a buddy of mine posts hard math problems on myspace. I'm no math whiz so I enlist the help of others... help me out please


What is the largest prime you can write using the digits from the 7th 4-digit prime in consecutive digits of (-1)^(1/(Pi * I))... where "i" of course equals sqrt(-1)

Hint: You can only use each digit from the above once, however you can use any number of combinations of the basic math functions to manipulate it: + - * / ( )

Think you got the largest? Then what is the smallest?

I don't quite understand your problem, but the 7th 4-digit prime is 1039.

And (-1)^(1/(pi*i))=e

So now he wants both the largest and smallest 4 digit prime using those 4 digits, since e is irrational, I suspect that you can argue that every combination will come up at some point, so that part is unneeded.

My interpretation is as follows:
Write out (-1)^(1/(pi*i))=e=2.7182818284590452353602874713527...
find the 7th 4 digit prime in 2.7182818284590452353602874713527.. use those 4 digits for the remainder of the question.

Ahhh that may be it

I wouldn't call this mathematically challenging... just tedious :)

Tedious indeed... thats what you are all for... I just fwd the questions...

FYI: the 7th 4 digit prime in the digits of e is 6277
Digits of e: http://www.math.utah.edu/~alfeld/math/e.html
Primes: http://www.math.utah.edu/~alfeld/math/p10000.html

I wrote some quick tcl to determine the result. Can anyone confirm?

I'll see what I can do about the next step also.

OK, I took all permutations of 6 2 7 7 (6277,6727,6772... )

inserted all combinations of + - * / between the numbers for all permutations
6+2+7+7
6+2+7-7
6+2+7*7
...

and the largest prime number I got was
6 * 2 + 7 * 7 = 61

Similarly, for the smallest prime
6 / 2 - 7 / 7 = 2

Anyone beat that? Or have a better algorithm?