Final answer:
The question asks for a program to store prime numbers from 1 to 1000 in a binary data file named PrimeNumbers.dat, by appending each new prime number as it is discovered.
Step-by-step explanation:
The subject of this question falls under Computers and Technology, specifically within the realm of programming and working with files. The task involves writing a program that effectively stores prime numbers between 1 and 1000 in a binary data file, and the file should be named PrimeNumbers.dat. The operation in focus is appending each new prime number found to this file, thus gradually compiling a list of prime numbers in binary format.
To achieve this, one must implement a program that cycles through the numbers up to 1000, checks for primality, and when a prime number is found, appends it to the binary file. It is important to handle file operations with care to ensure data integrity and to prevent errors during the write process.