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27-8=19 (Posted on 2015-03-31) Difficulty: 2 of 5
19 is the only prime which is equal to the difference of two cubes of primes.

Prove the above statement.

See The Solution Submitted by Ady TZIDON    
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Solution Solution | Comment 1 of 2
p^3-q^2=(p-q)(p^2+pq+q^2)

The difference of cubes is only prime if one of the factors is 1.
p^2+pq+q^2 > 1 for any primes
p-q=1 only for p=3, q=2 as they are the only primes that differ by 1.

  Posted by Jer on 2015-03-31 11:59:48
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