Mersenne prime factors of very large numbers

devarajkandadai · 2012-05-28, 12:00

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.

R. Gerbicz · 2012-05-28, 12:24

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.

science_man_88 · 2012-05-28, 12:33

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.

ATH · 2012-05-28, 15:53

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.

Puzzle-Peter · 2012-05-28, 17:03

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...

kar_bon · 2012-05-28, 17:23

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.

science_man_88 · 2012-05-28, 20:45

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 ?

science_man_88 · 2012-05-28, 23:04

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.

fivemack · 2012-05-28, 23:35

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.

ATH · 2012-05-29, 02:46

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 2^p+29 up to 10¹⁰ are: 31 and 1303 and 27737.

devarajkandadai · 2012-05-29, 03:02

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.

2012-05-28, 12:00	#1
devarajkandadai May 2004 2²×79 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 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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2012-05-28, 17:23	#6
kar_bon 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.