20080917, 21:51  #1 
"Kyle"
Feb 2005
Somewhere near M52..
3·5·61 Posts 
Interim and Res64 Residues
Can anyone point me to a source to help understand what the Interim Residues and Res64 residues actually mean or indicate? (i.e., the difference between the letters, numbers, etc). Thanks.
Last fiddled with by Primeinator on 20080917 at 21:52 
20080917, 21:58  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10AB_{16} Posts 
The letters and numbers are hexadecimal (base 16), which is represented with 0F. I think the res64/interim residues is the last 64 bits of the residue encoded in hexadecimal, but I'm not sure on this.

20080917, 23:15  #3  
"Richard B. Woods"
Aug 2002
Wisconsin USA
17014_{8} Posts 
Quote:
In the LucasLehmer test's series of iterations, the result value of the final iteration (which is zero only if the number being tested is prime) is called the residue. An "interim residue" is the value computed at some iteration before the last one. Because these residues can be millions of bits long, it has been traditional to save only the last (rightmost, loworder) few bits of it for later comparison. A "Res64 residue" means the last 64 bits of a (full) residue value. In the "old days", some saved residues were only the final 15 bits. For an explanation of hexadecimal notation, see the Wikipedia article at http://en.wikipedia.org/wiki/Hexadecimal. 

20080917, 23:43  #4  
"Kyle"
Feb 2005
Somewhere near M52..
3·5·61 Posts 
Quote:


20080918, 00:04  #5  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17×251 Posts 
Quote:
The fake residue is so easily spotted because the way to generate it is known, and becomes pretty easy to see when you look at the binary of the residue. See http://www.mersenneforum.org/showpos...9&postcount=25 for more information, which can be summed up in that certain parts of the exponent are taken in binary and used as certain parts of the fake residue. In case you're wondering why hex is used here for the last 64 bits instead of binary, it's because hex can use a fourth the space that binary does to show the same thing, while still showing a close connection to the binary digits. 

20080918, 00:31  #6  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
The subsection "Divisionremainder in source base" under "Converting from other bases" gives an algorithm that is correct as far as I can tell, but no explicitlyworkedout example (tsk, tsk). Then, in the next subsection, "Addition and multiplication" under "Converting from other bases", is, at last, an _explanatory_ conversion of hexadecimal B3AD to decimal 45997. Hard to find, under a misleading subheading, and no demonstration of decimaltohexadecimal conversion!    Here may be a better explanation: "How to convert between decimal and hexadecimal numbers" at http://www.ehow.com/how_2264926_conv...lnumbers.html (Ignore the injoke "Oct 31 = Dec 25".) Last fiddled with by cheesehead on 20080918 at 00:47 

20080918, 01:13  #7  
"Kyle"
Feb 2005
Somewhere near M52..
3×5×61 Posts 
Alright, then I understand how to get the decimal representation of the hexadecimal residue. Now, is that decimal remainder the remainder of the modulo arithmatic in the Lucas Lehmer test?
Quote:


20080918, 01:24  #8 
May 2008
2107_{8} Posts 
It is the last 64 bits of the remainder.
So it is the remainder modulo 2^64. 
20080918, 01:26  #9  
May 2008
2107_{8} Posts 
Quote:
Last fiddled with by jrk on 20080918 at 01:27 

20080918, 02:52  #10  
"Kyle"
Feb 2005
Somewhere near M52..
3×5×61 Posts 
Quote:
Quote:


20080918, 09:25  #11  
Einyen
Dec 2003
Denmark
2×7×223 Posts 
Here is a more detailed explaination of the fake residue algorithm: residue.txt
Quote:
0x1248, 0x36C8, 0x5A48, 0x7EC8, 0x9248, 0xB6C8, 0xDA48, 0xFEC8 Looking at the fake residues used there are many common sequences which make them look "suspicious", like 7EC801, C8012, 8013 and so on. real M39: 13466917 0x5A4800136C936D__ real M40: 20996011 0xB6C80125A48000__ real M41: 24036583 0x7EC80125B6DB7E__ real M42: 25964951 0x7EC80136C8136C__ real M43: 30402457 0x92480137EC937F__ fake M44:29225803 0xB6C80136DB7FED__ fake M45:20314069 0x5A480124936DA5__ fake M45:43021553 0x1248125A492480__ fake M46:32428427 0xB6C80137FEDB7E__ Last fiddled with by ATH on 20080918 at 09:28 

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