Vampire Numbers
mdenhoed C_K_Yang ironman353 liuguangxi mafia eulerscheZahl C3PO Philippe_57721 zilet mathpseudo sinan benito255 lesnik7 nielkh
Public  09/08/17  5xp  Programming  70.0% 
A vampire number is a 2kdigits number $n$ such as there exist two kdigits numbers $a$ and $b$ such as:
 $n=a \times b$
 the digits of $a$ and $b$ are exactly the digits of $n$
Example: $ 1001295697 = 19001 \times 52697$
The two factors $a$ and $b$ are called, quite logically, the fangs.
Find the first and last 10digits vampire numbers not containing the digit 0 with prime fangs.
Anwer format: $first,last$
Example : 11722657,79168819 (for 8 digits)
$(11722657 = 2267 \times 5171 \quad \blacksquare \quad 79168819 = 8171 \times 9689)$
[My timing: 82 sec]
Hint:
The first digits of $last$ are $945 \dots $
 $n=a \times b$
 the digits of $a$ and $b$ are exactly the digits of $n$
Example: $ 1001295697 = 19001 \times 52697$
The two factors $a$ and $b$ are called, quite logically, the fangs.
Find the first and last 10digits vampire numbers not containing the digit 0 with prime fangs.
Anwer format: $first,last$
Example : 11722657,79168819 (for 8 digits)
$(11722657 = 2267 \times 5171 \quad \blacksquare \quad 79168819 = 8171 \times 9689)$
[My timing: 82 sec]
Hint:
The first digits of $last$ are $945 \dots $
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