Prime Number Resources

A prime number is a natural number that can be divided by the numeral one and itself. For example, the natural number 17 is a prime number. 17 can be divided by 1. 17 can be divided by 17.

17 / 1 = 17.

17 / 17 = 1.

The C code below extracts all prime numbers between 0 and 1000.

#include <stdio.h>
#define MAX 1000
#define NUMBERS_PER_LINE 10

//This code prints the prime
//numbers between 0 and 1000
//sequentially.

int main()
{
	int i = 0;
	int j = 0;
	int k = 0;
	int count = NUMBERS_PER_LINE;
	int numbers[MAX];
	
	//manually store prime numbers 1 and 2
	numbers[0] = 1;
	numbers[1] = 2;
	
	for(i = 3; i < MAX; i++)
	{
		//initialize array starting with element 2
                numbers[i - 1] = i; 
                for(j = 2; j < i; j++)
		{
			if(i % j == 0) //not prime
			{
                                //replace non prime with zero
				numbers[i - 1] = 0; 
				break;
			}
		}
	}
	
	for(k = 0; k < MAX; k++)
	{
		if(numbers[k] != 0)
		{
			printf("%3d ", numbers[k]);
			if(count % NUMBERS_PER_LINE == 0)
			{
                                //print 10 numbers per line
				printf("\n"); 
			}
			count++;
		}
	}
	
	return 0;
}

When this code is compiled and executed, this is the output:

  1
  2   3   5   7  11  13  17  19  23  29
 31  37  41  43  47  53  59  61  67  71
 73  79  83  89  97 101 103 107 109 113
127 131 137 139 149 151 157 163 167 173
179 181 191 193 197 199 211 223 227 229
233 239 241 251 257 263 269 271 277 281
283 293 307 311 313 317 331 337 347 349
353 359 367 373 379 383 389 397 401 409
419 421 431 433 439 443 449 457 461 463
467 479 487 491 499 503 509 521 523 541
547 557 563 569 571 577 587 593 599 601
607 613 617 619 631 641 643 647 653 659
661 673 677 683 691 701 709 719 727 733
739 743 751 757 761 769 773 787 797 809
811 821 823 827 829 839 853 857 859 863
877 881 883 887 907 911 919 929 937 941
947 953 967 971 977 983 991 997

Prime numbers have a great deal of practical value in the cryptography discipline. Some cryptographic algorithms encode data in such a manner that to decode the data, enormous numbers must be factored. When factoring any number, we factor down to the number’s prime constituents. Robots do not inherently understand what a prime number is. Given the proper instructions, such as the C code above, a robot can be taught how to recognize prime numbers. This recognition enables the robot to know that it is time to stop the factoring process. When factoring is complete, the decoded or unencrypted data can then be presented in a human readable form that represents the exact same data prior to the encryption process.

In a future post, perhaps, I’ll demonstrate how encryption can be done with the C programming language.

Prime Number Resources