Question 838181
Volume = length * width * height
and that product has to be 70.
Prime numbers are 2, 3, 5, 7, 11, 13, ...
They are numbers that have only two different factors: 1 and the number itself.
In other words, they are not 1, and are only divisible by 1 and themselves.
6 is not prime because we can write it as
{{{6=1 * 6}}} , and as {{{6=2 * 3}}}.
It has four factors, so it is not prime.
On the other hand, 13  can only be written as
{{{13=1*13}}} , so it has just two factors: 1 and 13.
It is not divisible by anything else.
1 is not a prime number
{{{70=10*7=2*5*7}}}
The only set of three prime numbers whose product is 70 is 2, 5, and 7.
Luckily they comply with the other two conditions:
5 - 2 = 3 (the difference between two of the dimensions is 3), and
7 - 2 = 5(the difference between a different pair of dimensions is 5).