For example, here is some code I wrote to test my own prng:
srand(1000000); for( int i = 0; i < 10; i++ ) printf( "%d\n", rand() );
printf("====\n");
srand(1000001); for( int i = 0; i < 10; i++ ) printf( "%d\n", rand() );
And here is the result:
21585 18586 29373 4301 3304 21158 23657 21142 2144 26110 ==== 21589 29335 14469 28364 13618 25085 26770 18215 18656 19962
As you can see, they diverge really quickly.