what kind of integer is the hardest to be factored

aaa120 · 2008-10-30, 08:32

what kind of integer is the hardest to be factored at present?
I want to know,who can tell me ?

ixfd64 · 2008-10-30, 11:10

The integers that are the hardest to factor are semiprimes whose factors are similar in size, such as RSA numbers.

FactorEyes · 2008-10-30, 18:11

Þoſe be hardeſt to facktor which poſseſs more Þan a ſyngle pryme facktor of greater Þan Þree ſcore and fyve digits, ſwych as alſo reſyſte the p+1 and p-1 meÞoddes, ſiÞ Þeir facktors be not wiÞin one of a smooÞ nombre. Of these, moſt difficult be Þose as polynomialles of smalle integyrs inexpreſsyble -- ſwych are unfacktorable by Þe ſieve moſt eſpecial.

petrw1 · 2008-10-30, 18:20

Personally I have the hardest time factoring 0.
Everytime I try to divide it by a potential factor I get an error ... I suppose even modern day computers and theories cannot handle such a powerful number.

jrk · 2008-10-30, 19:33

Quote:

Originally Posted by petrw1

Personally I have the hardest time factoring 0.
Everytime I try to divide it by a potential factor I get an error ... I suppose even modern day computers and theories cannot handle such a powerful number.

I can factor 0 easily. Its factorization is the set of integers.

petrw1 · 2008-10-30, 22:43

Quote:

Originally Posted by jrk

I can factor 0 easily. Its factorization is the set of integers.

Not quite because if they are really the factors then you should be able to multiply the appropriate pairs of factors and get as a result 0.

CRGreathouse · 2008-10-31, 02:07

Quote:

Originally Posted by petrw1

Not quite because if they are really the factors then you should be able to multiply the appropriate pairs of factors and get as a result 0.

0 * 1 * -1 * 2 * -2 * ...

wblipp · 2008-10-31, 02:08

Quote:

Originally Posted by petrw1

Not quite because if they are really the factors then you should be able to multiply the appropriate pairs of factors and get as a result 0.

What's the problem? He didn't say "positive integers."

CRGreathouse · 2008-10-31, 02:12

Quote:

Originally Posted by FactorEyes

Numbers are hardest to factor when they have several prime factors with more than 305 digits, resist the p+1 and p-1 methods, and are not within one of a smooth number. Of these, the most difficult are those not expressible as polynomials of small integers -- they are unfactorable by SNFS.

Yes, indeed!

aaa120 · 2008-10-31, 02:19

Quote:

Originally Posted by aaa120

what kind of integer is the hardest to be factored at present?
I want to know,who can tell me ?

The integer here is referred to the integer which is great than 0!

2008-10-30, 08:32	#1
aaa120 Oct 2008 2⁴ Posts	what kind of integer is the hardest to be factored what kind of integer is the hardest to be factored at present? I want to know,who can tell me ?

2008-10-30, 18:11	#3
FactorEyes Oct 2006 vomit_frame_pointer 2³·3²·5 Posts	Integyrres of facktoring moſt diffikultte Þoſe be hardeſt to facktor which poſseſs more Þan a ſyngle pryme facktor of greater Þan Þree ſcore and fyve digits, ſwych as alſo reſyſte the p+1 and p-1 meÞoddes, ſiÞ Þeir facktors be not wiÞin one of a smooÞ nombre. Of these, moſt difficult be Þose as polynomialles of smalle integyrs inexpreſsyble -- ſwych are unfacktorable by Þe ſieve moſt eſpecial. Last fiddled with by FactorEyes on 2008-10-30 at 18:55

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2008-10-30, 11:10	#2
ixfd64 Bemusing Prompter "Danny" Dec 2002 California 2×5×239 Posts	The integers that are the hardest to factor are semiprimes whose factors are similar in size, such as RSA numbers.

2008-10-30, 18:20	#4
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 2²×7×167 Posts	Personally I have the hardest time factoring 0. Everytime I try to divide it by a potential factor I get an error ... I suppose even modern day computers and theories cannot handle such a powerful number.