I'm not far into this, so I will ask; Do you want the data as binary instead, seems easier to work with when analysing, not to mention the size.
#include <Entropy.h>
void setup()
{
Serial.begin(115200);
Entropy.Initialize();
}
void loop()
{
uint32_t u_Data = Entropy.random();
char *c_Data = ( char* ) &u_Data;
for( char c_Index = 0 ; c_Index < sizeof( uint32_t ) ; Serial.write( c_Data[ c_Index++ ] ) );
}