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04-12-2020 , 09:06 PM

FellaGaga-52

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Join Date: Oct 2018 Posts: 8,077

This number came up as a prime factor of 3749 in something I was doing. I saw where a mathematician called it, 163, his most fascinating number. Something about it being the first number in some arcane series of expanded primes and the last number in another one. Way over my head on the math, no mathematician here. Anybody know what he is referring to and can put it in non-mathematical terms?

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04-13-2020 , 06:28 AM

masque de Z

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Join Date: Aug 2009 Posts: 9,961

https://en.wikipedia.org/wiki/Heegner_number

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04-13-2020 , 12:50 PM

FellaGaga-52

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Join Date: Oct 2018 Posts: 8,077

Thanks. Did he mean every integer can be factored by primes?

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04-13-2020 , 06:51 PM

Morphismus

BBV Poker Player of 2022

Join Date: Feb 2008 Posts: 24,271

yes, and always in a unique manner

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04-13-2020 , 08:19 PM

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

Quote:

Originally Posted by Morphismus

yes, and always in a unique manner

Unless 1 is a prime number

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04-13-2020 , 08:48 PM

lastcardcharlie

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Join Date: Aug 2006 Posts: 10,435

Which it isn't.

Although 0 is an integer.

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04-13-2020 , 09:48 PM

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

1 ought be a prime number. It would reduce the number of conjectures, which, I think we can all agree, would be nice

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04-13-2020 , 09:50 PM

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

Edit: alternatively, it would increase the length of some conjectures and make them sound sillier, which would also be nice

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04-13-2020 , 10:30 PM

Aaron W.

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Quote:

Originally Posted by BrianTheMick2

1 ought be a prime number. It would reduce the number of conjectures, which, I think we can all agree, would be nice

It would make a lot of theorems far more annoying to state (or false).

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04-14-2020 , 04:27 AM

#10

BrianTheMick2

Long way to go and a short time to get there.

Join Date: May 2012 Posts: 19,410

So, basically, no downside at all

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04-14-2020 , 01:44 PM

#11

Zeno

Le Misanthrope

Join Date: Sep 2002 Posts: 22,356

Is there a proof 1 is not a prime number?, based on the axiom/definition of a prime? I don’t think so. It is just stated so*, that way there is less to get tripped up on for the whole number system.

*see Plato if you have any doubts. Plus you can’t have the house of cards known as the integers collapse into chaos.

Last edited by Zeno; 04-14-2020 at 01:49 PM. Reason: Added text

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04-14-2020 , 01:52 PM

#12

Zeno

Le Misanthrope

Join Date: Sep 2002 Posts: 22,356

It is against the law to divide by the integer 0. So saith The Lord!

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04-16-2020 , 12:34 AM

#13

chezlaw

Limey Bastard

Join Date: Jan 2004 Posts: 46,845

Quote:

Originally Posted by Zeno

It's a deeply important* semantic debate about the meaning of the word 'and' in the usual definition.

*It's what I call a 5 pinter (6 in american money)

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04-16-2020 , 01:37 AM

#14

PairTheBoard

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Join Date: Dec 2003 Posts: 10,037

Theorem
1 is an even number

proof:
1 is divisible by 1 and 1
1 and 1 is 2

therefore
1 is divisible by 2

Thus 1 is an even number
qed

PairTheBoard

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04-16-2020 , 01:56 AM

#15

chezlaw

Limey Bastard

Join Date: Jan 2004 Posts: 46,845

That is odd

Hence 1 is both even and odd

qed

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