WeixiangYan/CodeTransOcean huggingface dataset:
Task: AKS test for primes


C++: #include <iomanip>
#include <iostream>
using namespace std;

const int pasTriMax = 61;

uint64_t pasTri[pasTriMax + 1];

void pascalTriangle(unsigned long n)

{
    unsigned long j, k;

    pasTri[0] = 1;
    j = 1;
    while (j <= n)
    {
        j++;
        k = j / 2;
        pasTri[k] = pasTri[k - 1];
        for ( ;k >= 1; k--)
            pasTri[k] += pasTri[k - 1];
    }
}

bool isPrime(unsigned long n)
{
    if (n > pasTriMax)
    {
        cout << n << " is out of range" << endl;
        exit(1);
    }
    
    pascalTriangle(n);
    bool res = true;
    int i = n / 2;
    while (res && (i > 1))
    {
        res = res && (pasTri[i] % n == 0);
        i--;
    }
    return res;
}

void expandPoly(unsigned long n)
{
    const char vz[] = {'+', '-'};    
    
    if (n > pasTriMax)
    {
        cout << n << " is out of range" << endl;
        exit(1);
    }
    
    switch (n)
    {
        case 0:
            cout << "(x-1)^0 = 1" << endl;
            break;
        case 1:
            cout << "(x-1)^1 = x-1" << endl;
            break;
        default:
            pascalTriangle(n);
            cout << "(x-1)^" << n << " = ";
            cout << "x^" << n;
            bool bVz = true;
            int nDiv2 = n / 2;
            for (unsigned long j = n - 1; j > nDiv2; j--, bVz = !bVz)
                cout << vz[bVz] << pasTri[n - j] << "*x^" << j;
            for (unsigned long j = nDiv2; j > 1; j--, bVz = !bVz)
                cout << vz[bVz] << pasTri[j] << "*x^" << j;
            cout << vz[bVz] << pasTri[1] << "*x";
            bVz = !bVz;
            cout << vz[bVz] << pasTri[0] << endl;
            break;
    }
}

int main()
{
    for (unsigned long n = 0; n <= 9; n++)
        expandPoly(n);      
    for (unsigned long n = 2; n <= pasTriMax; n++)
        if (isPrime(n))
            cout << setw(3) << n;
    cout << endl;        
}


C#: using System;
    public class AksTest
    {
        static long[] c = new long[100];

        static void Main(string[] args)
        {
        for (int n = 0; n < 10; n++) {
		coef(n);
		Console.Write("(x-1)^" + n + " = ");
		show(n);
		Console.WriteLine("");
	}	 
	   Console.Write("Primes:");
	  for (int n = 1; n <= 63; n++)
	     if (is_prime(n))
	       Console.Write(n + " ");
	 
	    Console.WriteLine('\n');
            Console.ReadLine();
        }

        static void coef(int n)
        {
            int i, j;

            if (n < 0 || n > 63) System.Environment.Exit(0);

            for (c[i = 0] = 1L; i < n; c[0] = -c[0], i++)
                for (c[1 + (j = i)] = 1L; j > 0; j--)
                    c[j] = c[j - 1] - c[j];
        }

        static bool is_prime(int n)
        {
            int i;

            coef(n);
            c[0] += 1;
            c[i = n] -= 1;

            while (i-- != 0 && (c[i] % n) == 0) ;

            return i < 0;
        }

        static void show(int n)
	    {
		    do {
                Console.Write("+" + c[n] + "x^" + n);
		    }while (n-- != 0);
	    }
    }
Task: AKS test for primes




Go: package main

import "fmt"

func bc(p int) []int64 {
    c := make([]int64, p+1)
    r := int64(1)
    for i, half := 0, p/2; i <= half; i++ {
        c[i] = r
        c[p-i] = r
        r = r * int64(p-i) / int64(i+1)
    }
    for i := p - 1; i >= 0; i -= 2 {
        c[i] = -c[i]
    }
    return c
}

func main() {
    for p := 0; p <= 7; p++ {
        fmt.Printf("%d:  %s\n", p, pp(bc(p)))
    }
    for p := 2; p < 50; p++ {
        if aks(p) {
            fmt.Print(p, " ")
        }
    }
    fmt.Println()
}

var e = []rune("²³⁴⁵⁶⁷")

