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 2012-05-28, 12:00 #1 devarajkandadai     May 2004 31610 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 Mersenne-prime 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.
2012-05-28, 12:24   #2
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

64B16 Posts

Quote:
 Originally Posted by devarajkandadai 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 Mersenne-prime 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.
What would be the effort to give the exponent? On that super low quality video it is hard to recognize all digits.

2012-05-28, 12:33   #3
science_man_88

"Forget I exist"
Jul 2009
Dartmouth NS

841810 Posts

Quote:
 Originally Posted by R. Gerbicz What would be the effort to give the exponent? On that super low quality video it is hard to recognize all digits.
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 2012-05-28 at 12:37

2012-05-28, 15:53   #4
ATH
Einyen

Dec 2003
Denmark

2·17·101 Posts

Quote:
 Originally Posted by devarajkandadai 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 Mersenne-prime 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.
Your exponent p=97600641752017987211 is not prime.

Factors of 2^p + 29: 31 and 887 and 937 ( no others below 1010 )

7 and 127 are not factors of 2^p+29.

2012-05-28, 17:03   #5
Puzzle-Peter

Jun 2009

22·52·7 Posts

Quote:
 Originally Posted by ATH Your exponent p=97600641752017987211 is not prime.
And I thought I had forgotten how to read. I was not 100% sure with some digits but whatever I tried, the exponent was never prime...

 2012-05-28, 17:23 #6 kar_bon     Mar 2006 Germany BB516 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.
2012-05-28, 20:45   #7
science_man_88

"Forget I exist"
Jul 2009
Dartmouth NS

2·3·23·61 Posts

Quote:
 Originally Posted by kar_bon p=97500641752017987211 is prime. 31 | 2^p+29 for p==1 mod 10.
$63\equiv 1$ mod 31 so it actually doesn't happen at p=1 mod 5 ?

Last fiddled with by science_man_88 on 2012-05-28 at 20:46

2012-05-28, 23:04   #8
science_man_88

"Forget I exist"
Jul 2009
Dartmouth NS

2·3·23·61 Posts

Quote:
 Originally Posted by science_man_88 $63\equiv 1$ mod 31 so it actually doesn't happen at p=1 mod 5 ?
sorry doesn't it actually doh forgot over half aren't prime.

Last fiddled with by science_man_88 on 2012-05-28 at 23:05

2012-05-28, 23:35   #9
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

2·7·461 Posts

Quote:
 Originally Posted by devarajkandadai 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 Mersenne-prime 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.
You mean 'Mersenne primes known not to divide N' rather than 'non Mersenne-prime factors of N'.

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^q-1 for Mersenne exponents q up to 44497.

Please explain where the number came from.

2012-05-29, 02:46   #10
ATH
Einyen

Dec 2003
Denmark

1101011010102 Posts

Quote:
 Originally Posted by kar_bon 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.

Looking at the number again and zooming in it actually looks more like:

p=97600541752017987211 which is also prime.

In that case factors of 2p+29 up to 1010 are: 31 and 1303 and 27737.

Last fiddled with by ATH on 2012-05-29 at 02:47

2012-05-29, 03:02   #11
devarajkandadai

May 2004

22×79 Posts

Quote:
 Originally Posted by Puzzle-Peter And I thought I had forgotten how to read. I was not 100% sure with some digits but whatever I tried, the exponent was never prime...
Pari says p is prime.

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