🚀 go-pugleaf

Well , this bible code business came up and I though I'd take a "Crack"
at it.

>From what I can see the concept of takeing equidistant letters means
that you can go around and around.  (i.e for the 3 letter sequence [ABC]
you could take every fifth letter.)

However if you start at the first letter there are only N possible hops
you can make.  Because N+1 distance is just like hopping 1 space.
>From this you might think that you could start anywhere in the Sequence
and then make a sequence with 1 to N space hopes.
That normally gives an N lentgh string as it cycles through all N
letters.  Since there are N letters and N possible hop distances we
would get an N^2 long string from which to search for a word.

But sometimes there's a catch.  If you have say 10 letters.  And you
take every fifth one you only get 2 letters repeating over and over.
This actually happens for all hop distances which contain a prime number
found in N.

So if say 5 if a prime in N then any string which would normally cycle
through and have N different leteters will be divided by that prime and
have only N/5 unique letters.  (If two primes are in the hop distance
then the same holds. N/P1/P2 would be the unique string length.)

So for every prime in N 1/P of the numbers we use as possible hop
distances will be shortened by it's primes in common with N.
That means we shorten out total string by a factor of (1-N/P^2) for a
single prime.

So If god wanted to be really clever.  The Torah would contain a prime
number of letters! (Did they forget the put the title in the string?) 
If N were prime then total possible string to search from would be N^2
which if my information is correct is (304,805)^2 or about 92 billion.

Sadly 5 is an obvious prime factor.  I am not aware of others yet.
So the actual length would be more than (92 *10^10)*(1-4/25)
That still leaves a string of about 78 Billion letters.

BUT Wait.  These are not random any more.  No... They are cycled through
much like numbers on the odometer of your car.  They are recombined in
different ways each time but not randomly.  So that will add a a few
more distinct combinations to the mix than if they were just randomly
picked.   But we could ignore that aspect.

Yet the lack of vowels in the text which means most words are radically
shortened and much more likely to show up. (about 100  to 1000 times
more likely)  But let's ignore that as well.

Also the frequency of letters is a factor if we have a real text sample
and not a random one.  Correct letter frequencies will help  actual
eords to show up more often than random ones.
But let's ignore that.

So even if we ignore the these helping detailes above and even if we use
all 26 letters in english then any 7 letter words would be 1 in 26^7. 
That's a one in 8 billion chance of showing up.  Since we can look for
that word to start at each of the (70 billion -7) locations I'd say we
are likely to find what ever we need there.

I guess the bible really does have somthing for everyone.

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