func pp(c []int64) (s string) {
    if len(c) == 1 {
        return fmt.Sprint(c[0])
    }
    p := len(c) - 1
    if c[p] != 1 {
        s = fmt.Sprint(c[p])
    }
    for i := p; i > 0; i-- {
        s += "x"
        if i != 1 {
            s += string(e[i-2])
        }
        if d := c[i-1]; d < 0 {
            s += fmt.Sprintf(" - %d", -d)
        } else {
            s += fmt.Sprintf(" + %d", d)
        }
    }
    return
}

func aks(p int) bool {
    c := bc(p)
    c[p]--
    c[0]++
    for _, d := range c {
        if d%int64(p) != 0 {
            return false
        }
    }
    return true
}


Java: public class AksTest {
    private static final long[] c = new long[64];

    public static void main(String[] args) {
        for (int n = 0; n < 10; n++) {
            coeff(n);
            show(n);
        }

        System.out.print("Primes:");
        for (int n = 1; n < c.length; n++)
            if (isPrime(n))
                System.out.printf(" %d", n);

        System.out.println();
    }

    static void coeff(int n) {
        c[0] = 1;
        for (int i = 0; i < n; c[0] = -c[0], i++) {
            c[1 + i] = 1;
            for (int j = i; j > 0; j--)
                c[j] = c[j - 1] - c[j];
        }
    }

    static boolean isPrime(int n) {
        coeff(n);
        c[0]++;
        c[n]--;

        int i = n;
        while (i-- != 0 && c[i] % n == 0)
            continue;
        return i < 0;
    }

    static void show(int n) {
        System.out.print("(x-1)^" + n + " =");
        for (int i = n; i >= 0; i--) {
            System.out.print(" + " + c[i] + "x^" + i);
        }
        System.out.println();
    }
}
Task: AKS test for primes




Go: package main

import "fmt"

func bc(p int) []int64 {
    c := make([]int64, p+1)
    r := int64(1)
    for i, half := 0, p/2; i <= half; i++ {
        c[i] = r
        c[p-i] = r
        r = r * int64(p-i) / int64(i+1)
    }
    for i := p - 1; i >= 0; i -= 2 {
        c[i] = -c[i]
    }
    return c
}

func main() {
    for p := 0; p <= 7; p++ {
        fmt.Printf("%d:  %s\n", p, pp(bc(p)))
    }
    for p := 2; p < 50; p++ {
        if aks(p) {
            fmt.Print(p, " ")
        }
    }
    fmt.Println()
}

var e = []rune("²³⁴⁵⁶⁷")

func pp(c []int64) (s string) {
    if len(c) == 1 {
        return fmt.Sprint(c[0])
    }
    p := len(c) - 1
    if c[p] != 1 {
        s = fmt.Sprint(c[p])
    }
    for i := p; i > 0; i-- {
        s += "x"
        if i != 1 {
            s += string(e[i-2])
        }
        if d := c[i-1]; d < 0 {
            s += fmt.Sprintf(" - %d", -d)
        } else {
            s += fmt.Sprintf(" + %d", d)
        }
    }
    return
}

func aks(p int) bool {
    c := bc(p)
    c[p]--
    c[0]++
    for _, d := range c {
        if d%int64(p) != 0 {
            return false
        }
    }
    return true
}





VB: 



Const MAX = 99
Dim c(MAX + 1) As Variant
Private Sub coef(n As Integer)

    c(n) = CDec(1) 
    For i = n - 1 To 2 Step -1
        c(i) = c(i) + c(i - 1)
    Next i
End Sub
Private Function is_prime(fn As Variant) As Boolean
    fn = CDec(fn)
    Call coef(fn + 1)   
    For i = 2 To fn - 1 
        If c(i) - fn * Int(c(i) / fn) <> 0 Then 
            is_prime = False: Exit Function
        End If
    Next i
    is_prime = True
End Function
Private Sub show(n As Integer)

