20051228, 15:49  #254  
May 2004
FRANCE
2·281 Posts 
Mersennes can not be part of SophieGermain 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 SophieGermain(P). 2) (M(p)  1)/2 = (2^p  2)/2 = 2^(p1)  1 = M(p1) cannot be prime because p1 is even. So, M(p) cannot be SophieGermain(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:


20051228, 16:19  #255  
P90 years forever!
Aug 2002
Yeehaw, FL
2×3×1,193 Posts 
Quote:


20051228, 20:20  #256  
Jun 2003
3^{2}·5^{2}·7 Posts 
What are 2*p1 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^21? where p is a mersenne prime? @ Jean, Thanks for your explanation. Citrix Quote:


20051229, 00:04  #257  
"Mike"
Aug 2002
2^{3}×3×5^{2}×13 Posts 
Quote:


20051230, 03:14  #258 
Dec 2003
Hopefully Near M48
2·3·293 Posts 

20051230, 16:31  #259 
Jun 2003
Ottawa, Canada
10010010001_{2} Posts 
I'm now 94% complete with the verification and it should be complete in about 16 hours from now.

20051231, 09:01  #260 
Dec 2005
7 Posts 
alright. time's up. the 16 hours are over.
so is it finished? is it doubly verified now? 
20051231, 12:24  #261 
Jun 2003
Ottawa, Canada
7·167 Posts 
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 20051231 at 16:07 
20051231, 12:32  #262 
Dec 2005
7 Posts 
holy tethered cow indeed!
it's official! congratulations! 
20051231, 13:38  #263 
Jun 2005
Near Beetlegeuse
110000100_{2} Posts 
Absolutely marvellous.
Break out the bubbly! 
20051231, 14:33  #264 
Feb 2004
France
2·457 Posts 
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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