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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

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

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Something is wrong with their claim then...

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

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

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Here is one of the sixes they are talking about:

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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.

In biology, we use math like we know what we are talking about. Sad isn't it.

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

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

In biology, we use math like we know what we are talking about. Sad isn't it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

Obviously there is nothing special about 2013.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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.

In biology, we use math like we know what we are talking about. Sad isn't it.

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

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.

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

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

In biology, we use math like we know what we are talking about. Sad isn't it.

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

Thanks! So for 2013, 2014 and 2015, 2013=abc, 2014=def, and 2015=ghi where the nine letters

represent nine different prime integers.

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

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

- n872yt3r

Math Is Fun Rocks!

By the power of the exponent, I square and cube you!

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@Bob bundy,

Hasn't a few months passed already?

'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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,374

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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Very Well

'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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,374

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, youll get another chance to celebrate Fibonacci later in the year.

Bob

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,161

What a great day!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,374

Stefy wrote:

Just a hundred years to the next one!

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

Bob

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

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