Thread: Lucky 13 (M51 related) View Single Post 2019-01-12, 17:43   #271
JeppeSN

"Jeppe"
Jan 2016
Denmark

25·5 Posts Quote:
 Originally Posted by GP2 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  