For the factors of RSA 140:

6.2642e69 = e^231.8601

3.3987e69 = e^230.9780

Does this mean that the second number is one bit shorter than the other?

Also, for

5.7688e115 = e^384.55

2.1324e115 = e^383.11

Thanks,

Milton L. Brown

miltbrown@...

> [Original Message]

<rick.heylen@...>; <primenumbers@yahoogroups.com>

> From: Paul Leyland <pleyland@...>

> To: <miltbrown@...>; richard_heylen

> Date: 6/29/2004 7:52:06 AM

> Subject: RE: [PrimeNumbers] Re: Predicted partial factorization of RSA-576

>

> Yes, RSA-768. My typo. I've 576 on the mind these days.

>

> My conclusion still holds, once that silly typo is fixed.

>

>

> Paul

>

> > -----Original Message-----

> > From: Milton Brown [mailto:miltbrown@...]

> > Sent: 29 June 2004 15:40

> > To: Paul Leyland; richard_heylen; primenumbers@yahoogroups.com

> > Cc: miltbrown

> > Subject: RE: [PrimeNumbers] Re: Predicted partial

> > factorization of RSA-576

> >

> >

> > Small question. RSA 768 right?

> >

> > Also, can't the numbers be one bit longer or smaller

> > so 2^(384+/-1) ?

> >

> > Thanks,

> >

> > Milton L. Brown

> > miltbrown at earthlink.net

> > miltbrown@...

> >

> > > [Original Message]

> > > From: Paul Leyland <pleyland@...>

> > > To: richard_heylen <rick.heylen@...>;

> > <primenumbers@yahoogroups.com>

> > > Date: 6/29/2004 7:16:44 AM

> > > Subject: RE: [PrimeNumbers] Re: Predicted partial

> > factorization of RSA-576

> > >

> > >

> > > > Presumably there's a typo and this person means

> > > > 5768802686

> > > > instead of

> > > > 5768802668

> > > > as

> > > >

> > > > 5768802668999999999... * 2132481819999999... =

> > > > 123018668148...

> > > > which is clearly smaller than the required RSA 576

> > challenge number of

> > > > 123018668453...

> > >

> > > It's possible that there was a typo, I don't know.

> > >

> > > I'm pretty sure that the digits given are much more wrong than that,

> > though.

> > >

> > > RSA-576 is, by definition, a 576-bit number and suitable

> > for a RSA public

> > > modulus. 576-bit numbers lie in the range 2^575 to 2^576-1.

> > >

> > > The contest organizers tell us that the factors are both

> > the same size in

> > > bits, meaning that they are both 384-bit numbers and so

> > both lie in the

> > > range 2^383 to 2^384-1. All of the solved challenge

> > factorizations have

> > > two factors of equal size, and I see no reason to doubt

> > that RSA-576 also

> > > does.

> > >

> > > However, 2^383 is 19701....53408 and 2^384-1 is

> > 39402....06817 from which

> > > I conclude the larger factor is significantly smaller than the one

> > > predicted by our mysterious (partial-)factoring expert.

> > >

> > >

> > > Paul

> > >

> > >

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> > >

> > >

> > >

> > >

> >

> >

> >

>

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