- Another observation:

I presume that both factors have the same numbers of bits,

that means that of both numbers the most significant bits and the least significant bits are all 1's.

If this is so, than the quotient N1/N2 must be greater than 0,5 and less then 2.

As 57/21 > 2, I would not bet on these numbers !!!

Henk van der Griendt----- Original Message -----

From: richard_heylen

To: primenumbers@yahoogroups.com

Sent: Tuesday, June 29, 2004 4:01 PM

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

--- In primenumbers@yahoogroups.com, "Paul Leyland" <pleyland@m...>

wrote:

> Someone who may wish to remain nameless, so I'm not revealing

> his/her name or email address, sent me this prediction recently.

>

> > I have computed that the first 10 digits of RSA 768 as

> >

> > 57688 02668 and

> >

> > 21324 81819

>

>

> It will be interesting to see whether this prediction is

> borne out. We should find out within a year or two. In the

> mean time, the prediction will be saved here for posterity.

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...

Hope that helps!

Richard Heylen

Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

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[Non-text portions of this message have been removed] - 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]

<primenumbers@yahoogroups.com>

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

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

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

though.

> 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,

>

> 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

>

>

>

> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

> The Prime Pages : http://www.primepages.org/

>

>

> Yahoo! Groups Links

>

>

>

> - 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

> >

> >

> > ------------------------ Yahoo! Groups Sponsor

> --------------------~-->

> > Yahoo! Domains - Claim yours for only $14.70

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> > The Prime Pages : http://www.primepages.org/

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> >

> > Yahoo! Groups Links

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> >

> >

> >

>

>

> - The factor of 2 seems not to be true if one prime can be one bit shorter,

consider

1111111....1 divided by

100000...1

which is closer to 3.

Milton L. Brown

miltbrown@...

For the factors of RSA 140:

6.2642e69 = 2^231.8601

3.3987e69 = 2^230.9780

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

other?

Yes. Explicitly

3398717423028438554530123627613875835633986495969597423490929302771479 =

1111110000100001100000001100100110111010010011101100010010110111101000\

1000101010100011111101111010000111110010100000000100010010010001010001\

0100100111100010001011011011010011010010100110110011100010011001101100\

001010001011100010111

6264200187401285096151654948264442219302037178623509019111660653946049 =

1110100001011010001000110010001011111010010101101000000001110101011110\

0101100111001110000100000101100000001001001001001011001111011110111010\

1110001011000010010010110010011100000010000110000101001111011101001110\

0011001010010011000001

> [Original Message]

significant bits are all 1's.

> From: Henk van der Griendt <henk@...>

> To: <primenumbers@yahoogroups.com>

> Date: 6/29/2004 11:15:21 AM

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

>

> Another observation:

>

> I presume that both factors have the same numbers of bits,

> that means that of both numbers the most significant bits and the least

>

then 2.

> If this is so, than the quotient N1/N2 must be greater than 0,5 and less

>

----------------------------------------------------------------------------

> As 57/21 > 2, I would not bet on these numbers !!!

>

> Henk van der Griendt

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

> From: richard_heylen

> To: primenumbers@yahoogroups.com

> Sent: Tuesday, June 29, 2004 4:01 PM

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

>

>

> --- In primenumbers@yahoogroups.com, "Paul Leyland" <pleyland@m...>

> wrote:

> > Someone who may wish to remain nameless, so I'm not revealing

> > his/her name or email address, sent me this prediction recently.

> >

> > > I have computed that the first 10 digits of RSA 768 as

> > >

> > > 57688 02668 and

> > >

> > > 21324 81819

> >

> >

> > It will be interesting to see whether this prediction is

> > borne out. We should find out within a year or two. In the

> > mean time, the prediction will be saved here for posterity.

>

> 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...

>

> Hope that helps!

>

> Richard Heylen

>

>

>

>

> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

> The Prime Pages : http://www.primepages.org/

>

>

>

>

> Yahoo! Groups Sponsor

> ADVERTISEMENT

>

>

>

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>

--> Yahoo! Groups Links

Service.

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> a.. To visit your group on the web, go to:

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> c.. Your use of Yahoo! Groups is subject to the Yahoo! Terms of

>

>

>

> [Non-text portions of this message have been removed]

>

>

>

>

> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

> The Prime Pages : http://www.primepages.org/

>

>

> Yahoo! Groups Links

>

>

>

> - Milton

Yes but you have not addressed Richard Heylen's observation that say

(5768802668 + 1) * (2132481819 + 1) = 12301866814809977580

whose 12 leading digits are less than the 12 leading digits of RSA 576

which are 123018668453... ?

Regards

Alan Powell

> > From: richard_heylen

[Non-text portions of this message have been removed]

> > To: primenumbers@yahoogroups.com

> > Sent: Tuesday, June 29, 2004 4:01 PM

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

> >

> >

> > --- In primenumbers@yahoogroups.com, "Paul Leyland" <pleyland@m...>

> > wrote:

> > > Someone who may wish to remain nameless, so I'm not revealing

> > > his/her name or email address, sent me this prediction recently.

> > >

> > > > I have computed that the first 10 digits of RSA 768 as

> > > >

> > > > 57688 02668 and

> > > >

> > > > 21324 81819

> > >

> > >

> > > It will be interesting to see whether this prediction is

> > > borne out. We should find out within a year or two. In the

> > > mean time, the prediction will be saved here for posterity.

> >

> > 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...

> >

> > Hope that helps!

> >

> > Richard Heylen