Mersenne DigestThursday, April 8 1999Volume 01 : Number 542
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Date: Tue, 06 Apr 1999 14:26:53 -0700
From: Rudy Ruiz [EMAIL PROTECTED]
Subject: Mersenne: Re:Mersenne Twin Primes
Mon, 05 Apr 1999 "Foghorn Leghorn" wrote":
begin quote~
To be completely sure of this, I found as many first factors as possible
for numbers of this form.
p First factor of 2^p-3
- -
3* 5
5* 29
7 5
13 19
17 53
19 5
31 5
61 29
89 29
107 5
127 5
521 5296777
607 5
12795
22035
228119
321719
4253No factor to 2^32
44235
968953
994123
11213 No factor to 2^32
19937 47
21701 53
23209 53
44497 29
86243 5
110503 5
132049 17040433
216091 5
756839 5
859433 4219
1257787 5
1398269 29
2976221 293
3021377 10513
*Indicates that 2^p-3 is prime.
end quote~
Obviously "IFF p == 3 mod 4 " 2^p-3== 0 mod 5, so there you have a
trivial pattern.
Therefore, only cases where p==1 mod 4 need to be investigated.
For what it's worth, there are 15 incidences of a factor "5".
In the following chart, I'll simply put the factors 5 with their
occurrence.
"Table of Frequencies" (for the 21 instances where p==1 mod 4)
---Assuming that the two "factors 2^32" are different---
factor |ocurrence
+
29 | 5
53 | 4
19 | 3
23 | 1
47 | 1
293| 1
4219| 1
10513| 1
5296777 | 1
17040433 | 1
number2^32| 1
number2^32+2| 1
While there is no foreseeable reason for a number of the form
2^p-3, (subject to p==1 mod 4 and p5) _not_ to be prime,
the odds are so overwhelmingly stacked against it that if
ever "found" the probability of computer error, programmer error,
operator error would have to be a factor to consider.
The pattern seems interesting in that:
1.- there are no factors 7,11,13,17
2.- the distribution is somewhat skewed. (IMHO)
Rodolfo
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Date: Tue, 06 Apr 1999 19:34:16 -0400
From: "Allan G. Schrum" [EMAIL PROTECTED]
Subject: Mersenne: Testing of software
A couple of cents from the south on testing.
First, testing each version is exactly what is needed, but a full run of
an exponent is not. Using something similar to Prime95's current
self-test, let's develop a more complete set of exponents for testing.
Using a couple hundred iterations from each exponent would be more than
adequate for a test suite. Also, it is something that can be run and
tested in a reasonable amount of time.
So in that vain, let's extract a set of exponents and start putting
together a testing master of 100, 500, 1000, 5000 and 1 iterations
for each one. Make sure the list includes exponents near the beginning
and end of an FFT range, any just before and just after any power of two
for the exponent, etc.
Next, there are several independant programs already that work on
several architectures for independant verification. Namely, Richard
Crandall's lucdwt code is portable and works. The algorithm is used by
George's Prime95 but is completely in C so it works on many
architectures. Certainly a good starting point. I'm sure there are
others. Use these suites of programs to construct our testing master.
Test what needs testing. Exhaustive tests are tiring.
- -Allan
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Date: Wed, 07 Apr 1999 00:31:51 -0400
From: Pierre Abbat [EMAIL PROTECTED]
Subject: Mersenne: How to tell when mprime wants to get on the Net
This is a multi-part message in MIME format.
- --8311A01B738B12CC77DAA998
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
I am running mprime on my home machine and prime95 at the office.
Prime95 tells me when it wants to get on the Net, but I couldn't tell
with mprime. George Woltman told me about the -d option, but it resulted
in a humongous file which reset only when I rebooted, which wasn't very
often. Last I checked, it was half as big as the program itself. (Good
thing my cat has a tail.) So I wrote the attached tcl script (which can
be used with other programs too) and pipe the output of