    Dim ci As Variant
    For i = n To 1 Step -1
        ci = c(i)
        If ci = 1 Then
            If (n - i) Mod 2 = 0 Then
                If i = 1 Then
                    If n = 1 Then
                        ci = "1"
                    Else
                        ci = "+1"
                    End If
                Else
                    ci = ""
                End If
            Else
                ci = "-1"
            End If
        Else
            If (n - i) Mod 2 = 0 Then
                ci = "+" & ci
            Else
                ci = "-" & ci
            End If
        End If
        If i = 1 Then 
            Debug.Print ci
        Else
            If i = 2 Then 
                Debug.Print ci & "x";
            Else
                Debug.Print ci & "x^" & i - 1;
            End If
        End If
    Next i
End Sub
Public Sub AKS_test_for_primes()
    Dim n As Integer
    For n = 1 To 10 
        coef n
        Debug.Print "(x-1)^" & n - 1 & " = ";
        show n
    Next n
    Debug.Print "primes (<="; MAX; "):"
    coef 2 
    For n = 2 To MAX
        If is_prime(n) Then
            Debug.Print n;
        End If
    Next n
End Sub
Task: AKS test for primes







Python: def expand_x_1(n): 

    c =1
    for i in range(n//2+1):
        c = c*(n-i)//(i+1)
        yield c
        
def aks(p):
    if p==2:
        return True

    for i in expand_x_1(p):
        if i % p:

            return False
    return True


VB: 



Const MAX = 99
Dim c(MAX + 1) As Variant
Private Sub coef(n As Integer)

    c(n) = CDec(1) 
    For i = n - 1 To 2 Step -1
        c(i) = c(i) + c(i - 1)
    Next i
End Sub
Private Function is_prime(fn As Variant) As Boolean
    fn = CDec(fn)
    Call coef(fn + 1)   
    For i = 2 To fn - 1 
        If c(i) - fn * Int(c(i) / fn) <> 0 Then 
            is_prime = False: Exit Function
        End If
    Next i
    is_prime = True
End Function
Private Sub show(n As Integer)

    Dim ci As Variant
    For i = n To 1 Step -1
        ci = c(i)
        If ci = 1 Then
            If (n - i) Mod 2 = 0 Then
                If i = 1 Then
                    If n = 1 Then
                        ci = "1"
                    Else
                        ci = "+1"
                    End If
                Else
                    ci = ""
                End If
            Else
                ci = "-1"
            End If
        Else
            If (n - i) Mod 2 = 0 Then
                ci = "+" & ci
            Else
                ci = "-" & ci
            End If
        End If
        If i = 1 Then 
            Debug.Print ci
        Else
            If i = 2 Then 
                Debug.Print ci & "x";
            Else
                Debug.Print ci & "x^" & i - 1;
            End If
        End If
    Next i
End Sub
Public Sub AKS_test_for_primes()
    Dim n As Integer
    For n = 1 To 10 
        coef n
        Debug.Print "(x-1)^" & n - 1 & " = ";
        show n
    Next n
    Debug.Print "primes (<="; MAX; "):"
    coef 2 
    For n = 2 To MAX
        If is_prime(n) Then
            Debug.Print n;
        End If
    Next n
End Sub
Task: AKS test for primes

C: #include <stdio.h>
#include <stdlib.h>

long long c[100];

void coef(int n)
{
	int i, j;

	if (n < 0 || n > 63) abort(); 

	for (c[i=0] = 1; i < n; c[0] = -c[0], i++)
		for (c[1 + (j=i)] = 1; j > 0; j--)
			c[j] = c[j-1] - c[j];
}

int is_prime(int n)
{
	int i;

	coef(n);
	c[0] += 1, c[i=n] -= 1;
	while (i-- && !(c[i] % n));

	return i < 0;
}

void show(int n)
{
	do printf("%+lldx^%d", c[n], n); while (n--);
}

int main(void)
{
	int n;

	for (n = 0; n < 10; n++) {
		coef(n);
		printf("(x-1)^%d = ", n);
		show(n);
		putchar('\n');
	}

	printf("\nprimes (never mind the 1):");
	for (n = 1; n <= 63; n++)
		if (is_prime(n))
			printf(" %d", n);

	putchar('\n');
	return 0;
}




Go: package main

import "fmt"

func bc(p int) []int64 {
    c := make([]int64, p+1)
    r := int64(1)
    for i, half := 0, p/2; i <= half; i++ {
        c[i] = r
        c[p-i] = r
        r = r * int64(p-i) / int64(i+1)
    }
    for i := p - 1; i >= 0; i -= 2 {
        c[i] = -c[i]
    }
    return c
}

