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Old 2022-10-16, 18:52   #1244
masser
 
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I listened to a Grateful Dead show for three hours last night ... great song!
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Old 2022-12-18, 19:49   #1245
Reed_Young
 
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"Reed Young"
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Default 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.
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Old 2022-12-18, 20:03   #1246
Batalov
 
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Quote:
Originally Posted by Reed_Young View Post
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.
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Old 2022-12-19, 05:29   #1247
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Quote:
Originally Posted by Reed_Young View Post
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?
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Old 2022-12-19, 05:33   #1248
chalsall
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Quote:
Originally Posted by VBCurtis View Post
It didn't occur to you that 4 is divisible by 2?
Now... That's funny...
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Old 2022-12-19, 11:03   #1249
S485122
 
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Default Given the standard definition of a prime...

Quote:
Originally Posted by VBCurtis View Post
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 ;-)
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Old 2022-12-20, 05:21   #1250
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Quote:
Originally Posted by S485122 View Post
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.
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Old 2022-12-29, 07:16   #1251
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Did you see the new Star Wars movie?
Darth Vader gets married. … To Ella

She becomes EllaVador
She lifts him up.
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Old 2022-12-30, 02:48   #1252
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Quote:
Originally Posted by MattcAnderson View Post
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.
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Old 2023-01-17, 15:47   #1253
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What do you call a person without a body or a nose?

Nobody knows.
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Old 2023-01-17, 23:16   #1254
ZFR
 
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Why won't Dijkstra create a sequel for Pokemon GO?

Because GO 2 considered harmful.
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