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#26 2013-01-02 04:06:18

pellerinb
Member
Registered: 2012-12-26
Posts: 43

Re: Happy 2013

Yes, and I just got a message from one of the authors on the explanation:

"2013 is the smallest number that needs at least six squares to make."

That means that 2013 is the smallest number that *requires* at least six squares to produce. Yes, there are smaller numbers that can be made with six squares. But all of those numbers can also be made with five or fewer squares


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#27 2013-01-02 04:20:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,516

Re: Happy 2013

Hi;

It must be one of those that is "subtracted squares of prime numbers," because it is not the sum of six positive squares that are prime. At least I can't find it.


There are two answers for 5

2 x 3^2 + 5^2 + 11^2 + 43^2

2 x 3^2 + 5^2 + 17^2 + 41^2

do they mean different primes?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#28 2013-01-02 06:27:54

pellerinb
Member
Registered: 2012-12-26
Posts: 43

Re: Happy 2013

I believe so. Otherwise, I suppose there's a way to stuff in a bunch of small 2^2's and 3^2's to fill in the gaps...  Can't use any 2^1's though... I believe that's cheat'n smile


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#29 2013-01-02 11:24:37

pellerinb
Member
Registered: 2012-12-26
Posts: 43

Re: Happy 2013

Found it! Seems like 2013 = 47^2-19^2+13^2-2^2
So it can be made up by only 4 prime squares! Cool!


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#30 2013-01-02 13:00:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,516

Re: Happy 2013

Something is wrong with their claim then...


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#31 2013-01-02 14:38:21

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,895
Website

Re: Happy 2013

Is this the article we are talking about?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#32 2013-01-02 14:51:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,516

Re: Happy 2013

Hi Agnishom;

It does not mention anything about the sum of 6 prime squares.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#33 2013-01-02 14:59:41

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,895
Website

Re: Happy 2013

It does. Try to look at the bottom

This one is a little more abstruse. Imagine a game whereby you make numbers by adding or subtracting squares of prime numbers. E.g., 30 = (5 x 5) + (3 x 3) — (2 x 2). 2013 is the smallest number that needs at least six squares to make. (Can you figure them out?)


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#34 2013-01-03 01:15:39

pellerinb
Member
Registered: 2012-12-26
Posts: 43

Re: Happy 2013

True, it might be erroneous but it's worth claiming just for the inspiration!


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#35 2013-01-03 04:53:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,516

Re: Happy 2013

Here is one of the sixes they are talking about:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#36 2013-01-03 05:41:54

pellerinb
Member
Registered: 2012-12-26
Posts: 43

Re: Happy 2013

The article's comments also have
41^2 + 19^2 - 5^2 - 2^2
43^2 + 17^2 - 11^2 - 2^2

curious if I can pull it off with just three. smile


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#37 2013-01-03 06:18:26

pellerinb
Member
Registered: 2012-12-26
Posts: 43

Re: Happy 2013

Interesting that 2013 is composed of four sequential digits: 0, 1, 2 and 3. That hasn't happened since 1432... 581 years ago!


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#38 2013-01-03 06:48:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,516

Re: Happy 2013

Obviously there is nothing special about 2013.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#39 2013-01-03 07:07:41

pellerinb
Member
Registered: 2012-12-26
Posts: 43

Re: Happy 2013

Also interesting is that 2013 to 2015 are consecutive numbers each with unique factors. That happened last in 1885-1887 and happens again in 2665-2667.


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#40 2013-01-03 10:51:35

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Happy 2013

Hi pellerinb!

I don't understand what you mean y "each with unique factors" for the consecutive numbers
(necessarily odd since if even they would have 2 in common).  Any two consecutive odd integers
must have no factors in common other than 1 since the difference of the two (larger less smaller)
is 2.  This means the only possible common factors are 2 and 1 and certainly 2 is not a common
factor for these odd integers.

Please clarify. smile


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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#41 2013-01-04 00:36:10

pellerinb
Member
Registered: 2012-12-26
Posts: 43

Re: Happy 2013

Sorry about that. Each triple (2013 to 2015, 1885 to 1887 and 2665 to 2667) has numbers with exactly three distinct prime factors each.


Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.

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#42 2013-01-04 09:53:04

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Happy 2013

Thanks!  So for 2013, 2014 and 2015, 2013=abc, 2014=def, and 2015=ghi where the nine letters
represent nine different prime integers.  smile


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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#43 2013-01-25 12:11:58

n872yt3r
Member
Registered: 2013-01-21
Posts: 392

Re: Happy 2013

This is obvious. Has anyone noticed that 2013 has 0, 1, 2, and 3.


- n872yt3r
Math Is Fun Rocks! smile
By the power of the exponent, I square and cube you! cool

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#44 2013-03-03 23:48:41

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,895
Website

Re: Happy 2013

@Bob bundy,

Hasn't a few months passed already? sad


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#45 2013-03-04 07:01:27

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Happy 2013

bobbym wrote:

It only just started, let's give it a chance.

dictionary.com wrote:

few
adjective
1.
not many but more than one:

Obi-Wan Kenobi: Patience!, Luke Skywalker

Bob

Last edited by bob bundy (2013-03-04 07:04:26)


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#46 2013-03-04 14:25:05

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 15,895
Website

Re: Happy 2013

tongue Very Well


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#47 2013-05-07 23:23:04

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Happy 2013

The time is 11.23 GMT.  The date is May 8th   ’13.  Thus:        1  1  2  3  5  8  13 

If you are in a later time zone, you still have a chance to enjoy your own Fibonacci minute.     

For UK members, who like to put the day before the month, you’ll get another chance to celebrate Fibonacci later in the year.

Bob

View Image: fib1.gif View Image: fib2.gif View Image: fib3.gif View Image: fib4.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#48 2013-05-08 05:56:14

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Happy 2013

Happy Fibonacci day. Just a hundred years to the next one! smile


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#49 2013-05-08 06:13:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,516

Re: Happy 2013

What a great day!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#50 2013-05-08 06:52:18

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,311

Re: Happy 2013

Stefy wrote:

Just a hundred years to the next one!

Not for me!  I've got just 89 days to go.  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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