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37, the median value for the second prime factor of an integer

458 点作者 sacrosanct超过 1 年前

30 条评论

dataflow超过 1 年前
This doesn&#x27;t mean there&#x27;s anything interesting about 37.<p>Rather, the only interesting fact here is that a finite median here exists at all. Once you&#x27;ve established that, it&#x27;s guaranteed to be some prime number, because we&#x27;re defining the median of a list to be an element of the list. It just happens to be 37 for this list, but it may as well have been anything else.<p>What <i>could</i> make 37 interesting is if we relaxed the definition of the median to be outside the set itself (which is entirely possible), and yet the limit still, and it still converged to 37 somehow. <i>That</i> would be wild.
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magneticnorth超过 1 年前
Love it when an article so clearly explains the answer to my first burning question - in this case, &quot;How in the world do you prove that?&quot;
raghus超过 1 年前
Interestingly, 37 also shows up in the Optimal Stopping &#x2F; Secretary Problem.
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zmgsabst超过 1 年前
Coincidentally, 37 is also the first irregular prime. They’re why Fermat’s last theorem is hard.<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Regular_prime" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Regular_prime</a>
lvass超过 1 年前
&gt;0.000000000000000 of numbers have 2 as their second prime<p>Is the article title correct without explicitly mentioning &quot;non-repeating&quot;?
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rlupi超过 1 年前
Is there any interesting theorem or result from l-functions or modular forms that covers this result?<p>I am learning about them and I find the topic fascinating.<p>I discovered them watching <a href="https:&#x2F;&#x2F;www.peakmath.org&#x2F;quest-for-f1" rel="nofollow noreferrer">https:&#x2F;&#x2F;www.peakmath.org&#x2F;quest-for-f1</a> videos on youtube. Also worth exploring: <a href="http:&#x2F;&#x2F;lmfdb.org" rel="nofollow noreferrer">http:&#x2F;&#x2F;lmfdb.org</a>
mg超过 1 年前
I agree that this makes 37 somewhat interesting.<p>Certainly more interesting than - say - 31.<p>31 is a prime number too, and therefore somewhat interesting. But for sure not as interesting as 37, which as we just learned, is the median value for the second prime factor of an integer.<p>Any suggestions of integers which are even <i>more</i> interesting?<p>And while we are at it, is there an integer which qualifies to be the <i>most</i> interesting?
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joewferrara超过 1 年前
Amazing how simple the proof is. 37 is my new favorite prime number, haha.
floxy超过 1 年前
I wonder what the growth rate of the mean of the second prime factor is? I guess I&#x27;d expect it to grow without bound, but maybe pretty slowly?
thrusong超过 1 年前
I&#x27;ve been obsessed with this number for most of my life. It&#x27;s like I see it on every clock I look at, or on every license plate in front of me.<p>There are random things about it like channel 37 has significance: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Channel_37" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Channel_37</a>
NooneAtAll3超过 1 年前
&gt; If we write p_k for the median k-th prime, then they show: log log p_k = ...<p>is this natural log or some base?<p>why not to use ln to keep ambiguity out?
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abbaselmas超过 1 年前
Sheldon Cooper, the best number 73 (21st prime number), its mirror 37 (12th prime number)<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=HacqfsV7ug0">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=HacqfsV7ug0</a>
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spokeonawheel超过 1 年前
given this knowledge, does this have implications that RSA would twice as crackable? Given casting a wide net, you could assume one of the prime factors is 37 and just try it against the pub key
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nikhilsimha超过 1 年前
This is one of the best articles I have read in a long long time!
mcv超过 1 年前
I once heard of a (tongue-in-cheek) list of interesting facts about numbers, and I think it listed 37 as the first uninteresting number, but I guess that was wrong.
cubefox超过 1 年前
But what about the arithmetic, geometric or harmonic mean?
lubujackson超过 1 年前
This is slightly interesting but I wonder what the median 3rd prime is, and 4th etc. Is there some sort of interesting pattern?
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nuc1e0n超过 1 年前
37 is one of the &quot;scary&quot; large numbers on countdown. The others being 12, 62 and 87.
drudru超过 1 年前
No mention of 37 signals? Maybe the aliens are trying to test our math skills?
yieldcrv超过 1 年前
why is this kind of thing interesting? my undergrad math teachers were never able to convey that<p>is there something here to use this knowledge with? like cracking a lotto’s RNG by knowing a second prime probability? that would be interesting to me
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whatever1超过 1 年前
Question, has anyone tried Transformer networks for predicting prime numbers?
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Obscurity4340超过 1 年前
What is the association between good passwords and prime numbers?
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falseprofit超过 1 年前
2.5, the median value for the first prime factor of an integer
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XorNot超过 1 年前
Well, this is just in time for a few birthday card ideas...
zelda-mazzy超过 1 年前
It was a bit difficult to grasp at first, but it clicked after realizing it&#x27;s all primes up to 37, not just 37. Kind of a neat fact, and I enjoyed reading this. Thanks for posting!
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mbfg超过 1 年前
isn&#x27;t 37 the solution to the toilet problem, as well? i&#x27;m supposing the two problems are related.
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hugodan超过 1 年前
That’s the age that Jesus Christ died
Egidius超过 1 年前
Reminds me of &quot;move 37&quot; made by Alpha Go:<p>&gt; Michael Redmond noted that AlphaGo&#x27;s 19th stone (move 37) was &quot;creative&quot; and &quot;unique&quot;. It was a move that no human would&#x27;ve ever made Lee took an unusually long time to respond to the move. An Younggil called AlphaGo&#x27;s move 37 &quot;a rare and intriguing shoulder hit&quot; but said Lee&#x27;s counter was &quot;exquisite&quot;. He stated that control passed between the players several times before the endgame, and especially praised AlphaGo&#x27;s moves 151, 157, and 159, calling them &quot;brilliant&quot;.<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;AlphaGo_versus_Lee_Sedol" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;AlphaGo_versus_Lee_Sedol</a>
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lifeisstillgood超过 1 年前
forgive my lack of maths to support the intuition, but as we discover ever higher prime numbers the second factor will tend upwards - towards the correct answer of 42?
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fuzztester超过 1 年前
See:<p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;37_(number)" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;37_(number)</a><p>Also see:<p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;1" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;1</a><p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;2" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;2</a><p><a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;3" rel="nofollow noreferrer">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;3</a><p>etc.<p>Lots of interesting points in those, and not just about math
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