In: Computer Science
Project #1. Goldbach Conjecture.
“Every even integer greater than 2 can be represented as the sum of two prime numbers.”
For this project show the sums from 100,000 to 100,200.
(1) Print it as follows:
100,000 prime no. 1prime no. 2
100,002……
100,004……
………
………
100,200……
(Of course, if you find that there is no such pair of primes, indicate the first number that does have a Goldbach pair. I don’t think you’ll find such a number!)
(2) Also, print out the source code (hopefully well documented).
SOURCE CODE
#include<bits/stdc++.h>
using namespace std;
void prime(int n, bool isPrime[]) // to find all the numbers
upto n prime or not
{
isPrime[0] = isPrime[1] = false;
for (int i=2; i<=n; i++)
isPrime[i] = true;
for (int p=2; p*p<=n; p++)
{
if (isPrime[p] == true)
{
for (int i=p*p;
i<=n; i += p)
isPrime[i] = false;
}
}
}
void findPrimePair(int n)
{
bool isPrime[n+1]; // to srote all number upto n prime
or not
prime(n, isPrime);
for (int i=0; i<n; i++)
{
if (isPrime[i] &&
isPrime[n-i])
{
cout << n
<< "\t"<< i << "\t\t" << (n-i)
<<"\n";
return;
}
}
}
int main()
{ int i = 100000;
cout << "Number\t" << "Prime Number 1\t"
<< "Prime Number 2\t"<<"\n";
while(i<=100200)
findPrimePair(i++);
return 0;
}
OUTPUT
Number Prime Number 1 Prime Number
2
100000 11 99989
100002 11 99991
100004 13 99991
100005 2 100003
100006 3 100003
100008 5 100003
100010 7 100003
100012 23 99989
100014 11 100003
100016 13 100003
100018 29 99989
100020 17 100003
100021 2 100019
100022 3 100019
100024 5 100019
100026 7 100019
100028 37 99991
100030 11 100019
100032 13 100019
100034 31 100003
100036 17 100019
100038 19 100019
100040 37 100003
100042 23 100019
100044 41 100003
100045 2 100043
100046 3 100043
100048 5 100043
100050 7 100043
100051 2 100049
100052 3 100049
100054 5 100049
100056 7 100049
100058 67 99991
100059 2 100057
100060 3 100057
100062 5 100057
100064 7 100057
100066 17 100049
100068 11 100057
100070 13 100057
100071 2 100069
100072 3 100069
100074 5 100069
100076 7 100069
100078 29 100049
100080 11 100069
100082 13 100069
100084 41 100043
100086 17 100069
100088 19 100069
100090 41 100049
100092 23 100069
100094 37 100057
100096 47 100049
100098 29 100069
100100 31 100069
100102 53 100049
100104 47 100057
100105 2 100103
100106 3 100103
100108 5 100103
100110 7 100103
100111 2 100109
100112 3 100109
100114 5 100109
100116 7 100109
100118 61 100057
100120 11 100109
100122 13 100109
100124 67 100057
100126 17 100109
100128 19 100109
100130 61 100069
100131 2 100129
100132 3 100129
100134 5 100129
100136 7 100129
100138 29 100109
100140 11 100129
100142 13 100129
100144 41 100103
100146 17 100129
100148 19 100129
100150 41 100109
100152 23 100129
100153 2 100151
100154 3 100151
100155 2 100153
100156 3 100153
100158 5 100153
100160 7 100153
100162 11 100151
100164 11 100153
100166 13 100153
100168 17 100151
100170 17 100153
100171 2 100169
100172 3 100169
100174 5 100169
100176 7 100169
100178 109 100069
100180 11 100169
100182 13 100169
100184 31 100153
100185 2 100183
100186 3 100183
100188 5 100183
100190 7 100183
100191 2 100189
100192 3 100189
100194 5 100189
100195 2 100193
100196 3 100193
100198 5 100193
100200 7
100193
SCREENSHOT
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