Mersenne Digest Thursday, 18 February 1999 Volume 01 : Number 511
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From: "Olivier Langlois" [EMAIL PROTECTED]
Date: Wed, 17 Feb 1999 02:41:14 -0500
Subject: Re: Mersenne: Link from Knuth's Home Page
- -Original Message-
From: Todd Sauke [EMAIL PROTECTED]
To: [EMAIL PROTECTED] [EMAIL PROTECTED]
Date: 16 février, 1999 19:31
Subject: Re: Mersenne: Link from Knuth's Home Page
Paul Derbyshire wrote:
What the devil is a "fascicle"?
My first thought was "Why not just look it up in the dictionary?"
I was amused that my Webster's New Collegiate Dictionary's first definition
of fascicle is "an inflorescence consisting of a compacted cyme less
capitate than a glomerule"
. . . Okaa
fascicule is a french word which means a small publication.
Todd Sauke
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From: "Adam Atkinson" [EMAIL PROTECTED]
Date: 17 Feb 99 14:09:22 +
Subject: RE: Mersenne: Link from Knuth's Home Page
Note that the Fascist party in Italy was called this because its
symbol had a bundle of something (wheat? twigs?) in the middle, and
the Italian for bundle is "fascio".
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Adam Atkinson ([EMAIL PROTECTED])
It is a sobering thought, for example, that when Mozart was my age, he had
been dead for two years. (T. Lehrer)
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From: "Vincent J. Mooney Jr." [EMAIL PROTECTED]
Date: Wed, 17 Feb 1999 12:45:32 -0500 (EST)
Subject: RE: Mersenne: Link from Knuth's Home Page
Yes. The Romans used the word "fasces" to decribe a bundle of sticks bound
together to hold an axe at one end (a picture would be worth a lot but I
don't have one). The cord was wrapped around the bundle. The axe was used
in war as well as construction. Benito Mussolini and the Italians knew
about this, being well steeped in Italian, i.e., Roman history. Beniti
coined fascist from "fasces" telling the Italians that they were strong if
bound together.
History lesson for the day.
At 02:09 PM 2/17/99 +, you wrote:
Note that the Fascist party in Italy was called this because its
symbol had a bundle of something (wheat? twigs?) in the middle, and
the Italian for bundle is "fascio".
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Adam Atkinson ([EMAIL PROTECTED])
It is a sobering thought, for example, that when Mozart was my age, he had
been dead for two years. (T. Lehrer)
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From: "Sander Hoogendoorn" [EMAIL PROTECTED]
Date: Wed, 17 Feb 1999 11:47:53 PST
Subject: Mersenne: Completely Factored
Can sombody please tell me when a number is completely factored?
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From: [EMAIL PROTECTED]
Date: Thu, 18 Feb 1999 04:55:57 +0100 (MET)
Subject: Re: Mersenne: Completely Factored
"Sander Hoogendoorn" [EMAIL PROTECTED] asks
Can sombody please tell me when a number is completely factored?
The prime factors of 2^29 - 1 are 233, 1103, and 2089.
The equation
2^29 - 1 = 233 * 1103 * 2089
gives the _factorization_ or _complete factorization_ of 2^29 - 1.
Whereas
2^29 - 1 = 233 * 2304167 (where 2304167 = 1103 * 2089)
2^29 - 1 = 1103 * 486737 (where 486737 = 233 * 2089)
2^29 - 1 = 2089 * 256999 (where 256999 = 233 * 1103)
are _partial factorizations_ of 2^29 - 1. A complete factorization
factors a number into prime factors. A partial factorization
allows composite cofactors (which are smaller than the original number).
If someone finds the factor 233 of 2^29 - 1, he/she can compute
the cofactor 2304167, and subject the cofactor to a probable prime test.
If the cofactor is definitely composite, we have
only a partial factorization, and more work is needed.
If instead the cofactor passes the probable prime test,
we try to prove it prime so we can be sure the factorization is complete.
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From: Henk Stokhorst [EMAIL PROTECTED]
Date: Thu, 18 Feb 1999 08:48:11 +0100
Subject: Re: Mersenne: Completely Factored
