一个有趣的解决方案，使所有素数均小于n

这种方法基于威尔逊定理，并且利用DP可以轻松完成阶乘计算这一事实。
威尔逊定理说，如果数k为质数，则((k-1)！+ 1)％k必须为0。
以下是该方法的Python实现。请注意，该解决方案在Python有效，因为默认情况下Python支持大整数，因此可以计算大数阶乘。

C++

// C++ program to Prints prime numbers smaller than n
#include
using namespace std;
void primesInRange(int n)
{
    // Compute factorials and apply Wilson's
    // theorem.
    int fact = 1;
    for(int k=2;k

---

Java

// Java program prints prime numbers smaller than n
class GFG{
static void primesInRange(int n)
{
    // Compute factorials and apply Wilson's
    // theorem.
    int fact = 1;
    for(int k=2;k

---

Python3

# Python3 program to prints prime numbers smaller than n
def primesInRange(n) :
 
    # Compute factorials and apply Wilson's
    # theorem.
    fact = 1
    for k in range(2, n):
        fact = fact * (k - 1)
        if ((fact + 1) % k == 0):
            print k
 
# Driver code
n = 15
primesInRange(n)

C#

// C# program prints prime numbers smaller than n
class GFG{
static void primesInRange(int n)
{
    // Compute factorials and apply Wilson's
    // theorem.
    int fact = 1;
    for(int k=2;k

---

Javascript

// Javascript program to prints prime numbers smaller than n
function primesInRange(n)
{
    // Compute factorials and apply Wilson's
    // theorem.
    let fact = 1;
    for(let k = 2; k < n; k++){
        fact = fact * (k - 1);
        if ((fact + 1) % k == 0)
            document.write((k + "<br>"));
            }
}
 
// Driver code
let n = 15;
primesInRange(n);
 
// This code is contributed by _saurabh_jaiswal

输出 ：

2
3
5
7
11
13