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...
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Milton Brown
miltbrown@...
Jun 29, 2004 2:45 pm
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 ...
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Paul Leyland
pleyland@...
Jun 29, 2004 2:52 pm
Yes, RSA-768. My typo. I've 576 on the mind these days. My conclusion still holds, once that silly typo is fixed. Paul...
If you take the full sequence of primes starting at 11, and for each prime, p, obtain a value for 1-(1/p), and multiply each of the values, in turn, by the...
... Hash: SHA1 ... What's simple to you? I don't see how it could get simpler than the Lucas-Lehmer test. I could write a GP script less than a line long to ...
Here is a record Generalized Carol prime...... (273*2^117629 - 1)^2 - 2 I have sieved to 125K. Phil Comody wrote the sieve (ksieve) for this set of numbers....
In a message dated 29/06/04 17:10:22 GMT Daylight Time, tmgulland@... ... By Euler's product expansion, zeta(1) = {product: p prime, p>=2} 1/(1-1/p) =...
... This can be written as (k*2^n+1)^2-2. So is it a Generalized Kynea? Does one have to take a maximum? You may be interested to know that I have used 5 round...
Paul give me the site for the 321search .... ... This can be written as (k*2^n+1)^2-2. So is it a Generalized Kynea? Does one have to take a maximum? You may...
... We don't have a website per se but have a message board with a primative reservation system at: http://www.mersenneforum.org/forumdisplay.php?f=14 our bio...
Paul, Now I remember what 321search is. It is interesting......But gosh, so many interesting formulas and not enough time. I have my hands full now with the...
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Milton Brown
miltbrown@...
Jun 29, 2004 7:43 pm
Sorry, another small question. For the factors of RSA 140: 6.2642e69 = e^231.8601 3.3987e69 = e^230.9780 Does this mean that the second number is one bit...
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Milton Brown
miltbrown@...
Jun 29, 2004 7:44 pm
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 ...
Hi, I noticed this lemma at Will Edgington's Mersenne Page. - A prime number divides at most one prime-exponent Mersenne. However, it is also true that: - A...
Hi David, The only number that can divide a Mersenne is a base 2 pseudoprime or a prime. Now all composite Mersennes are, in fact, base 2 pseudoprimes. This...
... I assume you mean when 3n+1 is prime. First we find an a^2+3*b^2 that is some multiple of p, say kp Then we use three methods to find a c^2+3*d^2 that is a...
If a number is found that divides a given Mersenne and is less than the square root of that Mersenne is it safe to assume that the number is prime. Or can it...
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Paul Leyland
pleyland@...
Jun 30, 2004 8:59 am
... I downloaded the tools and experimented. It became clear that the PIII processor is relatively better at sieving than the P4, and the P4 is relatively...
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Paul Leyland
pleyland@...
Jun 30, 2004 9:02 am
My apologies: I made a typo. ... That should be 1.0e9. Paul...
Hi David, Thanks for that. To be safe then I have to compare with only the first or second possible x that can divide a given Mersenne, such as x = 2kp+1...
Hi David, I'm sorry, I don't understand exactly what you mean here. I show that 10169 divides 2^164-1 and 8009167 divides 2^1334861. My un-optimized software...
Hi David, I can only give you the numbers that I get here: 2 is even and won't be accepted. 3 divides 2^2 -1 191 divides 2^95 - 1 307 divides 2^102 - 1 593...
Would it not follow from the method used to resolve, if not necessarily the conclusion found from, Bertrand's Postulate, that there must always be at least one...
Milton Yes but you have not addressed Richard Heylen's observation that say (5768802668 + 1) * (2132481819 + 1) = 12301866814809977580 whose 12 leading digits...
Hi, I thought that I would pass this on, seeing as how it may be slightly different to the normal run of the mill algorithm. There is a trivial tranformation...
I have a couple of questions. (given below.) ... First, I hate to bring up semantics, but ALL numbers of the form 2^n - 1 are Mersenne numbers. The ones...
Hi David, First, in answer to your questions: I don't print the iteration number when I'm not doing the addition, this is why the number jumps the way that it...
I've been working through the ramifications of my new algorithm and it seems that it can be used as an encryption busting tool. Take the fictious case of a...
Kevin Acres writes: I've been working through the ramifications of my new algorithm and it seems that it can be used as an encryption busting tool. First, I'm...
