Prime numbers

jonbeeza

jonbeeza

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Me and the missus were just discussing prime numbers, this was after watching a quiz show and getting the answer wrong ourselves. I thought a prime number was something that could be divided equally by itself, is that correct, or is it more complex than that? Trawling the net brings up a multitude of stuff, and gives a headache.

Any Maths boffins on here who can give a simple demo of a prime number, oh and when you would apply it in daily life?
 
A prime number is a natural number that can only be divided by 1 or by itself

1 3 5 7 11 13 17 19 etc

Sorry that should be 2 and not 1 ...
 
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Martyn... said:
A prime number is a natural number that can only be divided by 1 or by itself

1 3 5 7 11 13 17 19 etc
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So is the missus correct, when she says any odd number is a prime? I thought it was a little more complex than that :thinking:
 
Daily life?
You probably use them every day without realising. They are used in encryption, so if you use a phone or computer you are using them.
They can be used in technology - think of vibrations. A turbine rotating can have harmonic vibration at certain frequencies.
Let's say the turbine has 60 blades. It is divisible by 2,3,4,5,6,10,15,20,30, and of course 60. The turbine would be very prone to vibrations at a lot of frequencies.
However, if you have 59 or 61 blades, prime numbers, you would cut down on the frequencies that would affect it.
 
jonbeeza said:
So is the missus correct, when she says any odd number is a prime? I thought it was a little more complex than that :thinking:
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Not any odd number: 9 is not a prime as you can divide it by 3, same with 15, 21,27...
 
kendo1 said:
Daily life?
You probably use them every day without realising. They are used in encryption, so if you use a phone or computer you are using them.
They can be used in technology - think of vibrations. A turbine rotating can have harmonic vibration at certain frequencies.
Let's say the turbine has 60 blades. It is divisible by 2,3,4,5,6,10,15,20,30, and of course 60. The turbine would be very prone to vibrations at a lot of frequencies.
However, if you have 59 or 61 blades, prime numbers, you would cut down on the frequencies that would affect it.
Click to expand...

I think it was on the Chase quiz show, the Chaser was trying to explain a prime number. Me and the missus replied, who really cares ( in not such a polite phrase I might add :D) but there is obvious a time when we might need to be able to work this out, or apply it even.
 
I remember Carl Sagan saying that it would be impossible to write down a googolplex in its decimal form because there wouldn't be enough space in the universe to do so.
 
Another one is teeth on gear wheels. To reduce wear, if the number of teeth is a prime number (and a different prime number on the connecting cog) you will spread the wear over the whole cog.
So if you have a bicycle or car you are using them.
 
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kendo1 said:
Another one is teeth on gear wheels. To reduce wear, if the number of teeth is a prime number (and a different prime number on the connecting cog) you will spread the wear over the whole cog.
So if you have a bicycle or car you are using them.
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My very very short spell working in a garage, I only got as far as being taught, adding an extra cog at a certain point, gave you reverse :rolleyes:
 
Tringa said:
A prime number is a natural number greater than 1 where the only positeve divisors are 1 and the number itself so, although it appears a little strange, 1 is not a prime number.

The simplest explanation I've seen for this is - http://www.askamathematician.com/2010/01/q-why-is-the-number-1-not-considered-a-prime-number/

Dave
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I may soon need the Paracetamol, although I do find numbers interesting. On facepuke, someone always posts a teaser, by asking what is the answer to a sequence of numbers. If I look hard enough I can normally work it out, just wish I was more clued up with numbers..
 
kendo1 said:
Another one is teeth on gear wheels. To reduce wear, if the number of teeth is a prime number (and a different prime number on the connecting cog) you will spread the wear over the whole cog.
Click to expand...

I used to run a 47/17 fixed gear on my winter hack bike back in the 80's for just that reason - not only did it mean you wore the cogs evenly, but if you had to do emergency "skid stops", the wear spots would be highly unlikely to hit the same place on the tyre...

