4 ms·

>presumably go on infinitely long prove it

• poincaredisk 2y ago
  It's well established that there are infinite prime numbers, for example https://www-users.york.ac.uk/~ss44/cyc/p/primeprf.htm https://www-users.york.ac.uk/~ss44/cyc/p/primeprf.htm
  • Jerrrrrrry 2y ago
    Should be able to trivially extend that logic to Mersenne Primes then, 'presumably'
    • NeoTar 2y ago
      It’s not. The traditional proof that there are an infinite number of primes relies on unique prime factorisation- i.e for any number, n, there is a unique set of primes p1, p2, p3, … etc. where p1 * p2 * p3 * … = n For instance 88 = 2 * 2 * 2 * 11, 42 = 2 * 3 * 7 It’s worth reading the proof if you haven’t - it’s comprehensible with high school maths. No such property exists for Mersenne primes, so we can’t trivially extend it. Many proofs of the properties of prime numbers are difficult because they, by definition, actively resist patterns.
    • af3d 2y ago
      Yes, the Mersenne primes do indeed extend to infinity. That is due to the simple fact that perfect numbers (for which they are intimately connected to) are also known to be infinite in number.
      • Jerrrrrrry 2y ago
        This was an instant deduction, thank you. I tried some flavors of primes but you'd think the most intuitive one by a magnitude would be listed on the Wiki for proofs.
• dataflow 2y ago
  I didn't claim there are an infinite number of Mersenne primes. I said the contest could presumably go on infinitely long. The latter doesn't require the former. It's only predicated on us lacking proofs about how many there must be.
  • Jerrrrrrry 2y ago
    >I didn't claim there are an infinite number of Mersenne primes. I didn't claim that you did, only that the contest... you actually almost got me :)
    • dataflow 2y ago
      I mean, that's what I took from your comment here, quoting my "presumably": https://news.ycombinator.com/item?id=41888609 https://news.ycombinator.com/item?id=41888609