# Euler's Lucky number

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• July 8th 2010, 07:39 PM
chiph588@
Quote:

Originally Posted by elim
To show lucky => prime, simply let m = 0

clearly prime numbers are not necessarily lucky (n=7)

Are there infinite many lucky number?

It has been shown that there are only $6$ Lucky Numbers of Euler.
• July 9th 2010, 01:59 AM
melese
Quote:

Originally Posted by chiph588@
It has been shown that there are only $6$ Lucky Numbers of Euler.

That's interesting... Can you please give an explantion?
• July 9th 2010, 10:39 AM
novice
Quote:

Originally Posted by elim
To show lucky => prime, simply let m = 0

clearly prime numbers are not necessarily lucky (n=7)

Are there infinite many lucky number?

If you interested, you can google "Lucky number". It will take you to Sieve of Eratosthenes. You can a little fun with it. It is still to be discovered whether there is infinite lucky numbers. You can write a computer program and find the lucky numbers.

You can also google Euler's Lucky Numbers and compare it. It says that someone has already proved that there are only six Euler's lucky numbers, but I didn't understand the material.
• July 9th 2010, 11:02 AM
chiph588@
Quote:

Originally Posted by novice
If you interested, you can google "Lucky number". It will take you to Sieve of Eratosthenes. You can a little fun with it. It is still to be discovered whether there is infinite lucky numbers. You can write a computer program and find the lucky numbers.

You can also google Euler's Lucky Numbers and compare it. It says that someone has already proved that there are only six Euler's lucky numbers, but I didn't understand the material.

Apparently the proof for finite Euler Lucky Numbers is a corollary of The Stark-Heegner Theorem.
• July 9th 2010, 11:41 AM
novice
Wow, interesting history. Too bad Heegner didn't get to see his work being appreciated.
I skipped the math part because I have not studied groups, rings, and fields. No comprehende.
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