Holy Saint Lucas! 2 new primes? (M45 related, and M47)

[uigrad]

Originally Posted by jrk

0x1248125A492480__

0xB6C80137FEDB7E__

Are these really the fake residues? They should have stood out. I can't quite figure out what George's method is, but there are a lot of patterns in those residues.

Let's take the first one:

0x1248125A492480 = 00010010010010000001001001011010010010010010010010000000 b2

Let k = 585 = 1001001001 b2 
   (palindrome in base 2 or 10)

k*2^7 + k*2^19 + k*2^27 + k*2^43
     =                                        10010010010000000 b2
       +                          10010010010000000000000000000 b2
       +                  1001001001000000000000000000000000000 b2
       +  10010010010000000000000000000000000000000000000000000 b2
       ________________________________________________________
     = 00010010010010000001001001011010010010010010010010000000 b2
     = 0x1248125A492480

The 14-digit residue is 56 bits.  19+27 = 56, so those two are
centered in the final residue.  43+7 = 50, which is why the
first and fourth group are not quite centered.

Now the second residue also has patterns, but they seem harder to explain:

0xB6C80137FEDB7E = 10110110110010000000000100110111111111101101101101111110 b2
= 1 011011011 0010000000000100 1101111111111011 011011011 11110 b2

I'm not sure why to split it this way, but it seems to work

Group 1: 1
   - lonely digit
Group 2: 011011011
   = 3*2^0 + 3*2^3 + 3*2^6 (repeating digits)
Group 3: 0010000000000100
   = 2^2 + 2^13 (palindrome)
Group 4: 1101111111111011
   - same as group 3, but bits reversed
Group 5: 011011011
   - same as group 2.
Group 6: 11110
   - equal to 30 in base 10.  I don't understand the significance here either.

If this was discussed in a different thread, let me know. I couldn't find it anywhere.

[jrk]

Originally Posted by uigrad

Are these really the fake residues? They should have stood out. I can't quite figure out what George's method is, but there are a lot of patterns in those residues.

The pseudocode that describes the fake residue generator is described here:

http://www.mersenneforum.org/showpos...0&postcount=30

When applied to those exponents it makes the fake residues that were posted.

[uigrad]

Originally Posted by jrk

When applied to those exponents it makes the fake residues that were posted.

Ah, you are right. For M(Aug), he used the fake exponent for the fake residue, and for M(Sep), he used the August exponent for the fake residue.

I checked it with the following perl script, and for some reason I'm off by 1 for the last residue:

#!/usr/bin/perl
foreach (13466917, 20996011, 32428427, 43112609) { f($_); }
sub f
{
  $prime = shift;
  $p = $prime;
  $residue = "";
  foreach (1..14) 
  {
    $digit = substr('0123456789ABCDEF',($p & 0xF)+0,1);
    $p = (($p & 0x8FFFFFFF) << 1) | ($p >> 28);
    $residue = $residue . $digit;
  }
  print ("$prime: ${residue}__\n");
}

13466917: 5A4800136C936D__
20996011: B6C80125A48000__
32428427: B6C80137FEDB7E__
43112609: 1248125A492481__

[philmoore]

I see that the banner is back to "Finding 10 World Record Primes!" How about changing it to "Finding 11 World Record Primes and 1 Near Miss!" ?

[jrk]

As far as I'm concerned the order of the two new primes isn't important.

The world learned about them at the same time, and they are the 1st and 2nd largest known primes, making them bigger than any previously known prime at the time of announcement.

I would simply say "Finding 12 world record primes" and be done with it.

[jinydu]

I'm seeing "Finding World Record Primes Since 1996". At least that will never become outdated.

[Uncwilly]

Originally Posted by jinydu

I'm seeing "Finding World Record Primes Since 1996". At least that will never become outdated.

However: The text banner on the site is inconsistant. Some still refer to 2006.

[uigrad]

The 2006 announcement is also at the top of the credits, math, and links pages:
http://mersenne.org/credits.htm
http://mersenne.org/math.htm
http://mersenne.org/links.htm

And, there's a number of places that scream at the user about how they could win the $100,000 prize!. They could just be changed to the $150,000 prize now. Maybe most of these are on the primenet server. ie:

http://mersenne.org/ips/index.html#contest
http://mersenne.org/cgi-bin/primenet...xxx&UserPW=yyy


The faq on primenet is really dated. For one, it still links to the (now defunct) entropia.com. It also recommends users should download IE 5.0 before trying to connect:
http://mersenne.org/ips/faq.html#wininet


And the download page at primenet gives 22.12 as the latest version (or version 18.1 for linux). It has a big exploding bubble that say "NEW!", just so users don't look through the download section without noticing the brand new 22.12 version:
http://mersenne.org/ips/#free_software

To top things off, all 6 mirrors at that site are down, so even if a user was willing to live with 22.12, they couldn't get it here!


While we're listing things that should be updated, I'd like to see what the growth history looks like since February 2006:
http://mersenne.org/ips/stats.html

Also, the links at the bottom of that stats.html page contain typos. Many of them have mersenne.orgips as the hostname

[M29]

Regarding outdated pages, maybe George would welcome some help?

But I'm not volunteering

[ixfd64]

The banners need updating as well. They're still talking about M38!

By the way, is George the only one who can edit the GIMPS website?

[cheesehead]

"It exists. Hiding. Cloaked. Find Mersenne Prime #39." !!

Will someone please create a replacement for that banner (or show me how to do it with Paint -- I will if I can)?

And create a few more (#48, #49, #50, ...) for the future -- keep them offline until the time comes, but send copies to Scott, George, and whoever else can update the PrimeNet site. (Hmmmm ... actually, it wouldn't do any harm to display one of those now, would it?)

- - -

Shucks, I volunteer to update _all_ the banners, if someone shows me how to do it with Paint.