | 79 |
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 this article 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: 14
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