Haiku proof

Filed under: math — jlm @ 12:01

Product of all primes
Incremented won’t factor
Thus a larger prime.

I wonder if it’ll catch on…


  1. Sadly, that particular proof is incorrect. It only applies to the primes that were used to create the composite prior to the increment. If it were true, then creating the largest prime ever seen would be simple: generate primes, multiply them together, get a resulting really big prime.

    Comment by Josiah C. — 30-Mar-2012 @ 15:23

  2. I guess this is a problem in boiling proofs down to 17 syllables. I have no room to make it clear that I’m starting from the assumption of finitude of primes in order to produce a contradiction, not making a recipe for a large prime per se. I could use a verse form with a bit more space to play in, but it won’t be as tight:

    Let primes be but a finite list
    So their product must thus exist
    Make it one bigger
    And now this figure
    does all factorization resist.

    Comment by jlm — 30-Mar-2012 @ 15:55

  3. I think the original haiku could still work, if you titled it “Disproof of a finite number of primes, by contradiction”, but then the title is only 2 syllables shorter than the poem.

    Comment by Jeremy Leader — 24-Apr-2012 @ 12:22

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