6 digit numbers and the mersenne numbers

[henryzz]

http://www.mersenneforum.org/showthread.php?t=2038
i just found this and thought people might like to try it with the latest mersenne primes
how did people do it then

[TimSorbet]

Originally Posted by henryzz

http://www.mersenneforum.org/showthread.php?t=2038
i just found this and thought people might like to try it with the latest mersenne primes
how did people do it then

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.

With the numbers exchanged with the newest, that means...

There are about 9.81 million six digit sequences in M44. For any particular six digit sequence, we would expect to find it, on average, 9.81 times. From the Poisson approximation, the probabilty of finding that particular sequence zero times is exp(-9.81) = 5.49E-5. 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*5.49E-5 = 54.9. With 54.9 expected, it's unlikely the observed number is really zero.

Someone would have to run a script to see exactly, but I think it's quite unlikely.

[Xyzzy]

http://www.mersenneforum.org/showthread.php?t=5414