**The problem:**

Consider the polynomial n^2 + n + 41 Disprove: If

*n*is a positive integer, then n^2 + n + 41 is prime.

**Here is my answer (the programming):**

public class Proof {

static int n = 10;

static boolean prime = true;

static double formula;

static double mod;

public static void test (){

while (prime == true){

formula = (n*n) + n + 41;

double a = formula / formula;

double b = formula / 1;

for (int i=2; i<>{

mod = formula % i;

if (mod == 0.00) {

double div = formula / i;

System.out.println( i + " divides non-prime " + div + " times");

prime = false;

}

}

if (a == 1 &&amp;amp;amp; b == formula && prime != false){

System.out.println("Value of n: " + n + " Value of prime: " + formula + " A: "+ a + " B: " + b); } n = n + 1;

}

n= n - 1;

System.out.println("Value of n: " + n + " Value of non-prime: " + formula);

}

public static void main (String[] args){

test();

}

}

**Here is the output:**

C:\CS2100>javac Proof.java

C:\CS2100>java Proof

Value of n: 10 Value of prime: 151.0 A: 1.0 B: 151.0

Value of n: 11 Value of prime: 173.0 A: 1.0 B: 173.0

Value of n: 12 Value of prime: 197.0 A: 1.0 B: 197.0

Value of n: 13 Value of prime: 223.0 A: 1.0 B: 223.0

Value of n: 14 Value of prime: 251.0 A: 1.0 B: 251.0

Value of n: 15 Value of prime: 281.0 A: 1.0 B: 281.0

Value of n: 16 Value of prime: 313.0 A: 1.0 B: 313.0

Value of n: 17 Value of prime: 347.0 A: 1.0 B: 347.0

Value of n: 18 Value of prime: 383.0 A: 1.0 B: 383.0

Value of n: 19 Value of prime: 421.0 A: 1.0 B: 421.0

Value of n: 20 Value of prime: 461.0 A: 1.0 B: 461.0

Value of n: 21 Value of prime: 503.0 A: 1.0 B: 503.0

Value of n: 22 Value of prime: 547.0 A: 1.0 B: 547.0

Value of n: 23 Value of prime: 593.0 A: 1.0 B: 593.0

Value of n: 24 Value of prime: 641.0 A: 1.0 B: 641.0

Value of n: 25 Value of prime: 691.0 A: 1.0 B: 691.0

Value of n: 26 Value of prime: 743.0 A: 1.0 B: 743.0

Value of n: 27 Value of prime: 797.0 A: 1.0 B: 797.0

Value of n: 28 Value of prime: 853.0 A: 1.0 B: 853.0

Value of n: 29 Value of prime: 911.0 A: 1.0 B: 911.0

Value of n: 30 Value of prime: 971.0 A: 1.0 B: 971.0

Value of n: 31 Value of prime: 1033.0 A: 1.0 B: 1033.0

Value of n: 32 Value of prime: 1097.0 A: 1.0 B: 1097.0

Value of n: 33 Value of prime: 1163.0 A: 1.0 B: 1163.0

Value of n: 34 Value of prime: 1231.0 A: 1.0 B: 1231.0

Value of n: 35 Value of prime: 1301.0 A: 1.0 B: 1301.0

Value of n: 36 Value of prime: 1373.0 A: 1.0 B: 1373.0

Value of n: 37 Value of prime: 1447.0 A: 1.0 B: 1447.0

Value of n: 38 Value of prime: 1523.0 A: 1.0 B: 1523.0

Value of n: 39 Value of prime: 1601.0 A: 1.0 B: 1601.0

Value of n: 40 Value of prime: 1681.0 A: 1.0 B: 1681.0

Value of n: 41 Value of prime: 1763.0 A: 1.0 B: 1763.0

Value of n: 42 Value of prime: 1847.0 A: 1.0 B: 1847.0

Value of n: 43 Value of prime: 1933.0 A: 1.0 B: 1933.0

43 divides non-prime 47.0 times

Value of n: 44 Value of non-prime: 2021.0

C:\CS2100>

Well... the formatting is all messed up. I really should spend some time here so taht I can make formatted code part of my style sheet. Anyway, cheers to the number 44 for making my homework problem go away!

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