There is a ten-digit mystery number (no leading 0), represented by ABCDEFGHIJ, where each numeral, 0 through 9, is used once.

1. A + B + C + D + E is a multiple of 6.
2. F + G + H + I + J is a multiple of 5.
3. A + C + E + G + I is a multiple of 9.
4. B + D + F + H + J is a multiple of 2.
5. AB is a multiple of 3.
6. CD is a multiple of 4.
7. EF is a multiple of 7.
8. GH is a multiple of 8.
9. IJ is a multiple of 10.
10. FE, HC, and JA are all prime numbers.

Determine the number from the abovementioned clues.