The fact that it came out at around a 72" gear, which was pretty much spot on for general riding around here at my then level of fitness was a bonus - though I did have a "flip-flop hub" with a 19 sprocket on the other side, which also happened to be a prime combo, and gave a slightly more sensible 65" gear for hillier rides.
 
And it's great for the Fibonacci sequence...although my mate Paul from Alpha Centauri reckons it's all a bit fanciful..
 
Good way of remembering prime numbers is that they always end with 1, 3, 7, 9:
11 13 17 19
23 29
31 37
41 43 47
53 59
61 67
71 73 79
83 89
97

At primary school in China, we had to memorise all prime numbers under 100. So I worked out the pattern. I must admit, it has had its uses later on when learning to find the common denominator of fractions. But it has yet to be proven useful in adult life...... until now!
 
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wuyanxu said:
Good way of remembering prime numbers is that they always end with 1, 3, 7, 9
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But unfortunately that's not especially useful, because the gaps between successive primes can be arbitrarily large. (In other words, for any integer N there is a sequence of N consecutive integers, none of which is a prime.)

There's a quite good example low down in the infinite sequence of integers. 1327 is prime and 1361 is prime, but none of the 33 numbers between them are prime. If we only look at numbers ending in 1, 3, 7 and 9 we still have
1329
1331, 1333, 1337, 1339
1341, 1343, 1347, 1349
1351, 1353, 1357, 1359
none of which are prime.
 
jonbeeza said:
So is the missus correct, when she says any odd number is a prime? I thought it was a little more complex than that :thinking:
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No, although all primes other than 2 are odd numbers.

TheBigYin said:
I used to run a 47/17 fixed gear on my winter hack bike back in the 80's for just that reason - not only did it mean you wore the cogs evenly, but if you had to do emergency "skid stops", the wear spots would be highly unlikely to hit the same place on the tyre...

The fact that it came out at around a 72" gear, which was pretty much spot on for general riding around here at my then level of fitness was a bonus - though I did have a "flip-flop hub" with a 19 sprocket on the other side, which also happened to be a prime combo, and gave a slightly more sensible 65" gear for hillier rides.
Click to expand...

IIRC, Vincent motorcycles were fitted with flip-flop rear wheels to allow the easier fitment of sidecars.

DorsetDude said:
I prefer perfect numbers.
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36/24/36?
 
Nod said:
No, although all primes other than 2 are odd numbers.



IIRC, Vincent motorcycles were fitted with flip-flop rear wheels to allow the easier fitment of sidecars.
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Wouldn't help with single direction tyres though.
Matt
 
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Just so happens that I spotted an HRD Vincent with a flip flop rear wheel today! What's most surprising is that I remembered this conversation so snapped it to post here. I have a feeling that the tyre fitted is unidirectional, which might help explain why the slower rear sprocket is rusty and shows no wear! The rest of the bike (and it's older sibling) looked well and regularly used, complete with full pannier sets and such modern fancies as indicators and horns!

DSCF3726 by Nod on Talk Photography
 
Nod said:
Just so happens that I spotted an HRD Vincent with a flip flop rear wheel today! What's most surprising is that I remembered this conversation so snapped it to post here. I have a feeling that the tyre fitted is unidirectional, which might help explain why the slower rear sprocket is rusty and shows no wear! The rest of the bike (and it's older sibling) looked well and regularly used, complete with full pannier sets and such modern fancies as indicators and horns!

DSCF3726 by Nod on Talk Photography
Click to expand...

Nice bit of info there @Nod :) .
 
I suppose I should have counted the teeth on both sprockets but I'm not that an@l!!!

A vaguely interesting snip from vincent-hrd.co.uk offers "The rear wheel, which was reversible, could carry a second sprocket for easy changes of ratio - very handy in long-distance trials combining miles of main road, followed by mountain sections. With a tommy-bar pull-out axle and quickly-detachable torque arms, the wheel could be removed without using any spanners in under a minute, the operation being aided by a rear stand and a hinged section on the mudguard." but doesn't give the numbers. Googling turns up a slight surprise - the standard rear sprocket has 46 teeth - not a prime number!
 
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