20101026, 11:04  #1 
Sep 2009
2^{2}×3^{2} Posts 
mersenne prime as a factor of another number
I wonder if there are a special class of number which have mersenne primes as factors?
Thanx... 
20101026, 11:50  #2 
Nov 2003
2^{6}·113 Posts 

20101026, 12:29  #3 
"Forget I exist"
Jul 2009
Dumbassville
8,369 Posts 

20101026, 13:15  #4  
Aug 2006
172B_{16} Posts 
Quote:
For the former, that's all subsets of 1 U A056652. For the latter... that's pretty dense, natural density 0.4514311155... if I'm not mistaken. The sequence starts 3,6,7,9,12,14,15,18,21,24,27,28,30,31,... and includes sequences like 2^{2n}  1. 

20101026, 16:41  #5 
Noodles
"Mr. Tuch"
Dec 2007
Chennai, India
3·419 Posts 
23209 is factor of M967
Or do you rather mean that list of Wieferich primes? such as that cases for that of q^{2}  2^{p}1 1093, 3511 For example, please notice that 1093^{2} indeed divides up with that Wagstaff number: (2^{182}+1)/3 Really following up within that way 1093^{2}  M1092 3511^{2}  M3510 of course for ever 
20101027, 19:22  #6  
∂^{2}ω=0
Sep 2002
República de California
9,791 Posts 
Quote:
Initialize x[0] = 4 (other values are also possible, but we'll keep it simple for now) For m := 2^p1 prime, do p2 of the following iterations: x[i] = x[i1]^2  2 Then x[p2] is divisible by m. Simplest case: p=3, m=7, and x[p2] = x[1] = 14, which is divisible by 7. 

20101027, 20:25  #7  
Nov 2003
16100_{8} Posts 
Quote:
question to mean whether there is some a priori interesting set of numbers divisible by Mersenne primes. One can always construct such classes. Perfect numbers are an example of such a constructed class (and are the original reason for the study of M_p). 

20101030, 21:26  #8  
May 2005
Argentina
2×3×31 Posts 
Quote:
Is there a similar primality test for numbers of the form for some prime number ? Thanks. Last fiddled with by Damian on 20101030 at 21:26 

20101031, 19:49  #9  
Oct 2007
London, UK
10100011100_{2} Posts 
Quote:
Code:
2 3 5 17 29 31 53 59 101 277 647 1061 2381 2833 3613 3853 3929 5297 7417 

20101031, 20:55  #11  
Oct 2007
London, UK
1308_{10} Posts 
Quote:
http://2721.hddkillers.com/3^n2^n/ 

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