From 69eb5748a9c01f7e2515329306405b541271f057 Mon Sep 17 00:00:00 2001
From: Jonathan Chan <jonathanhwchan@gmail.com>
Date: Thu, 1 Dec 2016 00:57:25 -0800
Subject: [PATCH] Problem 28

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 27.txt | 13 -------------
 28.txt | 10 ++++++++++
 2 files changed, 10 insertions(+), 13 deletions(-)
 delete mode 100644 27.txt
 create mode 100644 28.txt

diff --git a/27.txt b/27.txt
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-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+4 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
-
-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.
diff --git a/28.txt b/28.txt
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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