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Old 2005-12-28, 15:49   #254
Jean Penné
 
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May 2004
FRANCE

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Default Mersennes can not be part of Sophie-Germain pairs

The only exception is the pair 3 = M(2), 7 = M(3)

For all odd exponents p > 3 :

1) 2*M(p) + 1 = 2^(p+1) - 2 + 1 = M(p+1) cannot be prime because p+1 is even. So, M(p) cannot be Sophie-Germain(P).

2) (M(p) - 1)/2 = (2^p - 2)/2 = 2^(p-1) - 1 = M(p-1) cannot be prime because p-1 is even. So, M(p) cannot be Sophie-Germain(2*P+1).

3) For p>2, M(p) + 2 = 2^p + 1 is always multiple of 3, so M(p) cannot be the smallest number of a Twin pair...

For M(p) - 2 = 2^p - 3, I cannot conclude, so perhaps an M(p) can be the biggest of a Twin pair ?

Quote:
Originally Posted by Citrix
Has any one looked at, if mersenne numbers are a Sophie Germain pair etc. I did some work some time back.(1 number with no factor.) Has anyone else done such work? Does anyone want to do the latest prime?

eg. 2*p+1 and 2*p-1 where p is a mersenne primes


M(p) Smallest factor for 2*M(p)-1.

2 prime
3 prime
5 prime
7 11*23
13 prime
17 11*23831
19 prime
31 9241*464773
61 37
89 1823
107 11
127 11
521 193
607 11
1279 98807
2203 47
2281 131
3217 11
4253 23
4423 313

9689 289935200473
9941 419303
11213 Trial factor to 2^32; 20@b1=11000;50@b1=50000;composite by Base 3-PRP.
19937 11
21701 22313687645759
23209 37
44497 11
86243 6553
110503 313
132049 2348788960811
216091 23
756839 757
859433 193
1257787 11
1398269 96997
2976221 1451
3021377 11
6972593 103869349
13466917 11
20996011 86183
24036583 59
25964951 76382783
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Old 2005-12-28, 16:19   #255
Prime95
P90 years forever!
 
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Aug 2002
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Quote:
Originally Posted by Kosmaj
I think you mean this. I'll be interested to help such a search.
That is what I meant. What is needed is someone to organize the search. That is, contact Brent and Zimmermann and make sure they aren't already working on it. Get their recommendations and experiences in using their sieve and test software. Get their expected CPU time required. Put up a web page to hand out software and ranges and collect results.
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Old 2005-12-28, 20:20   #256
Citrix
 
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Jun 2003

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What are 2*p-1 kind of primes called? I think there is a special name to them? Does anyone know? Any analysis on this form?

What about 2*p^2-1? where p is a mersenne prime?

@ Jean, Thanks for your explanation.

Citrix


Quote:
Originally Posted by Jean Penné
The only exception is the pair 3 = M(2), 7 = M(3)

For all odd exponents p > 3 :

1) 2*M(p) + 1 = 2^(p+1) - 2 + 1 = M(p+1) cannot be prime because p+1 is even. So, M(p) cannot be Sophie-Germain(P).

2) (M(p) - 1)/2 = (2^p - 2)/2 = 2^(p-1) - 1 = M(p-1) cannot be prime because p-1 is even. So, M(p) cannot be Sophie-Germain(2*P+1).

3) For p>2, M(p) + 2 = 2^p + 1 is always multiple of 3, so M(p) cannot be the smallest number of a Twin pair...

For M(p) - 2 = 2^p - 3, I cannot conclude, so perhaps an M(p) can be the biggest of a Twin pair ?
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Old 2005-12-29, 00:04   #257
Xyzzy
 
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Aug 2002

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Quote:
Originally Posted by Prime95
What is needed is someone to organize the search. That is, contact Brent and Zimmermann and make sure they aren't already working on it. Get their recommendations and experiences in using their sieve and test software. Get their expected CPU time required. Put up a web page to hand out software and ranges and collect results.
We could just do it as a sub forum under "Other Projects". I know nothing about the math but I'd be willing to help with the admin side.
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Old 2005-12-30, 03:14   #258
jinydu
 
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Dec 2003
Hopefully Near M48

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The full official press release is up:

http://www.mersenne.org/30402457.htm
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Old 2005-12-30, 16:31   #259
Jeff Gilchrist
 
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Jun 2003
Ottawa, Canada

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I'm now 94% complete with the verification and it should be complete in about 16 hours from now.
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Old 2005-12-31, 09:01   #260
tywebb
 
Dec 2005

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alright. time's up. the 16 hours are over.

so is it finished?

is it doubly verified now?
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Old 2005-12-31, 12:24   #261
Jeff Gilchrist
 
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Jun 2003
Ottawa, Canada

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Its all good! I found this waiting this morning:

[Sat Dec 31 02:29:42 2005]
UID: /20554, M30402457 is prime! G29: 00000000,0
NEW MERSENNE PRIME DISCOVERED !!!!
PLEASE, send email to woltman@alum.mit.edu AND
gbv_at_oxixares.com with the file "s30402457_last" attached.
(You can find it in your working directory)
Terminated all the queued job in file: glucas.que.


Second verification complete, just in time for end of 2005.

Last fiddled with by Prime95 on 2005-12-31 at 16:07
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Old 2005-12-31, 12:32   #262
tywebb
 
Dec 2005

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holy tethered cow indeed!

it's official!

congratulations!
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Old 2005-12-31, 13:38   #263
Numbers
 
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Jun 2005
Near Beetlegeuse

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Absolutely marvellous.

Break out the bubbly!
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Old 2005-12-31, 14:33   #264
T.Rex
 
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Feb 2004
France

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Congratulations, Jeff !
The full verification of M43 has been done entirely in 2005 !
So we have 365 days for finding M44 ! (I guess the GIMPS will find it before 2007 !)
Tony
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