Mersenne Prime Sequence

Stan · 2012-01-20, 19:37

Could someone please check the attached theorem for errors and post a reply for the location of any errors?Mersenne Primes.pdf

ccorn · 2012-01-20, 20:10

Quote:

Originally Posted by Stan

Could someone please check the attached theorem for errors and post a reply for the location of any errors?Attachment 7579

See here and here.

Stan · 2012-01-20, 20:57

Quote:

Originally Posted by ccorn

See here and here.

ccorn quotes "5*phi(5) | phi(33) but 25 does not divide 33", but my statement includes that the prime 5 has to divide (33 - 1) and it does not.

ccorn · 2012-01-20, 21:15

Quote:

Originally Posted by Stan

ccorn quotes "5*phi(5) | phi(33) but 25 does not divide 33", but my statement includes that the prime 5 has to divide (33 - 1) and it does not.

The second " $\Rightarrow$ " in the fifth line from the bottom and the following " $\Rightarrow$ " aren't. (non sequitur, so to say.)
I expect that you will notice the gaps (if you have not done so already) when you try to improve the written reasoning at those points.

Batalov · 2012-01-21, 03:20

Stan,

Could you please explain how your proof path would differ for a similar sequence:
n₀ = 2^5-1 (prime)
n₁ = 2^n₀-1 (prime)
n₂ = 2^n₁-1 (composite, has known factors)

What is the specific reason that we wouldn't be able to plug it in the same proof and demonstrate that n₂ is actually prime?

Stan · 2012-01-21, 12:28

Quote:

Originally Posted by Batalov

Stan,

Could you please explain how your proof path would differ for a similar sequence:
n₀ = 2^5-1 (prime)
n₁ = 2^n₀-1 (prime)
n₂ = 2^n₁-1 (composite, has known factors)

What is the specific reason that we wouldn't be able to plug it in the same proof and demonstrate that n₂ is actually prime?

2^5-1 = 1+2.3.5 and phi(2^5-1) = 2.3.5
phi(2^5-1) does not divide phi(2^n₀-1), therefore no sequence.
My proof relies on the chain:
phi(2^n₀-1) | phi(2^n₁-1) | phi(2^n₂-1) etc.

Stan · 2012-01-21, 21:36

I believe the proof of my theorem to be now complete but I still need it checking. Any comments would be appreciated.Mersenne Primes.pdf
The attached PDF file has been updated.

Batalov · 2012-01-22, 07:50

n₀ = 19 (prime)
n₁ = 2^n₀-1 (prime)
n₂ = 2^n₁-1 (?composite?)

ccorn · 2012-01-22, 12:05

Quote:

Originally Posted by Stan

I believe the proof of my theorem to be now complete but I still need it checking. Any comments would be appreciated.Attachment 7581
The attached PDF file has been updated.

There is still no attempt to thoroughly derive the two alleged non sequiturs. Try to actually prove those points. This will turn out to be insightful, whatever the outcome.

ccorn · 2012-01-22, 15:07

Quote:

Originally Posted by Stan

ccorn quotes "5*phi(5) | phi(33) but 25 does not divide 33", but my statement includes that the prime 5 has to divide (33 - 1) and it does not.

Well then: 5*phi(5) | phi(66) and 5 | (66-1), but 25 does not divide 66.

Stan · 2012-01-23, 19:37

Quote:

Originally Posted by Stan

2^5-1 = 1+2.3.5 and phi(2^5-1) = 2.3.5
phi(2^5-1) does not divide phi(2^n₀-1), therefore no sequence.
My proof relies on the chain:
phi(2^n₀-1) | phi(2^n₁-1) | phi(2^n₂-1) etc.

.

2012-01-20, 19:37	#1
Stan Dec 2011 2²×3² Posts	Mersenne Prime Sequence Could someone please check the attached theorem for errors and post a reply for the location of any errors?Mersenne Primes.pdf

2012-01-21, 03:20	#5
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 7×23×61 Posts	Stan, Could you please explain how your proof path would differ for a similar sequence: n₀ = 2^5-1 (prime) n₁ = 2^n₀-1 (prime) n₂ = 2^n₁-1 (composite, has known factors) What is the specific reason that we wouldn't be able to plug it in the same proof and demonstrate that n₂ is actually prime? Last fiddled with by Batalov on 2012-01-21 at 03:27 Reason: a better sequence

2012-01-21, 21:36	#7
Stan Dec 2011 2²×3² Posts	Mersenne Primes I believe the proof of my theorem to be now complete but I still need it checking. Any comments would be appreciated.Mersenne Primes.pdf The attached PDF file has been updated. Last fiddled with by Stan on 2012-01-21 at 21:38 Reason: Update of PDF file

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2012-01-22, 07:50	#8
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 7×23×61 Posts	n₀ = 19 (prime) n₁ = 2^n₀-1 (prime) n₂ = 2^n₁-1 (?composite?)