62 lines
1.7 KiB
Plaintext
62 lines
1.7 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Euler Problem 27\n",
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"\n",
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"Euler discovered the remarkable quadratic formula:\n",
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"\n",
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"$n^2 + n + 41$\n",
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"\n",
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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 $n=41,41^2+41+41$ is clearly divisible by 41.\n",
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"\n",
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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 $−126479$.\n",
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"\n",
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"Considering quadratics of the form:\n",
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"\n",
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"$n^2 + an +b$, where |a|<1000 and |b|≤1000\n",
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"\n",
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"where |n| is the modulus/absolute value of n e.g. |11|=11 and |−4|=4.\n",
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"\n",
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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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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"completion_date": "Mon, 21 Aug 2017, 21:11",
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.4"
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},
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"tags": [
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"quadratic primes"
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]
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},
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}
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