# Unknown number

An unknown number is divisible by exactly three different primes. When we compare these primes in ascending order, the following applies:

• Difference between the first and second prime numbers is half the difference between the third and second prime numbers.

• The product of the difference between the second with the first primes

and the difference between the third and the second prime number is a multiple of 17.

Determine the smallest number that has all the above properties.

• Difference between the first and second prime numbers is half the difference between the third and second prime numbers.

• The product of the difference between the second with the first primes

and the difference between the third and the second prime number is a multiple of 17.

Determine the smallest number that has all the above properties.

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