Can every even integer be expressed as the difference of two primes? If so, is there any elementary proof?
Can every even integer be expressed as the difference of two primes?
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number-theory
prime-numbers
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5You could strengthen this to "Every even integer can be expressed as the difference of a pair of *consecutive* primes" or "Every even integer can be expressed as the difference of *an infinite number* of pairs of primes", or even to "Every even integer can be expressed as the difference of an infinite number of pairs of consecutive primes". They are all open questions. – 2011-03-21
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0See https://oeis.org/A020483 – 2011-03-21
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2@Charles: seen it. – 2011-04-19
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2Isn't this an implication of Goldbach's conjecture being true? – 2016-01-31
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0@AnantSaxena why? – 2017-06-21