func main() {
    for p := 0; p <= 7; p++ {
        fmt.Printf("%d:  %s\n", p, pp(bc(p)))
    }
    for p := 2; p < 50; p++ {
        if aks(p) {
            fmt.Print(p, " ")
        }
    }
    fmt.Println()
}

var e = []rune("²³⁴⁵⁶⁷")

func pp(c []int64) (s string) {
    if len(c) == 1 {
        return fmt.Sprint(c[0])
    }
    p := len(c) - 1
    if c[p] != 1 {
        s = fmt.Sprint(c[p])
    }
    for i := p; i > 0; i-- {
        s += "x"
        if i != 1 {
            s += string(e[i-2])
        }
        if d := c[i-1]; d < 0 {
            s += fmt.Sprintf(" - %d", -d)
        } else {
            s += fmt.Sprintf(" + %d", d)
        }
    }
    return
}

func aks(p int) bool {
    c := bc(p)
    c[p]--
    c[0]++
    for _, d := range c {
        if d%int64(p) != 0 {
            return false
        }
    }
    return true
}
Task: AKS test for primes


C++: #include <iomanip>
#include <iostream>
using namespace std;

const int pasTriMax = 61;

uint64_t pasTri[pasTriMax + 1];

void pascalTriangle(unsigned long n)

{
    unsigned long j, k;

    pasTri[0] = 1;
    j = 1;
    while (j <= n)
    {
        j++;
        k = j / 2;
        pasTri[k] = pasTri[k - 1];
        for ( ;k >= 1; k--)
            pasTri[k] += pasTri[k - 1];
    }
}

bool isPrime(unsigned long n)
{
    if (n > pasTriMax)
    {
        cout << n << " is out of range" << endl;
        exit(1);
    }
    
    pascalTriangle(n);
    bool res = true;
    int i = n / 2;
    while (res && (i > 1))
    {
        res = res && (pasTri[i] % n == 0);
        i--;
    }
    return res;
}

void expandPoly(unsigned long n)
{
    const char vz[] = {'+', '-'};    
    
    if (n > pasTriMax)
    {
        cout << n << " is out of range" << endl;
        exit(1);
    }
    
    switch (n)
    {
        case 0:
            cout << "(x-1)^0 = 1" << endl;
            break;
        case 1:
            cout << "(x-1)^1 = x-1" << endl;
            break;
        default:
            pascalTriangle(n);
            cout << "(x-1)^" << n << " = ";
            cout << "x^" << n;
            bool bVz = true;
            int nDiv2 = n / 2;
            for (unsigned long j = n - 1; j > nDiv2; j--, bVz = !bVz)
                cout << vz[bVz] << pasTri[n - j] << "*x^" << j;
            for (unsigned long j = nDiv2; j > 1; j--, bVz = !bVz)
                cout << vz[bVz] << pasTri[j] << "*x^" << j;
            cout << vz[bVz] << pasTri[1] << "*x";
            bVz = !bVz;
            cout << vz[bVz] << pasTri[0] << endl;
            break;
    }
}

int main()
{
    for (unsigned long n = 0; n <= 9; n++)
        expandPoly(n);      
    for (unsigned long n = 2; n <= pasTriMax; n++)
        if (isPrime(n))
            cout << setw(3) << n;
    cout << endl;        
}




Java: public class AksTest {
    private static final long[] c = new long[64];

    public static void main(String[] args) {
        for (int n = 0; n < 10; n++) {
            coeff(n);
            show(n);
        }

        System.out.print("Primes:");
        for (int n = 1; n < c.length; n++)
            if (isPrime(n))
                System.out.printf(" %d", n);

        System.out.println();
    }

    static void coeff(int n) {
        c[0] = 1;
        for (int i = 0; i < n; c[0] = -c[0], i++) {
            c[1 + i] = 1;
            for (int j = i; j > 0; j--)
                c[j] = c[j - 1] - c[j];
        }
    }

    static boolean isPrime(int n) {
        coeff(n);
        c[0]++;
        c[n]--;

        int i = n;
        while (i-- != 0 && c[i] % n == 0)
            continue;
        return i < 0;
    }

    static void show(int n) {
        System.out.print("(x-1)^" + n + " =");
        for (int i = n; i >= 0; i--) {
            System.out.print(" + " + c[i] + "x^" + i);
        }
        System.out.println();
    }
}
Task: AKS test for primes





