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Old 2019-01-12, 17:43   #271
JeppeSN
 
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"Jeppe"
Jan 2016
Denmark

25·5 Posts
Cool

Quote:
Originally Posted by GP2 View Post
Never mind larger examples, there's no smaller example.

The only other p=2^k+k which is a Mersenne prime exponent is k=1, p=3, but then W(k) = 1.
Not sure I know what you mean. With k=1 you are describing the smaller example. It gives \(2^k+k = 3\) and \(2^k=2\) and the prime (seven) is \[M(3)=2^3-1=2\cdot 2^2 - 1=W(2)\]
The other example k=9 written the same way, since \(2^k+k = 521\) and \(2^k=512\), is \[M(521)=2^{521}-1=512\cdot 2^{512} - 1=W(512)\]

For the fun of it, we can merge the lists of Mersennes and Woodalls like this:

Code:
   M(2)
   M(3) = W(2)
          W(3)
   M(5)
   M(7)
          W(6)
  M(13)
  M(17)
  M(19)
  M(31)
          W(30)
  M(61)
          W(75)
          W(81)
  M(89)
 M(107)
          W(115)
 M(127)
          W(123)
          W(249)
          W(362)
          W(384)
          W(462)
 M(521) = W(512)
 M(607)
          W(751)
          W(822)
M(1279)
M(2203)
M(2281)
M(3217)
M(4253)
M(4423)
          W(5312)
      .   .
      .   .
      .   .

Last fiddled with by JeppeSN on 2019-01-12 at 18:42 Reason: adding W(512) for comparison
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