Q:

Find the nth Fibohexaprime

The challenge this time is to find the nth Fibohexaprime. The definition of a Fibohexaprime is as following:
We first observe a list with Fibonacci numbers:
N  | Fibonacci number
1  | 1 
2  | 1 
3  | 2 
4  | 3 
5  | 5 
6  | 8 
7  | 13 
8  | 21 
9  | 34 
10 | 55 
11 | 89 
12 | 144 
13 | 233 
14 | 377 
15 | 610
16 | 987 
17 | 1597

After that, we convert the numbers to hexadecimal:
N  | Fib  | Hex 
1  | 1    | 1
2  | 1    | 1
3  | 2    | 2
4  | 3    | 3
5  | 5    | 5
6  | 8    | 8
7  | 13   | D
8  | 21   | 15
9  | 34   | 22
10 | 55   | 37
11 | 89   | 59
12 | 144  | 90
13 | 233  | E9
14 | 377  | 179
15 | 610  | 262
16 | 987  | 3DB
17 | 1597 | 63D

From the hexadecimal numbers, we filter out the letters. All we are left with are numbers. We need to check if these numbers are prime:
hex |  filtered |  is prime? |  N =
1   >  1        >  false
1   >  1        >  false
2   >  2        >  true         1
3   >  3        >  true         2
5   >  5        >  true         3
8   >  8        >  false
D   >  0        >  false
15  >  15       >  false
22  >  22       >  false
37  >  37       >  true         4
59  >  59       >  true         5
90  >  90       >  false
E9  >  9        >  false
179 >  179      >  true         6
262 >  262      >  false
3DB >  3        >  true         7
63D >  63       >  false

If the filtered number is a prime, we call this a Fibohexaprime. You can see that for N = 7, the related fibonacci number is 987.
The task is simple, when given an input using STDIN or an acceptable alternative, write a program or a function which outputs the nth Fibohexaprime using STDOUT or an acceptable alternative.
Test cases
Input - Output
1     - 2
2     - 3
3     - 5
4     - 55
5     - 89
6     - 377
7     - 987
8     - 28657
9     - 75025
10    - 121393
11    - 317811
12    - 5702887
13    - 9227465
14    - 39088169
15    - 102334155
16    - 32951280099
17    - 4052739537881
18    - 806515533049393
19    - 7540113804746346429

The rules:

Given an integer between 1 and 19 (the values above 20 exceed the max value for a 64-bit signed integer), output the corresponding value.
You may write a function or a program.
This is code-golf, so the submission with the least amount of bytes wins!

A:

MATL, 28 bytes
This uses MATL version 1.0.0, which was published in Esolangs on December 12, earlier than this challenge.
1Hi:"`tb+t16YAt58<)YtZp~]]1$

Example
>> matl 1Hi:"`tb+t16YAt58<)YtZp~]]1$
> 10
121393

Explanation
The code is similar to that in Martin Büttner's answer.
1           % number literal
H           % paste from clipboard H. Initial contents: 2
i:          % vector of equally spaced values from 1 to input value           
"           % for                      
  `         % do...while         
    t       % duplicate                           
    b       % bubble up element in stack          
    +       % addition 
    t       % duplicate                   
    16YA    % convert integer to string representation in base 16
    t       % duplicate             
    58      % number literal: first ASCII code after '9'           
    <       % is less than? (element-wise)    
    )       % reference () indexing with logical index from previous comparison
    Yt      % convert string to number 
    Zp      % true for prime numbers                                
    ~       % logical 'not'
  ]         % end                                                   
]           % end                                                   
1$          % input specification for final implicit display function

A:

CJam, 28 bytes
TXri{{_@+_Gb{A<},Abmp!}g}*p;

Test it here. 
Explanation
TX        e# Push 0 and 1 to initialise Fibonacci computation.
ri        e# Read input and convert to integer N.
{         e# Run this block N times...
  {       e#   While the condition on top of the stack is truthy...
    _@+   e#     Compute next Fibonacci number (dropping the second-to-last one).
    _Gb   e#     Duplicate and convert to base 16.
    {A<}, e#     Keep only digits less than 10.
    Ab    e#     Convert from base 10.
    mp!   e#     Check that it's not a prime.
  }g
}*
p;        e# Print the last number we found and discard the one before.

A:

Perl 6, 62 bytes
My first pass of just get it to work was:
{(grep *[1].is-prime,map {$_,+[~] .base(16)~~m:g/\d/},(1,1,*+*...*))[$_-1;0]} # 77

By combining the grep and the map, I can remove 10 bytes
{(map {$_ if is-prime [~] .base(16)~~m:g/\d/},(1,1,*+*...*))[$_-1]} # 67

If I use grep instead of map, I save 5 more bytes:
{(grep {is-prime [~] .base(16)~~m:g/\d/},(1,1,*+*...*))[$_-1]} # 62

usage:
# give it a name
my &code = {...}

say code $_ for 1..^20;

2
3
5
55
89
377
987
28657
75025
121393
317811
5702887
9227465
39088169
102334155
32951280099
4052739537881
806515533049393
7540113804746346429

