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^{2}·5·373 Posts 

20101026, 12:29  #3 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 

20101026, 13:15  #4  
Aug 2006
3×1,993 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
2^{2}·3·7·139 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
16444_{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
Manchester, UK
1362_{10} 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
Manchester, UK
10101010010_{2} Posts 
Quote:
http://2721.hddkillers.com/3^n2^n/ 

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