Re: As Stakes Increase, Prime-Number Theory Moves Closer to Proof

"MrPepper11" <MrPepper11@xxxxxx> writes:

> Wall Street Journal
> April 8, 2005
> As the Stakes Increase, Prime-Number Theory Moves Closer to Proof
> By SHARON BEGLEY

[...]

> This last string is curious because the primes in it all are
> separated by 210. Last spring, two mathematicians proved that there
> exist strings (separated not by 210 but by other intervals) that
> contain an arbitrarily-long run of primes.

Wrong. Such "strings" do not exist. First you have to pick the
desired length of the run, _then_ you can be sure to find a string,
not the other way round.

> That is, you can find a number, keep adding another number to it and
> get a run of primes as long as you like.

Quantifier dyslexia at its best. Mückenheim seems to have good
connections.

> An early discovery about the primes was that there is an infinite
> number of them, sprinkled "like indivisible stars scattered without
> end throughout a boundless numerical universe," Prof. Rockmore
> writes. But how infinite? Although most of us think of infinity as
> one big number, some infinities are bigger than others. The number
> of numbers divisible by 2 is infinite, and so is the number
> divisible by 9. But the first infinity is bigger. There also is an
> infinite number of squares (4, 9, 16 ...) and cubes (8, 27, 64 ...),
> but more primes than either.

More and more Mückenheim.

> In 1859, Riemann got an inkling of how the primes thin out as you go
> along the number line. The number of primes around a particular
> number, he knew, equals the reciprocal of (that is, 1 divided by)
> the natural logarithm of that number.

Wow. This sounds like heavy theory straight from JSH's mouth.

> The natural logarithm of a number equals how many times you have to
> multiply a number called e (about 2.718) by itself to get that
> number. At around one million, whose logarithm is about 13,

More like 14. And so on.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.

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