In the film The
Mirror has Two Faces, Mathematics professor
Jeff Bridges explains one of the great prime
number mysteries in his first date with
English Literature professor, Barbara Streisand:
The Twin Primes Conjecture. Once again this
film illustrates how mathematician equals
socially inept, unworldly thinker who finds
it impossible to engage with the physical,
in this case sex. As they sit drinking their
aperitif, he explains how he doesn't like
to dance but prefers to watch:
Bridges: "pairs…its
interesting how coupling appears all through
nature…in mathematics…"
Streisand: "You
were telling me something about primes."
Bridges: "Yes,
the Twin Prime Conjecture. It explores pairs
of prime numbers, like 11, 13 or 17,19.
What was discovered was that it often occurred
that primes were separated by…"
Streisand: "…one
number in between."
Bridges: "Exactly,
exactly…did you read my book. This
is really marvellous."
Streisand: "First
date that I feel like I'm winning on a game
show."
Bridges: "Sorry.
It's just so rare that I meet a person that
I can discuss these things with."
Streisand: "This
Twin Prime Conjecture is interesting. What
would happen if you counted passed a million?
Would there still be pairs like that?"
At this point Bridges almost falls off his
chair with excitement:
Bridges: "I
can't believe you thought of that. This
is exactly what has yet to be proven in
the Twin Prime Conjecture."
The Conjecture says that you will always
find clusters of primes where N and N+2
are both prime. The first twin that Streisand
would find beyond a million is the pair
of primes 1,000,037 and 1,000,039. In our
numbers around 10,000,000 we have two twin
pairs 9,999,929 and 9,999,931 and then again
at 9,999,971 and 9,999,973. (Note that N
and N+1 cannot both be prime because at
least one of these numbers is even and divisible
by 2.)
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