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I have sat for about 8 hours doing trial and error and I have tried all combinations of different prime numbers but I am totally stuck..

I know that prime power decomposition is suppose to be prime number to the power of integers and their product gives you the original number... but I am asked to break this number down into its prime power decomposition.

412023436986659543855531365332575948179811699844327982845455626433876445565248426198098870423161841879261420247188869492560931776375033421130982397485150944909106910269861031862704114880866970564902903653658867433731720813104105190864254793282601391257624033946373269391

i have tried trial division which miserably failed after 1000, and now I am trying to divide the number into the largest prime number I can find and take the quotient I get and try to factor that into the largest prime number it can fit and so on until i have it all factored....is this even possible?

There is some browser problem I am having where comment button on stack isnt working.

This is one of the 8 assignment questions I have been assigned. I have finished all others and this I cant do from past 8 hours...

Should I write down all the prime numbers that are smaller than this number /2? and then try to break this up into those?

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    Reading the first response to this question made my crack up so freaking hard. I think I am falling in love with you guys. By the way, will this ever be factored?2012-03-04

1 Answers 1

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We shall put the question to rest. The number

412023436986659543855531365332575948179811699844327982 845455626433876445565248426198098870423161841879261420 247188869492560931776375033421130982397485150944909106 910269861031862704114880866970564902903653658867433731 720813104105190864254793282601391257624033946373269391

is called RSA-896; it is a large semiprime (the product of two distinct primes, neither too small).

There was a 75k$ bounty on it at one point. It has not been factored so far. There is absolutely no reason to believe someone can factor this with their own ability and a common PC and only sane amounts of time, short of strange and mystical number-theoretic methods beyond all present-day knowledge delivered from the distant future. You've been punked, smile for the camera!