Prime dots

I wanted to show that the last digits in prime numbers did not occur randomly, rather the 1,3,7,9 that they all end with occur in patterns. So I found some random number lists and played with them using gawk and c until I had a nice list of the last digits of all the primes up to one million. There are about 79,000 of them. This is the file that's opened in the following line:

ptr_file =fopen("upTo1GlastNum3.txt","r");

I gave each of 1,3,7,9 a dot-colour and put them in a 79k 256-colour BMP using great library I found called EasyBMP.

To compare the dot picture I did the same for a 640 x 480 BMP of random 1,3,7,9 digits generated bu normal random number function in C.

Here is the the picture that's generated from actual prime numbers.:

And here's the one generated by rand() in C.

There's more in the lower picture because I kept going til full 640 x 480 BMP was filled. That is 307K dots whereas the number of dots generated from real primes came from a list of only 78k digits = dots.

Upshot. They look very similar. Not sure this BMP method is a good way to generate non-randomness of prime last digits.

The program I used follows.

//BMPDots7 makes a BMP of last digit of all randoms up to 1M. Plus does similar to program generated random numbers' last digit.

// Gives two BMPs. One for last digit of prmes, other for random 1,3,7,9. Hard to tell the difference.

//To do: Create file of 1,3,7,9 from rand(). Read file in a place relevant dot on BMP.

#include "EasyBMP.h"

#include<stdlib.h>

#include<conio.h>

using namespace std;

int main( int argc, char* argv[] )

{

    

BMP PrimePic0;

PrimePic0.SetSize(640,480);

PrimePic0.SetBitDepth(8);

int xxcount3 = 0; 

int ones2=0;

int threes2=0; int sevens2=0; int nines2=0; long nonPrimes2 = 0; long allLines=0;

FILE *ptr_file; 

char buf[1000];

ptr_file =fopen("upTo1GlastNum3.txt","r");

int h=0; int k=0;

while ((fgets(buf,1000, ptr_file)!=NULL) && (k<480)){

allLines++;

switch (buf[0]) {

case '1':

PrimePic0(h,k)->Red = 255; 

PrimePic0(h,k)->Green = 255;

PrimePic0(h,k)->Blue = 0;

ones2++;

break;

case '3':

PrimePic0(h,k)->Red = 255; 

PrimePic0(h,k)->Green = 0;

PrimePic0(h,k)->Blue = 0;

threes2++;

break;

case '7':

PrimePic0(h,k)->Red = 0; 

PrimePic0(h,k)->Green = 255;

PrimePic0(h,k)->Blue = 0;

sevens2++;

break;

case '9':

PrimePic0(h,k)->Red = 0; 

PrimePic0(h,k)->Green = 0;

PrimePic0(h,k)->Blue = 255;

nines2++;

break;

default:

cout << "Not prime" << allLines <<endl;

nonPrimes2++;

printf("Non prime");

}

h++;

if (h==640) {

h=0;

k++;

}

}

fclose(ptr_file);

PrimePic0.WriteToFile("prime0Pic.bmp");

//Now do case where 1,3,7,9 are generated by random numbers via c-rand().

BMP AnImage;

AnImage.SetSize(640,480);

AnImage.SetBitDepth(8);

cout << "File info:" << endl; 

cout << AnImage.TellWidth() << " x " << AnImage.TellHeight() << " at " << AnImage.TellBitDepth() << " bpp" << endl;

cout << "colors: " << AnImage.TellNumberOfColors() << endl;

cout << "(" << (int) AnImage(14,18)->Red << "," << (int) AnImage(14,18)->Green << "," << (int) AnImage(14,18)->Blue << "," << (int) AnImage(14,18)->Alpha << ")" << endl; 

int randDigit,i,j,ones,threes,sevens,nines;

long nonPrimes=0;

long allNums = 0;

j=0; ones=threes=sevens=nines=0; i=0;

while (j<480) 

{

randDigit = rand()%10;

allNums++;

switch (randDigit)

{

case 1:

AnImage(i,j)->Red = 255; 

AnImage(i,j)->Green = 255;

AnImage(i,j)->Blue = 0;

ones++;

break;

case 3:

AnImage(i,j)->Red = 255; 

AnImage(i,j)->Green = 0;

AnImage(i,j)->Blue = 0;

threes++;

break;

case 7:

AnImage(i,j)->Red = 0; 

AnImage(i,j)->Green = 255;

AnImage(i,j)->Blue = 0;

sevens++;

break;

case 9:

AnImage(i,j)->Red = 0; 

AnImage(i,j)->Green = 0;

AnImage(i,j)->Blue = 255;

nines++;

break; 

default:

nonPrimes++;

i--;

}

i++;

if (i==640) {

i=0;

j++;

}

}

AnImage.WriteToFile("copied1dots3.bmp");

cout << "Non primes= " << nonPrimes << endl;

cout << "Ones =" << ones;

cout << "  Threes =" << threes;

cout << "  Sevens =" << sevens;

cout << "  Nines =" << nines << endl;

cout << "  xxcount3 " << xxcount3 << endl;

cout << "  allNums " << allNums << endl;

cout << "  ones2 " << ones2 << endl;

cout << "  Threes2 =" << threes2;

cout << "  Sevens2 =" << sevens2;

cout << "  Nines2 =" << nines2 << endl;

cout << "Non primes2 = " << nonPrimes2 << endl;

cout << "allLines = " << allLines << endl;

cout << "Sum of primes = " << ones2+threes2+sevens2+nines2 << endl;

 return 0;

}