[HN Gopher] How to identify a prime number without a computer
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       How to identify a prime number without a computer
        
       Author : beardyw
       Score  : 22 points
       Date   : 2025-11-12 17:50 UTC (7 days ago)
        
 (HTM) web link (www.scientificamerican.com)
 (TXT) w3m dump (www.scientificamerican.com)
        
       | politelemon wrote:
       | This is behind a paywall. "A Subscription Is Required to Continue
       | Reading"
        
         | xeonmc wrote:
         | I guess that's the answer then -- you need a subscription
         | instead of a computer.
        
         | zamadatix wrote:
         | The scourge of HN submission rules - "you can submit anything
         | and it's up to everyone else to actually be able to access it".
         | 
         | https://archive.is/8R0Fq
        
           | Terr_ wrote:
           | If I had my 'druthers designing a new link-share/comment
           | system, the visibility (and mirrors or excerpts) for the
           | target would be part of the model.
           | 
           | In other words, an icon showing whatever-wall status,
           | submitter can add an alternate link, etc.
        
       | Nevermark wrote:
       | Just grab some paper, a pen, and check that no number equal or
       | smaller than its square root divides into it evenly.
       | 
       | That is it. That is all. Pish posh.
        
         | WCSTombs wrote:
         | The example given in the article is 2^127 - 1, which was
         | historically proved to be prime without computers using a
         | clever method now known as the Lucas-Lehmer test. Your
         | algorithm is not practical for that number.
        
           | great_wubwub wrote:
           | /r/whoosh
        
           | Nevermark wrote:
           | Ah, but I can assure you, it is just that simple.
           | 
           | If a number is not prime, then it is the product of at least
           | two numbers smaller than itself.
           | 
           | If any of them are larger than its square root, the all
           | others must be smaller, or their product would be larger than
           | the candidate prime.
           | 
           | Ergo, just check that the candidate is not evenly divisible
           | by any number equal or lower than its square root.
           | 
           | QED. Check mate. Shazam.
        
       | IsTom wrote:
       | My favourite prime checking algorithm is that for n < 100 if it
       | looks prime, it is prime.
        
         | throwaway81523 wrote:
         | Like the famous Grothendieck prime of course.
        
           | xorbax wrote:
           | Definitely makes me feel better about my own work
        
         | emaccumber wrote:
         | The annoying child in me will always remember correcting my
         | freshman math teacher when he needed a prime number and wrote
         | 91 on the chalkboard.
        
         | GMoromisato wrote:
         | Are there any numbers that _don 't_ look prime but are, in
         | fact, prime? [Other than 2, I suppose.]
        
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