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 2022-10-16, 18:52 #1244 masser     Jul 2003 Behind BB 24×3×41 Posts I listened to a Grateful Dead show for three hours last night ... great song!
 2022-12-18, 19:49 #1245 Reed_Young     "Reed Young" Sep 2009 Oregon 1F16 Posts Given the standard definition of a prime... Have you ever noticed, how the standard textual definition of a prime integer, taken literally, also includes all the perfect squares as well as perfect cubes and whatever hyper-geometric terms would be used as analogy for the higher powers of each given prime number which has no divisors but 1 and arbitrarily many multiples of a single, other prime number? (for example 4, 8, 9, 16, 25, 27, 32, 49, etc.) I know, I learned in elementary school that the perfect squares 4, 9, 16, 25, 49, etc. aren't really primes and we were taught that in such a way that 8, 16, 27, 32, 81, 125, etc. were so obviously not prime that nobody even asked. But as soon as this little irony occurred to me today, I searched the Internet to be sure I was remembering the "usual" definition right and sure enough, the definition that I see on the first few results is not quite the actual operational definition. The full definition in actual use but rarely if ever printed is, a number is prime if and only if it is divisible only by one and (only once) by itself. The bit in parentheses is usually omitted and if we take what is usually printed at face value, then 4, 8, 9, 16, 25, 27, 32, etc. are all prime! If this omission has negatively impacted anybody's mathematics education they haven't told me about it, and I don't suppose that's likely, as anybody who doesn't still recall that from their early math education is probably not a mathematician as an adult. I just find it interesting that people who talk about and work with prime numbers professionally take such a functionally relevant part of the definition for granted, and that it doesn't seem to cause even a hiccup.
2022-12-18, 20:03   #1246
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

89·113 Posts

Quote:
 Originally Posted by Reed_Young Have you ever noticed, how the standard textual definition of a prime integer, taken literally, <<268 more words>>, and that it doesn't seem to cause even a hiccup.
We cannot be picky in this thread, but a joke is usually short and preferably has a punchline.

2022-12-19, 05:29   #1247
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

10110000000112 Posts

Quote:
 Originally Posted by Reed_Young The full definition in actual use but rarely if ever printed is, a number is prime if and only if it is divisible only by one and (only once) by itself. The bit in parentheses is usually omitted and if we take what is usually printed at face value, then 4, 8, 9, 16, 25, 27, 32, etc. are all prime!
It didn't occur to you that 4 is divisible by 2?

2022-12-19, 05:33   #1248
chalsall
If I May

"Chris Halsall"
Sep 2002

2·72·113 Posts

Quote:
 Originally Posted by VBCurtis It didn't occur to you that 4 is divisible by 2?
Now... That's funny...

2022-12-19, 11:03   #1249
S485122

"Jacob"
Sep 2006
Brussels, Belgium

3×5×127 Posts
Given the standard definition of a prime...

Quote:
 Originally Posted by VBCurtis It didn't occur to you that 4 is divisible by 2?
This kind of thing could happen when one gets so seduced by an idea, that one forgets the obvious : "a number is prime if and only if it is divisible only by one and by itself", the itselfpart has gone wrong in the presented reasoning.

But might it be that that was the intended joke ? The choice of thread should be a clue ;-)

2022-12-20, 05:21   #1250
Reed_Young

"Reed Young"
Sep 2009
Oregon

31 Posts

Quote:
 Originally Posted by S485122 This kind of thing could happen when one gets so seduced by an idea, that one forgets the obvious : "a number is prime if and only if it is divisible only by one and by itself", the itselfpart has gone wrong in the presented reasoning.
Yes, that's it exactly. I thought I had noticed something funny, not something mathematically relevant, and I rushed off to tell the joke without checking the math. Should have left the "have you ever noticed" schtick to Jerry Seinfeld.

 2022-12-29, 07:16 #1251 MattcAnderson     "Matthew Anderson" Dec 2010 Oregon, USA 23·149 Posts Did you see the new Star Wars movie? Darth Vader gets married. … To Ella She becomes EllaVador She lifts him up.
2022-12-30, 02:48   #1252
sdbardwick

Aug 2002
North San Diego County

22·3·67 Posts

Quote:
 Originally Posted by MattcAnderson Did you see the new Star Wars movie? Darth Vader gets married. … To Ella She becomes EllaVador She lifts him up.
And she is formidable in her own right, as she can take him down just as quickly.

 2023-01-17, 15:47 #1253 masser     Jul 2003 Behind BB 36608 Posts What do you call a person without a body or a nose? Nobody knows.
 2023-01-17, 23:16 #1254 ZFR     Feb 2008 Meath, Ireland 18510 Posts Why won't Dijkstra create a sequel for Pokemon GO? Because GO 2 considered harmful.

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