Inhaltsverzeichnis

Development of
Algorithmic Constructions

06:18:21
DeutschEnglish
20.Apr 2024

Search for quadratic irreducible polynominals f(x)=ax^2+bx+c

All combinations for a, b, c are calculated with the following limitations:
a=1, 2, 3, 4 for other values there were no results found.
-400 < b < 400 for other values there were no results found.
c=+/-1, +/-(first 46 primes) for other values there were no results found.

The sequence start for x=0 and abs(f(0)) should be a prime or equal 1.

Only polynominals are choosen which are suitable to generate an infinity of primes
by use of a certain algorithm which is described later for each polynominal.
The algorithm found the primes p=f(x) and p|f(x) in a not arising sort order.

f(x)=ax^2+bx+c

a=1
a=2
a=3
a=4

a=1,2,3,4

Discriminant

all discriminants

all positiv discriminants
all negativ discriminants

Singularity

all singularities

no singularity
only one singularity
only two singularities

Distance

all distances

only natural distances
only *.5 distances