The power of your favorite number starting with your birth date

[Sekr Gray 520]

Might as well join in. Always fun to see math/science used for entertainment

 

Favorite number: 9 

Birthdate: 1996-07-20

[Gernia 690]

Favorite Number: 7

Birth Date: 1993-11-21

[paradoxical 1,735]

i

(just kidding, my favorite is)

pi

 

5736/07/20

(not on your calendar, but it's my birthday)

Edited January 25, 2015 by paradoxical

[SasQ 1,355]

i

Another trickster, huh? ;-J

Well, with i the thing is a bit more... complex (badum tss!). The problem is that it is unit length, and any multiplication by it whatsoever won't change that, so all its powers lay on a unit circle. It's similar to what would happen if your favorite number were 1: it would stay that way no matter the exponent. Those are the exceptional cases where my spell cannot work, unless you were born at some imaginary date laying on the unit circle. But I guess you're a real person, not an imaginary one

 

just kidding, my favorite is pi

I like pies too

And my spell can deal with them too.

Actually, I invented this spell to debunk some guy's theory that there are some fancy relationships between the atomic spectral lines' frequencies and the Golden Ratio. I asked him for his birth date and conjured up a power of Φ (the Golden Number) which started with his birth date, and asked him whether this means that there's some conspiracy involving his birth date too So if it works for Φ, it will work for π as well.).

 

OK, so here's your magic number:

π^18287338 = 57360720315806787447461203824865314511599638449194490...

And you broke the record, since this number has an infinite number of digits ;-) The decimal point is somewhere after the 9091547-th digit. At least Wolfram won't make problems, since for "real numbers" it has to use digital approximations anyway and cannot avoid displaying the digits ;-J

 

 

@others: I'll tell you your numbers later, because now I must go somewhere.

Edited January 25, 2015 by SasQ

[SCS 7,443]

This is pretty awesome.

 

My favorite number is 5, and my birthdate is 1996-12-08.

[Odyssey 5,713]

Favourite number: 68

Birthdate: 1999-02-16

 

This seems like fun. :3

[SasQ 1,355]

@@JRex95:

4^20531300 = 19950408573423097171...8623205376

And this number is 12361075 decimal digits long (around 12 million). Proof.

 

 

@@Sekr Gray:

9^28919040 = 199607205064582428804...5333657601

And this number is 27595778 decimal digits long (over 27 million). Proof.

 

 

@@Gernia:

7^58342449 = 199311215829588158393...0867401607

And this number is 49305090 decimal digits long (nearly 50 million). Proof.

 

 

@@SCS:

5^20156007 = 19961208242257093222...3330078125

And this number is 14088445 decimal digits long (around 14 million). Proof.

 

 

@@Odyssey:

68^26459227 = 199902161960694459531...1835538432

And this number is 48486769 decimal digits long (over 48 million). Proof.

 

 

Also, I have good news:

My friend accidentally figured out a loophole in Wolfram Alpha, which allows for displaying digits of bigger numbers. It seems that Wolfram has a hard time when crunching huge natural numbers, but it can handle them when expressed in exponential/scientific notation, because then it switches to floating point mode. Now, when the limitation is gone, you can verify my answers which you couldn't before. When I find some more time, I'll add the links to the proofs where they were lacking previously.

 

One more thing:

If it happens that your lucky number is 0, 1, any power of 10, i, or anything which lies on the unit circle, my spell cannot apply. Here's why:

0 to any natural power except 0 is 0.

1 to any natural power is 1.

10 to any natural power is just 1 followed by zeros.

i to any natural power is 1, i, -1 or -i.

So none of these bases can produce your birth date, no matter which power it is raised to. Tough luck

If you're unlucky to have one of these as your lucky number, let's say that I just raise your birth date to some power other than 1 (since this would obviously give your birth date back), and give you the next smallest power which also starts with the digits of your birth date.

 

But any other numbers, including irrational numbers, such as π, Φ, e etc. should be OK I guess. For example, here's my birth date in the first digits of these special numbers:

Φ^22331590 = 1.9821203601917551793...×10^4667026 (Proof)

π^49632591 = 1.9821203195767834112...×10^24674836 (Proof)

e^2875515 = 1.9821203902590900310...×10^1248820 (Proof)

Edited January 26, 2015 by SasQ