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Math Help - Proof By Induction: Infinitely many pairs of consecutive pprime-ish numbers

  1. #1
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    Proof By Induction: Infinitely many pairs of consecutive pprime-ish numbers

    Call an integer pprime-ish if each of its prime factors occurs with power two or higher. Prove by induction that there are in finitely many pairs of consecutive pprime-ish positive integers.

    I know how to prove that there are infinitely number primes, but am unsure of how to prove this.
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  2. #2
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    Re: Proof By Induction: Infinitely many pairs of consecutive pprime-ish numbers

    Hint: If k and k+1 are pprime-ish, then so are 4(k)(k+1) and 4k(k+1)+1.
    Thanks from TheHowlingLung
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