From Newsgroup: comp.lang.forth
In article <
cc2168f2a41861f350e75d472385c5ba@www.novabbs.com>,
mhx <
mhx@iae.nl> wrote:
Factoid from Fermat's library:
"Every number of the form ABABAB (basis 10) is divisible by 37."
Example: 111111 37 /mod . . is 3003 0, 13691369 37 /mod . . is
370037 0.
This is obvious once you know how it is done, and then you
also see it works for 13, 7, and 3.
Does the approach work for other number bases (yes), and can
it be used to prove primeness of numbers which have
a repeating digit pattern in a certain number base?
Primeness is the absence of dividers. Testing cannot
prove the absence of bugs.
A repeating digit pattern can reveal the presence of
dividers. For instance a pattern repeated n times
where n is not a prime has a divider.
77777777777777 is divisable by 7 (huh)
11111111111111 is divisable by 11 (7 repetitions of 11)
You can convince yourself by doing a long division.
Mersenne primes are in fact a sequence of n 1's in binary, M_n.
I have just proven that for such a prime M_n , n itself
must be prime. The great internet mersenne prime search
would not be interesting, if you can tell for p whether
M_p would be prime.
So no. Not a silver bullet.
-marcel
Groetjes Albert
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