Java: public class AksTest {
    private static final long[] c = new long[64];

    public static void main(String[] args) {
        for (int n = 0; n < 10; n++) {
            coeff(n);
            show(n);
        }

        System.out.print("Primes:");
        for (int n = 1; n < c.length; n++)
            if (isPrime(n))
                System.out.printf(" %d", n);

        System.out.println();
    }

    static void coeff(int n) {
        c[0] = 1;
        for (int i = 0; i < n; c[0] = -c[0], i++) {
            c[1 + i] = 1;
            for (int j = i; j > 0; j--)
                c[j] = c[j - 1] - c[j];
        }
    }

    static boolean isPrime(int n) {
        coeff(n);
        c[0]++;
        c[n]--;

        int i = n;
        while (i-- != 0 && c[i] % n == 0)
            continue;
        return i < 0;
    }

    static void show(int n) {
        System.out.print("(x-1)^" + n + " =");
        for (int i = n; i >= 0; i--) {
            System.out.print(" + " + c[i] + "x^" + i);
        }
        System.out.println();
    }
}




VB: 



Const MAX = 99
Dim c(MAX + 1) As Variant
Private Sub coef(n As Integer)

    c(n) = CDec(1) 
    For i = n - 1 To 2 Step -1
        c(i) = c(i) + c(i - 1)
    Next i
End Sub
Private Function is_prime(fn As Variant) As Boolean
    fn = CDec(fn)
    Call coef(fn + 1)   
    For i = 2 To fn - 1 
        If c(i) - fn * Int(c(i) / fn) <> 0 Then 
            is_prime = False: Exit Function
        End If
    Next i
    is_prime = True
End Function
Private Sub show(n As Integer)

    Dim ci As Variant
    For i = n To 1 Step -1
        ci = c(i)
        If ci = 1 Then
            If (n - i) Mod 2 = 0 Then
                If i = 1 Then
                    If n = 1 Then
                        ci = "1"
                    Else
                        ci = "+1"
                    End If
                Else
                    ci = ""
                End If
            Else
                ci = "-1"
            End If
        Else
            If (n - i) Mod 2 = 0 Then
                ci = "+" & ci
            Else
                ci = "-" & ci
            End If
        End If
        If i = 1 Then 
            Debug.Print ci
        Else
            If i = 2 Then 
                Debug.Print ci & "x";
            Else
                Debug.Print ci & "x^" & i - 1;
            End If
        End If
    Next i
End Sub
Public Sub AKS_test_for_primes()
    Dim n As Integer
    For n = 1 To 10 
        coef n
        Debug.Print "(x-1)^" & n - 1 & " = ";
        show n
    Next n
    Debug.Print "primes (<="; MAX; "):"
    coef 2 
    For n = 2 To MAX
        If is_prime(n) Then
            Debug.Print n;
        End If
    Next n
End Sub
Task: Parallel calculations

C: #include <stdio.h>
#include <omp.h>

int main()
{
        int data[] = {12757923, 12878611, 12878893, 12757923, 15808973, 15780709, 197622519};
        int largest, largest_factor = 0;

        omp_set_num_threads(4);
        
        #pragma omp parallel for shared(largest_factor, largest)
        for (int i = 0; i < 7; i++) {
                int p, n = data[i];

                for (p = 3; p * p <= n && n % p; p += 2);
                if (p * p > n) p = n;
                if (p > largest_factor) {
                        largest_factor = p;
                        largest = n;
                        printf("thread %d: found larger: %d of %d\n",
                                omp_get_thread_num(), p, n);
                } else {
                        printf("thread %d: not larger:   %d of %d\n",
                                omp_get_thread_num(), p, n);
                }
        }

        printf("Largest factor: %d of %d\n", largest_factor, largest);
        return 0;
}



C#: using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    public static List<int> PrimeFactors(int number)
    {
        var primes = new List<int>();
        for (int div = 2; div <= number; div++)
        {
            while (number % div == 0)
            {
                primes.Add(div);
                number = number / div;
            }
        }
        return primes;
    }

    static void Main(string[] args)
    {
        int[] n = { 12757923, 12878611, 12757923, 15808973, 15780709, 197622519 };
        
        var factors = n.AsParallel().Select(PrimeFactors).ToList();
        
        var smallestFactors = factors.Select(thisNumbersFactors => thisNumbersFactors.Min()).ToList();
        
        int biggestFactor = smallestFactors.Max();
        int whatIndexIsThat = smallestFactors.IndexOf(biggestFactor);
        Console.WriteLine("{0} has the largest minimum prime factor: {1}", n[whatIndexIsThat], biggestFactor);
        Console.WriteLine(string.Join(" ", factors[whatIndexIsThat]));
    }
}
Task: Parallel calculations

