Re: relation between twin primes and Sophie Germain primes

"Antony Clements" <antony.clements@xxxxxxxxxxxxxxx> (07-04-25 20:49:34):

We expect programmers to have at least elementary knowledge about
number theory and group theory.

programmers are just that, programmers, some have greater knowledge
than others admittedly, a programmer takes an algorithm and produces
working code from it. the college where i did my software dev course
(and apparently was following suite of many other colleges around the
world) was at the time i finished, making the distinction between an
analyst and a programmer. an analyst examines a problem and produces
the algorithm, the programmer takes the algorithm and turns it into
working code. so given the current trends, number theory and group
theory would need to be known by the analyst, not the programmer. now
if one is an analyst/programmer, that is a different can of beans
entirely. if number theory and group theory was taught, it would have
been in the optional discrete math classes which was largely take home
and do at your own pace. i finished the first semester course work for
the discrete math module in about 3 weeks and then didnt bother with
the assignment or sitting the exam before i left the class.

Like ink said, this is not correct. Mathematicians need to be
programmers, so they can implement and test algorithms. Programmers
need to have certain mathematical skills to even understand an algorithm
in the first place. You can't implement an algorithm you don't
understand.

Back in the 80's and 90's, where the whole art of programming was to
optimize that critical inner loop in assembly, your statement would
hold. Today the story is completely different. The border between
programmer and mathematician will more and more collapse.


That would include 1 as a prime. My favourite definition of prime
numbers is that a prime number is a natural number with exactly four
distinct integer factors.

wouldn't that exclude 2, 3 and 7 as well?

Integer factors of 2: { -2, -1, 1, 2 }
Integer factors of 3: { -3, -1, 1, 3 }
Integer factors of 7: { -7, -1, 1, 7 }

Exactly four in all three cases. ;)


No. There is an infinite number of prime numbers. Since we have a
proof for that fact, no "change in science" (however you define
that) and no new tool could change that.

this is true for some things but not all things. by 'change in
science' i define as mathematics/physics/chemistry and any other
science where there is a significant mathematical basis. this excludes
things like psychology and biology, unless of course one is refering
to biometrics or biochemistry.

Sciences do not change. They get extended. New hypotheses appear,
deprecated or invalidated hypotheses disappear. But the science itself
remains the same.

Now there may be discoveries, which invalidate an earlier hypothesis.
But unless our thinking and understanding of the environment and the
universe is completely flawed, even in test-based sciences, proven
things will remain valid, no matter what happens. Otherwise our view of
a proof itself would be invalidated, and we would need to go back to the
fundaments of research.

Now mathematics is a science, which is not test-based. It's
proof-based. The difference between mathematics and all other sciences
is that it is well defined and already `complete' in a certain sense.
For all discoveries you can say that it has been that way all the time;
we just didn't specifically know.

In the natural numbers, as we define them, there is no way to make 10 a
prime number, or even non-natural. There is no bijection between the
real numbers and the rational numbers. That's the way it is. We know
that and there is no chance to change that. Changing that would require
a fundamental change in both nature itself and our understanding of her.


Regards,
Ertugrul Söylemez.


--
From the fact that this CGI program has been written in Haskell, it
follows naturally that this CGI program is perfectly secure.
.

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