Problem 28

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-Euler discovered the remarkable quadratic formula:
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-n^2+n+41
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-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+4 is clearly divisible by 41.
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-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.
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-Considering quadratics of the form:
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-n^2+an+b, where |a|<1000 and |b|≤1000
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-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.

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+Upper-right: (2n-1)²
+Upper-left : (2n-1)² - (2n-2)
+Lower-left : (2n-1)² - 2(2n-2)
+Lower-right: (2n-1)² - 3(2n-2)
+
+Total (nth spiral): 4(2n-1)² - 6(2n-2)
+Spirals: ceiling(1001/2) = 501
+Sum_{n=2}^{n=501} 16n²-28n+16 = 669 171 000
+
+Answer = 669171001