If it really is that bad, then it's probably not worth doing. I once
tested all the prime exponent Mersennes with exponents from about 10
million thru about 21 million for factors smaller than 2^33 or so,
using mersfacgmp on a Pentium 90MHz, in a couple of days.
The factoring program I used
Will Edgington commented:
Chris Nash writes:
The smallest factor of 2^p-1, p a prime, is at least as big as
2p+1. All factors of a Mersenne number of prime exponent are of the
form 2kp+1 - similarly for all 'new' factors of a composite
exponent (ie that haven't appeared in any
[EMAIL PROTECTED] writes:
Using the wonderful modpwr() from Paul Pollack's NTH library for
the TI-92, I have quickly verified the following results I found on
Entropia.com: [...]
Good.:)
For each of them, the TI-92 quickly returned that 2^exponent mod
factor = 1, and very
However, a semi-reasonable task would be to test numbers for factors up to
2^16.
Done.
Pitiful, I know, but a TI could test a single number in 12 hours.
An optimized algorithm will do it in about zero seconds.
B) To Mr. Woltman or Mr. Kurowski - how "useful" would factoring (most
likely
Foghorn Leghorn writes:
Could you factor a Mersenne number without storing it in memory?
(Answer: I don't *think* so) Ptoo bad. If we could factor
Mersenne numbers on an unmodified TI-92+, then there'd be a lot of
people who'd run that program.
Uh, that's exactly what
[EMAIL PROTECTED] writes:
So, is this:
(2^p mod f) - 1
Congruent to this:
(2^p -1) mod f
Yes, though be careful about the case of 2^p mod f being 0. The first
will give you -1 and the second is f-1. They are congruent, mod f, of
course, but not identical.
This is doubly
Using the wonderful modpwr() from Paul Pollack's NTH library for the TI-92, I
have quickly verified the following results I found on Entropia.com:
7017133 61 F 1901619961404080441 14-May-99 11:35 jay2001
PII_40
7029787 62 F 3764452186385609519 31-May-99
There is a conjecture that the nth Mersenne exponent resulting in a prime
is approximately (3/2)^n. Consider Mersenne primes through M37. (I don't
know exactly what M38 is yet, and there may be other small ones. Also, the
double checks of the range through M37 haven't been completed.)
You can
Also, to ease finding factors, using a number which is a multiple of 8 is
a good idea. However, how much work has been done on checking other mods
other than 120? Like 80, or even 720 to see what happens? just
wondering...
As often happens (to me at least), as soon as I tell someone
If you take the following comma delimited file into a spreadsheet, and
graph it (say with a line chart) it shows the relationship of Mersenne
exponents to their index, for the first 37 Mersenne primes. The first
column is the log of (3/2)^n, the second column is the log of the exponent
of
Brian J. Beesley writes:
If it really is that bad, then it's probably not worth doing. I once
tested all the prime exponent Mersennes with exponents from about 10
million thru about 21 million for factors smaller than 2^33 or so,
using mersfacgmp on a Pentium 90MHz, in a couple
For those of you who read PC Magazine, there is a short column by Bill
Machrone in the July 1999 issue on page 85 that talks about GIMPS, Aaron
Blosser, and the US West episode. Not a detailed examination of what
happened but some good press on why you might want to participate
in such a
Well, looks like factoring on TI calculators won't be feasible or useful. :-(
Before more data comes in, I'd like to state that I believe three things:
A) The 38th Mersenne prime discovered has an exponent in the neighborhood of
6,900,000.
B) We *are* missing a Mersenne prime between 3021377
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