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pe0027.mathematica
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pe0027.mathematica
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Project Euler Problem 27
Quadratic primes
(*
Euler discovered the remarkable quadratic formula:
n2+n+41n2+n+41
It turns out that the formula will produce 40 primes for the consecutive integer values 0≤n≤390≤n≤39. However, when n=40,402+40+41=40(40+1)+41n=40,402+40+41=40(40+1)+41 is divisible by 41, and certainly when n=41,412+41+41n=41,412+41+41 is clearly divisible by 41.
The incredible formula n2−79n+1601n2−79n+1601 was discovered, which produces 80 primes for the consecutive values 0≤n≤790≤n≤79. The product of the coefficients, −79 and 1601, is −126479.
Considering quadratics of the form:
n2+an+bn2+an+b, where |a|<1000|a|<1000 and |b|≤1000|b|≤1000
where |n||n| is the modulus/absolute value of nn
e.g. |11|=11|11|=11 and |−4|=4|−4|=4
Find the product of the coefficients, aa and bb, for the quadratic expression that produces the maximum number of primes for consecutive values of nn, starting with n=0n=0.
*)
Times @@ Flatten@Values@Last@SortBy[((a = #[[1]]; b = #[[2]];
n = 0; boolQ = True;
While[boolQ == True,
boolQ = PrimeQ[eq];
n++]; <|(n - 1) -> {a, b}|>) & /@
Tuples[Range[-1000, 1000], {2}]), Keys]