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• Hi! Maybe Kaveh could use a Monte Carlo-type test - i.e. pick a fixed number of randomly chosen k s to test and look whether the respective difference exists.
Message 1 of 4 , Nov 12, 2006
Hi!

Maybe Kaveh could use a Monte Carlo-type test - i.e. pick a fixed number of
randomly chosen k's to test and look
whether the respective difference exists. This can be done in O( min(m,n) *
iterationCount)
[assuming you can check in O(1) whether a given number belongs to a set].

Furthermore if there are at least two solutions to a given k, return false.

Another simple tests that may speed up the process is to check first whether
min_element(A) < max_element(B)
If this holds return false, since one can construct a negative number thus
missing at least one number from [0,mn-1].
Runtime: O(max(m,n))

I have constructed some covering sets - there aren't that many (if you bound
the members of the set to be in [0,mn-1]!).
So unless explicitly constructed it is very unlikely that two sets have the
desired property
[exponentially small in the number of iterations - if you choose each set
member uniformly at random].

HTH,
Ronny
• Hi, I am new to this group, and I have been doing some work on prime numbers that I feel I should share with others interested in prime numbers. I have
Message 2 of 4 , Nov 13, 2006
Hi,

I am new to this group, and I have been doing some
work on prime numbers that I feel I should share with
others interested in prime numbers.

I have attached a document that supports my claim,

Thanks,

Billy Hamathi.

___________________________________________________________

[Non-text portions of this message have been removed]
• ... Actually there are _exactly_ 0% prime numbers in the naturals... There are about x/log(x) prime numbers less than x - see:
Message 3 of 4 , Nov 14, 2006
>There are approxiametly 29 % prime numbers in the positive integers range

Actually there are _exactly_ 0% prime numbers in the naturals...

There are about x/log(x) prime numbers less than x - see:
http://primes.utm.edu/howmany.shtml

Now the ratio primes/naturals = (x/log(x)) / x = 1/log(x) which converges to
0 as x approaches infinity.

Ronny
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