mersenneforum.org Large runs of Mersenne composites
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 2017-06-27, 09:01 #1 manasi   Jun 2017 13 Posts 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 }
 2017-06-29, 10:08 #2 manasi   Jun 2017 D16 Posts 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
2017-06-29, 12:38   #3
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

8,369 Posts

Quote:
 Originally Posted by manasi 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.

2017-06-29, 13:05   #4
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

22×2,281 Posts

Quote:
 Originally Posted by manasi 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.

For example, you can start by reading this.

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