*Heavily inspired by [Programming a Pristine World](https://codegolf.stackexchange.com/q/63433/42545). Also closely related to [this challenge](https://codegolf.stackexchange.com/q/41648/31625).*

---

Let's define a *pristine prime* as a number which is itself prime, but will no longer be prime if you remove any contiguous substring of N base 10 digits, where `0 < N < digits in number`.

For example, 409 is a pristine prime because 409 itself is prime, but all numbers resulting from removing a substring of 1 digit are not prime:

```
40
49
09 = 9

```

and all numbers resulting from removing substrings of length 2 are not prime:

```
4
9

```

On the other hand, the prime number 439 is not pristine. Removing the different substrings results in:

```
43
49
39
4
9

```

While 49, 39, 4, and 9 are all non-prime, 43 *is* prime; thus, 439 is not pristine.

2, 3, 5, and 7 are trivially pristine, since they cannot have any substrings removed. 

Challenge
---------

Your challenge is to create a program or function that takes in a positive integer N and outputs the Nth pristine prime. The code should finish in under 1 minute on any modern PC for any input up to 50.

**The shortest code in bytes wins.**

As a reference, here are the first 20 pristine primes:

```
N    Pristine prime
1    2
2    3
3    5
4    7
5    11
6    19
7    41
8    61
9    89
10   409
11   449
12   499
13   821
14   881
15   991
16   6299
17   6469
18   6869
19   6899
20   6949

```

[Here](http://pastebin.com/dfVwn8Yr) is a full list of pristine primes up to 1e7, or N = 376.

Finally, here are two related OEIS entries:

* [A033274](http://oeis.org/A033274): very similar, but generated by keeping substrings instead of removing them.
* [A071062](http://oeis.org/A071062): oddly similar, but generated in a much different manner.