August 26, 2024
P44 - A list of Goldbach compositions (3)
Given a range of integers by its lower and upper limit, print a list of all even numbers and their Goldbach composition.
> printGoldbachList(9..20)
10 = 3 + 7
12 = 5 + 7
14 = 3 + 11
16 = 3 + 13
18 = 5 + 13
20 = 3 + 17In most cases, if an even number is written as the sum of two prime numbers, one of them is very small. Very rarely, the primes are both bigger than, say, 50. Example (minimum value of 50 for the primes):
> printGoldbachListLimited(2..3000, 50)
992 = 73 + 919
1382 = 61 + 1321
1856 = 67 + 1789
...kotlin
package org.kotlin99.arithmetic
import com.natpryce.hamkrest.assertion.assertThat
import com.natpryce.hamkrest.equalTo
import org.junit.Test
fun goldbachList(range: IntRange) =
range.filter { it % 2 == 0 }.map { it.goldbach() }
fun printGoldbachList(range: IntRange) =
goldbachList(range).forEach { println(it.toStringSum()) }
fun goldbachListLimited(range: IntRange, minPrime: Int) =
goldbachList(range).filter { it.first > minPrime && it.second > minPrime }
fun printGoldbachListLimited(range: IntRange, minPrime: Int) =
goldbachListLimited(range, minPrime).forEach { println(it.toStringSum()) }
private fun Pair<Int, Int>.toStringSum() = "${first + second} = $first + $second"
class P41Test {
@Test fun `list of Goldbach compositions`() {
printGoldbachList(9..20)
assertThat(goldbachList(9..20), equalTo(listOf(
Pair(3, 7),
Pair(5, 7),
Pair(3, 11),
Pair(3, 13),
Pair(5, 13),
Pair(3, 17)
)))
}
@Test fun `limited list of Goldbach compositions`() {
printGoldbachListLimited(2..3000, 50)
assertThat(goldbachListLimited(2..3000, 50), equalTo(listOf(
Pair(73, 919),
Pair(61, 1321),
Pair(67, 1789),
Pair(61, 1867),
Pair(61, 2017),
Pair(61, 2377),
Pair(53, 2459),
Pair(53, 2477),
Pair(61, 2557),
Pair(103, 2539)
)))
}
}
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