6 digit numbers and the mersene 40

I was just playing around with the find word command and the 40th mersene prime and it appears that every single 6 digit combination is contained within the number itself. I have not tested this for certain, but every single number i have trried showed up in it somewhere. Is it just probability or are all the 999999 combinations actually found in the 40th mersene prime?

[wblipp]

Originally Posted by Sykes1024

I was just playing around with the find word command and the 40th mersene prime and it appears that every single 6 digit combination is contained within the number itself. I have not tested this for certain, but every single number i have trried showed up in it somewhere. Is it just probability or are all the 999999 combinations actually found in the 40th mersene prime?

You would have to check to be sure, but my quick estimation suggests that it is unlikely. I used the Poisson Approximation like this:

There are about 6.32 million six digit sequences in M40. For any particular six digit sequence, we would expect to find it, on average, 6.32 times. From the Poisson approximation, the probabilty of finding that particular sequence zero times is exp(-6.32) = 0.0018. There are 1,000,000 six digit sequences (did you forget 000000?), so the expected number of sequences that do not occur is 1,000,000*0.0018 = 1800. With 1800 expected, it's very unlikely the observed number is really zero.

[axn]

Originally Posted by wblipp

You would have to check to be sure, but my quick estimation suggests that it is unlikely. I used the Poisson Approximation like this:

There are about 6.32 million six digit sequences in M40. For any particular six digit sequence, we would expect to find it, on average, 6.32 times. From the Poisson approximation, the probabilty of finding that particular sequence zero times is exp(-6.32) = 0.0018. There are 1,000,000 six digit sequences (did you forget 000000?), so the expected number of sequences that do not occur is 1,000,000*0.0018 = 1800. With 1800 expected, it's very unlikely the observed number is really zero.

Spot on ! 1765 missing ! See the attachment

[jinydu]

1765 is missing? That means not every 4-digit natural number is present. Using the same computation, that seems highly unlikely. Using the same logic that wblipp applied:

6.32M four-digit numbers
Any particular four-digit number should be found 632 times
Probability of finding a particular sequence 0 times: e^(-632) = 10^(-274.52)
Expected number of such sequences: 10^(-270.5)

[patrik]

axn1 means that there are 1765 6-digit sequences missing.

[wblipp]

Originally Posted by jinydu

1765 is missing?

"1765" is the count of six digit sequences that are missing - within 2% of the estimate. To see which six digit sequences are missing, look at the attachment.

[Maybeso]

jinydu,
It's so late it's early, so I can't tell if you're kidding or not.

Axn1 meant that wblipp had estimated there should be 1800 six digit sequences missing, and the actual number missing was 1765.
Not that "1765" was missing.

Until I've had enough , It's easy to make a of me.

[jinydu]

Oh, I did misunderstand, thought you meant that the sequence "1765" was missing. Never mind.