20170627, 09:01  #1 
Jun 2017
1101_{2} 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_21)^n2 (p_31)^n3…(p_k1)^nk+j)1∶ 2≤j≤n+1 ,l_1,l_2,…,l_n∈Ν, n_2,…,n_k∈Ν } 
20170629, 10:08  #2 
Jun 2017
D_{16} Posts 
I wanted to edit the above post
l_i = max { t_i : [n/ t_i ] } Last fiddled with by manasi on 20170629 at 10:10 
20170629, 12:38  #3  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
Quote:


20170629, 13:05  #4  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3·3,229 Posts 
Quote:
Read first, post later. For example, you can start by reading this. 

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