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New Mersenne Prime discovered (probably)

(www.mersenne.org)
359 points sdsykes | 4 comments | 16 Oct 24 11:51 UTC | HN request time: 0.219s | source
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dataflow ◴[19 Oct 24 05:04 UTC] No.41885759[source]▶
Given this contest can presumably go on infinitely long, what is the ultimate point of the contest? Is there some kind of theoretical or practical benefit to discovering a new Mersenne prime?
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Jerrrrrrry ◴[19 Oct 24 06:59 UTC] No.41886159[source]▶

  >presumably go on infinitely long
prove it
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poincaredisk ◴[19 Oct 24 14:30 UTC] No.41887955[source]▶
It's well established that there are infinite prime numbers, for example https://www-users.york.ac.uk/~ss44/cyc/p/primeprf.htm
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1. Jerrrrrrry ◴[19 Oct 24 16:06 UTC] No.41888609[source]▶
Should be able to trivially extend that logic to Mersenne Primes then, 'presumably'
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2. NeoTar ◴[19 Oct 24 18:08 UTC] No.41889454[source]▶
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.

3. af3d ◴[21 Oct 24 20:00 UTC] No.41907922[source]▶
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.
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4. Jerrrrrrry ◴[21 Oct 24 22:40 UTC] No.41909330[source]▶
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.