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Old 2017-06-27, 09:01   #1
manasi
 
Jun 2017

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Default Large runs of Mersenne composites

Hi! I am new to this forum and still clueless about how to use manual testing. I tried to post some observations earlier in manual testing. I am not sure whether this current post is necessary.

For any given n ∈Ν, there exists infinitely many runs of Mersenne composites.

Let {2=p_1,3=p_2,…,p_k} be all the listed primes ≤n.

Then { 2^(n!+j)-1∶ 2≤j≤n } ,

{ 2^(2^l1 3^l2….n^ln+j)-1∶2≤j≤n ,l_1,l_2,…,l_n∈Ν},

{ 2^(2^l1 3^l2….〖pk〗^lk (p_2-1)^n2 (p_3-1)^n3…(p_k-1)^nk+j)-1∶ 2≤j≤n+1 ,l_1,l_2,…,l_n∈Ν, n_2,…,n_k∈Ν }
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Old 2017-06-29, 10:08   #2
manasi
 
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I wanted to edit the above post

l_i = max { t_i : [n/ t_i ] }

Last fiddled with by manasi on 2017-06-29 at 10:10
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Old 2017-06-29, 12:38   #3
science_man_88
 
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Quote:
Originally Posted by manasi View Post
Hi! I am new to this forum and still clueless about how to use manual testing. I tried to post some observations earlier in manual testing. I am not sure whether this current post is necessary.

For any given n ∈Ν, there exists infinitely many runs of Mersenne composites.

Let {2=p_1,3=p_2,…,p_k} be all the listed primes ≤n.

Then { 2^(n!+j)-1∶ 2≤j≤n } ,

{ 2^(2^l1 3^l2….n^ln+j)-1∶2≤j≤n ,l_1,l_2,…,l_n∈Ν},

{ 2^(2^l1 3^l2….〖pk〗^lk (p_2-1)^n2 (p_3-1)^n3…(p_k-1)^nk+j)-1∶ 2≤j≤n+1 ,l_1,l_2,…,l_n∈Ν, n_2,…,n_k∈Ν }
you could just use LaTeX and make this all look nice.
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Old 2017-06-29, 13:05   #4
Batalov
 
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Quote:
Originally Posted by manasi View Post
For any given n ∈Ν, there exists infinitely many runs of Mersenne composites.
Mersenne numbers can only prime for prime indices, so what you are saying is obvious because there are infinitely many runs of composites of length > n.

Read first, post later.
For example, you can start by reading this.
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