027.cpp File Reference

Find a quadratic formula that produces the maximum number of primes for consecutive values of n. More...

#include <iostream>

Go to the source code of this file.

Classes
class	prime_table
Functions
unsigned	test (prime_table &prime, int a, int b)
int	main (int argc, char **argv)
Variables
const unsigned	MAX = 1000000

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Detailed Description

Find a quadratic formula that produces the maximum number of primes for consecutive values of n.

Euler published the remarkable quadratic formula: n + n + 41 It turns out that the formula will produce 40 primes for the consecutive values n = 0 to 39. However, when n = 40, 402 + 40 + 41 = 40(40 + 1) + 41 is divisible by 41, and certainly when n = 41, 41 + 41 + 41 is clearly divisible by 41. Using computers, the incredible formula n 79n + 1601 was discovered, which produces 80 primes for the consecutive values n = 0 to 79. The product of the coefficients, 79 and 1601, is 126479. Considering quadratics of the form:

n + an + b, where |a| 1000 and |b| 1000 where |n| is the modulus/absolute value of ne.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.

Definition in file 027.cpp.