From f995791a6f52bc7abe505a26392927a32ebe47a2 Mon Sep 17 00:00:00 2001 From: filifa Date: Sat, 19 Jul 2025 22:55:27 -0400 Subject: [PATCH] reorganize beginning --- notebooks/problem0027.ipynb | 62 ++++++++++++++++++++++++------------- 1 file changed, 41 insertions(+), 21 deletions(-) diff --git a/notebooks/problem0027.ipynb b/notebooks/problem0027.ipynb index e1b6948..e54a2bb 100644 --- a/notebooks/problem0027.ipynb +++ b/notebooks/problem0027.ipynb @@ -7,6 +7,30 @@ "source": [ "# [Quadratic Primes](https://projecteuler.net/problem=27)\n", "\n", + "We can easily write a function to test how many consecutive primes $n^2 + an + b$ generates." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "a9751bc6", + "metadata": {}, + "outputs": [], + "source": [ + "from itertools import count\n", + "\n", + "def consecutive_primes(a, b):\n", + " f = lambda x: x^2 + a*x + b\n", + " for n in count(0):\n", + " if not is_prime(f(n)):\n", + " return n" + ] + }, + { + "cell_type": "markdown", + "id": "ce6a48ba", + "metadata": {}, + "source": [ "Couple of observations to speed up iterating through values of $a$ and $b$:\n", "1. $0^2 + 0a + b = b$ must be prime. Additionally, since $|b| \\leq 1000$, the largest possible value for $b$ is 997.\n", "2. $1^2 + 1a + b = 1 + a + b$ must be prime. Therefore $a = p - b - 1$ for some prime $p$. Furthermore, since $|a| < 1000$, it follows that $-1000 < p - b - 1 < 1000 \\implies b - 999 < p < b + 1001$, so $p$ must be less than $997 + 1001 = 1998$ in the most extreme case.\n", @@ -16,28 +40,22 @@ }, { "cell_type": "code", - "execution_count": 1, - "id": "a9751bc6", + "execution_count": 2, + "id": "03a9f808", "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "-59231\n" - ] + "data": { + "text/plain": [ + "(-61, 971)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" } ], "source": [ - "from itertools import count\n", - "\n", - "def consecutive_primes(a, b):\n", - " f = lambda x: x^2 + a*x + b\n", - " for n in count(0):\n", - " if not is_prime(f(n)):\n", - " return n\n", - "\n", - "\n", "coeffs = dict()\n", "primes = prime_range(2000)\n", "for b in primes:\n", @@ -52,7 +70,7 @@ " coeffs[(a, b)] = consecutive_primes(a, b)\n", "\n", "a, b = max(coeffs, key=coeffs.get)\n", - "print(a * b)" + "a, b" ] }, { @@ -60,7 +78,9 @@ "id": "cbd83361", "metadata": {}, "source": [ - "It's worth noting that the coefficients end up being $a=-61$ and $b=971$. If you iterate through $n=0,1,2,\\ldots$ for the resulting quadratic and the other formula given, $n^2 - 79n + 1601$, you'll see that these polynomials don't actually generate any new prime numbers compared to Euler's formula - they just repeat primes that Euler's formula already gives.\n", + "Their product is -59231.\n", + "\n", + "If you iterate through $n=0,1,2,\\ldots$ for the resulting quadratic and the other formula given, $n^2 - 79n + 1601$, you'll see that these polynomials don't actually generate any new prime numbers compared to Euler's formula - they just repeat primes that Euler's formula already gives.\n", "\n", "Furthermore, both of these polynomials are actually just shifts of Euler's formula:\n", "$$n^2 - 61n + 971 = (n-31)^2 + (n-31) + 41$$\n", @@ -73,18 +93,18 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "id": "93c85dea", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, - "execution_count": 2, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" }