20120528, 12:00  #1 
May 2004
2^{2}×79 Posts 
Mersenne prime factors of very large numbers
Let N = 2^p + 29 where p is the 20 digit prime exponent in the Number Theory video ( go to You Tube and search for A.K. Devaraj ).
Known Mersenne prime factor of N : 31 known Non Mersenneprime factors of N: 7, 127, and a few more to be listed. Q: If any member can identify a few more Mersenne prime factors I would be happy. 
20120528, 12:24  #2  
"Robert Gerbicz"
Oct 2005
Hungary
5×17^{2} Posts 
Quote:


20120528, 12:33  #3 
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} Posts 
97600641752017987211 is what I got from it but I zoomed in to like 200% . of course PARI said it's not a prime exponent and 7 and 127 are both mersenne primes so they already have 3 mersenne prime factors but no non mersenne prime factors.
Last fiddled with by science_man_88 on 20120528 at 12:37 
20120528, 15:53  #4  
Einyen
Dec 2003
Denmark
3,037 Posts 
Quote:
Factors of 2^p + 29: 31 and 887 and 937 ( no others below 10^{10} ) 7 and 127 are not factors of 2^p+29. 

20120528, 17:03  #5 
Jun 2009
683 Posts 

20120528, 17:23  #6 
Mar 2006
Germany
2·1,439 Posts 
p=97500641752017987211 is prime.
31  2^p+29 for p==1 mod 10. 101  2^p+29 for p==41 mod 100. 61  2^p+29 for p==5 mod 60. 
20120528, 20:45  #7 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
mod 31 so it actually doesn't happen at p=1 mod 5 ?
Last fiddled with by science_man_88 on 20120528 at 20:46 
20120528, 23:04  #8 
"Forget I exist"
Jul 2009
Dumbassville
20C0_{16} Posts 
sorry doesn't it actually doh forgot over half aren't prime.
Last fiddled with by science_man_88 on 20120528 at 23:05 
20120528, 23:35  #9  
(loop (#_fork))
Feb 2006
Cambridge, England
2×3,191 Posts 
Quote:
N almost surely does not have any other Mersenne prime factors. N doesn't have any prime factors less than 10^8 other than 31, and it's not divisible by 2^q1 for Mersenne exponents q up to 44497. Please explain where the number came from. 

20120529, 02:46  #10  
Einyen
Dec 2003
Denmark
101111011101_{2} Posts 
Quote:
Looking at the number again and zooming in it actually looks more like: p=97600541752017987211 which is also prime. In that case factors of 2^{p}+29 up to 10^{10} are: 31 and 1303 and 27737. Last fiddled with by ATH on 20120529 at 02:47 

20120529, 03:02  #11 
May 2004
474_{8} Posts 

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