I've been playing around with MPQS on UBASIC, to
see if I could find a factor of M727 and/or RSA232 ...
First I tried the approach of using very large
factor bases ... i.e. I'd sieve to 131071 using UBASIC's PRMDIV function,
thencheck the remaining residues up to about 2^48 using P-1 ...
Yeah, but most virus checkers have a scheduler,
whereby it kicks in when the system is "quiet", and scans your hard disk for
viruses, innoculates new files etc. If the slowdown is sporadic, and rectifies
itself after 5 or 10 minutes, I'd guess this is the case.
Dave
- Original
Osher Doctorow,
I was following you right up until the last
paragraph, where you seem to have some misinformation on Perfect Numbers and
Mersenne Primes.
... Also, any even perfect number has form
2^^(r-1)(2^^r - 2)...
Nope, perfect numbers have the form 2^^(r - 1)(2^^r
- 1), examples :-
I remember looking at this myself a while back - is
this what you meant ?
For a given modulus e.g. M(7) = 127, ignoring the
-2for a while ...
1 ^ 2 = 1 (mod 127)
2 ^ 2 = 4 (mod 127)
...
63 ^ 2 = 32 (mod 127)
and then the results are the same but in reverse
order i.e.
64 ^ 2 = 32 (mod
I was thinking more in terms of ...
Let's assume that every cycle of the LL test for
M(M(19)), we took the LSB and wrote it to a file - you might find the
code for the virus there !
(Remember that Bill Gates seems to do this with
every application he creates - whatever the glitch, error,
I was wondering about M(M(19)) ...
If there are an infinite number on Mersenne
Primes, then by the"infinite monkeys at infinite typewriters" theory,
M(M(19)) could actually contain a complete copy of the code for the "I Love You"
virus. This would explain all Brian and Henrik's resent
Ironic you should mention this, and then
makethe most common omission.
From the top, the rules are ...
If year / 100then leap year
If year / 400 then not leap year
If year / 1000 then leap year
2000 was a Leap Year,as will be 3000 and
4000. Although, as the world's spinning is slowing
I just shot myself in the foot again. Please ignore
the last message. This is what happens when I wake up at 3am to read my
E-Mail.
Sorry Richard !!
Dave
I'd just like to get a clarification on some files
I downloaded from the Entropia FTP.
Re the file of exponents, and how far they have
been trial factored.
I extracted a range using the decomp program. Each
exponent has a number by the side, but I am unclear to what this number
refers.
Perhaps I'm a little under-speed here
...
I understood that the $100,000 award was for the
first 10 million digit (that is to say 10 million decimal digit Mersenne
Prime).
Now a number of 10 million decimals is approx.
33 million bits long i.e. the Prime Exponent would be approx. 33
I was wondering if base-3
pseudo-prime testing might be considerably faster than LL testing for Mersenne
Primes ?
The base-3 pseudo-prime test is defined as :-
3 ^ P == 3 (mod P) where P is a probable-prime (base-3
prp)
3 ^ P 3 (mod P) where P is composite
We know that using binary
).
88855 exponents x 2358 multipliers = 20952090 tests = 1616
tests per second = 618 microsecs per test on a P133.
Brian, I'd be very interested in a copy of
that code, if you'd care to E-Mail it.
Regards
Dave Mullen
If you're factoring numbers in the 1165-1166 (bit) range, the first
factor could be anywhere in the root(1165) - root(1166) range i.e.
3413 - 3414 bits long !!
George's system prechecks to 2^52, and you are checking 2^52 - 2^64.
There's still a long way from 2^64 to 2^3413
Sorry, I'm no mathematician, and new to the
Mersenne field.
No, in the x-y bit range (remember that n bit integers
are about 2^n) thefirst factor could be x/2 to y/2 bits long (powers of a
power multiply).
What I was trying to say in my disjointed way was
...
(Example) M11 = 2047 (11
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