The lone prime number?
Number Theory
Level
2
What is the only positive prime that can be expressed as the difference of the squares of two primes?
The answer is 5.
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1 solution
The difference of any two squares can be factored into ( a − b ) ( a + b ) . If you want a prime to be the difference, then a − b = 1 . And if a and b are both primes, the only solution would be ( a , b ) = ( 3 , 2 ) , as 2 is the only even prime number.
prime difference
= 3 2 − 2 2
= 5