euler's polynomial proof

thats the proposition made by Euler that P(n)=n^2+n+41 can generate all primes and it was suddenly proven false by using a counter example, isnt there any way he can be proven to be false?

...is a polynomial inequality in 26 variables, and the set of prime numbers is identical to the set of positive values taken on by this polynomial inequality as the variables a, b, …, z range over the nonnegative integers.

A general theorem of Matiyasevich says that if a set is defined by a system of Diophantine equations, it can also be defined by a system of Diophantine equations in only 9 variables. Hence, there is a prime-generating polynomial as above with only 10 variables. However, its degree is large (in the order of 10^45). On the other hand, there also exists such a set of equations of degree only 4, but in 58 variables (Jones 1982).

It is possible with polynomials in more variables, as the same wiki article points out:

See also http://en.wikipedia.org/wiki/Formula_for_primes Euler's formula for primes as posted in this thread was once widely thought to generate primes for any integer n

but the same polynominal would generate composites also with large enough variables. Think how easy it would be to exceed the largest prime otherwise

That no polynominal can generate all primes is easily shown using the reference given already http://en.wikipedia.org/wiki/Formula_for_primes

Let P(1) = a prime S. [tex] Then P(1+kS) \equiv P(1) \equiv 0 Mod S.[/tex]

Was that in response to my post? I was incredulous about the claim that "once widely thought to generate primes for any integer n". It's obvious that no nonconstant polynomial can produce primes for all n, so it's hard for me to believe that this was ever believed. But it could be true, so I was looking for ramsey2879 or someone else to comment on that.