What 5-digit number am I thinking of?

It has two prime digits.

Digit 3 is the highest digit.

Digit 2 is the lowest digit.

Digit 1 is higher than the sum of digits 4 and 5.

Digit 5 is half of digit 4.

Digit 1 is one smaller than digit 3.

Digit 5 is between digit 2 and digit 1

There are no duplicates and the digit 0 doesn't appear.

Don't forget that 1 isn't prime.

Puzzle Copyright © Kevin Stone

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Hint

What can digits 4 and 5 be?

Answer

71842.

Reasoning

The number can be represented as:

* * * * *

Since digit 5 is half of digit 4 we have four possibilities:

* * * 2 1

* * * 4 2

* * * 6 3

* * * 8 4

But since digit 1 is higher than the sum of digit 4 and digit 5 we can eliminate two possibilities leaving:

* * * 2 1

* * * 4 2

Since digit 5 is between digit 2 and digit 1, we can eliminate * * * 2 1, leaving:

* * * 4 2

Since digit 1 must be higher than the sum of digit 4 and digit 5 we have three possibilities:

7 * * 4 2

8 * * 4 2

9 * * 4 2

But digit 1 is 1 smaller than digit 3 we can eliminate 9 * * 4 2, leaving

7 * 8 4 2

8 * 9 4 2

Since digit 2 is the lowest number, it must be 1:

7 1 8 4 2

8 1 9 4 2

The answer has exactly 2 prime digits, which only leaves

7 1 8 4 2.