Project Euler Solutions
Functions
python.p0027 Namespace Reference

Functions

def quadratic
 
def primes_and_negatives
 
def main ()
 

Detailed Description

Project Euler Problem 27

Another good problem for code golf

Problem:Euler discovered the remarkable quadratic formula:

n**2+n+41

It turns out that the formula will produce 40 primes for the consecutive
integer values 0≤n≤39. However, when n=40,40**2+40+41=40(40+1)+41 is divisible
by 41, and certainly when n=41,41**2+41+41 is clearly divisible by 41.

The incredible formula n**2−79n+1601 was discovered, which produces 80 primes
for the consecutive values 0≤n≤79. The product of the coefficients, −79 and
1601, is −126479.

Considering quadratics of the form:

n**2+an+b

, where |a|<1000 and |b|≤1000

where |n| is the modulus/absolute value of n, e.g. |11|=11 and |−4|=4

Find the product of the coefficients, a and b, for the quadratic expression
that produces the maximum number of primes for consecutive values of n,
starting with n=0.

Function Documentation

def python.p0027.main (   int)

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def python.p0027.primes_and_negatives (   stop)

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def python.p0027.quadratic (   n)