C: #include <stdio.h>
#include <omp.h>

int main()
{
        int data[] = {12757923, 12878611, 12878893, 12757923, 15808973, 15780709, 197622519};
        int largest, largest_factor = 0;

        omp_set_num_threads(4);
        
        #pragma omp parallel for shared(largest_factor, largest)
        for (int i = 0; i < 7; i++) {
                int p, n = data[i];

                for (p = 3; p * p <= n && n % p; p += 2);
                if (p * p > n) p = n;
                if (p > largest_factor) {
                        largest_factor = p;
                        largest = n;
                        printf("thread %d: found larger: %d of %d\n",
                                omp_get_thread_num(), p, n);
                } else {
                        printf("thread %d: not larger:   %d of %d\n",
                                omp_get_thread_num(), p, n);
                }
        }

        printf("Largest factor: %d of %d\n", largest_factor, largest);
        return 0;
}


C++: #include <iostream>
#include <iterator>
#include <vector>
#include <ppl.h> 
#include <concurrent_vector.h> 

struct Factors
{
    int number;
    std::vector<int> primes;
};

const int data[] =
{
    12757923, 12878611, 12878893, 12757923, 15808973, 15780709, 197622519
};

int main()
{
    
    Concurrency::concurrent_vector<Factors> results;

    
    Concurrency::parallel_for_each(std::begin(data), std::end(data), [&](int n)
    {
        Factors factors;
        factors.number = n;
        for (int f = 2; n > 1; ++f)
        {
            while (n % f == 0)
            {
                factors.primes.push_back(f);
                n /= f;
            }
        }
        results.push_back(factors); 
    });
    

    
    auto max = std::max_element(results.begin(), results.end(), [](const Factors &a, const Factors &b)
    {
        return a.primes.front() < b.primes.front();
    });

    
    std::for_each(results.begin(), results.end(), [&](const Factors &f)
    {
        if (f.primes.front() == max->primes.front())
        {
            std::cout << f.number << " = [ ";
            std::copy(f.primes.begin(), f.primes.end(), std::ostream_iterator<int>(std::cout, " "));
            std::cout << "]\n";
        }
    });
    return 0;
}
Task: Parallel calculations

C: #include <stdio.h>
#include <omp.h>

int main()
{
        int data[] = {12757923, 12878611, 12878893, 12757923, 15808973, 15780709, 197622519};
        int largest, largest_factor = 0;

        omp_set_num_threads(4);
        
        #pragma omp parallel for shared(largest_factor, largest)
        for (int i = 0; i < 7; i++) {
                int p, n = data[i];

                for (p = 3; p * p <= n && n % p; p += 2);
                if (p * p > n) p = n;
                if (p > largest_factor) {
                        largest_factor = p;
                        largest = n;
                        printf("thread %d: found larger: %d of %d\n",
                                omp_get_thread_num(), p, n);
                } else {
                        printf("thread %d: not larger:   %d of %d\n",
                                omp_get_thread_num(), p, n);
                }
        }

        printf("Largest factor: %d of %d\n", largest_factor, largest);
        return 0;
}





Java: import static java.lang.System.out; 
import static java.util.Arrays.stream;
import static java.util.Comparator.comparing;
 
public interface ParallelCalculations {
    public static final long[] NUMBERS = {
      12757923,
      12878611,
      12878893,
      12757923,
      15808973,
      15780709,
      197622519
    };
 
    public static void main(String... arguments) {
      stream(NUMBERS)
        .unordered()
        .parallel()
        .mapToObj(ParallelCalculations::minimalPrimeFactor)
        .max(comparing(a -> a[0]))
        .ifPresent(res -> out.printf(
          "%d has the largest minimum prime factor: %d%n",
          res[1],
          res[0]
        ));
    }
 
    public static long[] minimalPrimeFactor(long n) {
      for (long i = 2; n >= i * i; i++) {
        if (n % i == 0) {
          return new long[]{i, n};
        }
      }
      return new long[]{n, n};
    }
}