We have a 10-digit number (the first digit is not zero) represented by ABCDEFGHIJ wherein each digit is used exactly once.
Given the following conditions, what is the number?
1) A + B + C + D + E is a multiple by 6.
2) F + G + H + I + J is a multiple by 5.
3) A + C + E + G + I is a multiple by 9.
4) B + D + F + H + J is a multiple by 2.
5) AB is a multiple by 3.*
6) CD is a multiple by4.*
7) EF is a multiple by 7.*
8) GH is a multiple by 8.*
9) IJ is a multiple by 10.*
10) FE, HC and JA are all prime numers.*
*This is not multiplication, but refers to concatenation. For example, if , then .
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