Riesel number

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a Riesel number is an <a href="/facts/Parity_(mathematics)/7zq2UM4V">odd</a> <a href="/facts/Natural_number/u65og8JE">natural number</a> k for which 
 
 
 
 k
 ×
 
 2
 
 n
 
 
 −
 1
 
 
 {\displaystyle k\times 2^{n}-1}
 
 is <a href="/facts/Composite_number/SPtW9ftC">composite</a> for all natural numbers n (sequence A101036 in the <a href="/facts/On-Line_Encyclopedia_of_Integer_Sequences/yow6cVsU">OEIS</a>). In other words, when k is a Riesel number, all members of the following <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> are composite:

{
          
            
            k
            ×
            
              2
              
                n
              
            
            −
            1
            :
            n
            ∈
            
              N
            
            
          
          }
        
        .
      
    
    {\displaystyle \left\{\,k\times 2^{n}-1:n\in \mathbb {N} \,\right\}.}

If the form is instead 
 
 
 
 k
 ×
 
 2
 
 n
 
 
 +
 1
 
 
 {\displaystyle k\times 2^{n}+1}
 
, then k is a <a href="/facts/Sierpi%C5%84ski_number/3t2DxTql">Sierpiński number</a>.

Riesel number open-in-new

Riesel number