RoseCode

Problem #424

Vampire Numbers
 Public ★(x14) 09/08/17 by Philippe_57721 5xp Programming 70.0%

A vampire number is a 2k-digits number $n$ such as there exist two k-digits 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 10-digits 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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