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Old 2012-05-28, 12:00   #1
devarajkandadai
 
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Default 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.
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Old 2012-05-28, 12:24   #2
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Quote:
Originally Posted by devarajkandadai View Post
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.
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Old 2012-05-28, 12:33   #3
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Quote:
Originally Posted by R. Gerbicz View Post
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
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Old 2012-05-28, 15:53   #4
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Quote:
Originally Posted by devarajkandadai View Post
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.
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Old 2012-05-28, 17:03   #5
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Originally Posted by ATH View Post
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...
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Old 2012-05-28, 17:23   #6
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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.
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Old 2012-05-28, 20:45   #7
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Quote:
Originally Posted by kar_bon View Post
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
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Old 2012-05-28, 23:04   #8
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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
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Old 2012-05-28, 23:35   #9
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Quote:
Originally Posted by devarajkandadai View Post
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.
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Old 2012-05-29, 02:46   #10
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Quote:
Originally Posted by kar_bon View Post
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
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Old 2012-05-29, 03:02   #11
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Quote:
Originally Posted by Puzzle-Peter View Post
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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