Around 1945, who developed the idea of a stored program computer that was to hold programs and data in a memory and then data would move between the memory and the processor?

The correct option is John Von Neumann.

Detailed Explanation:
In 1945, the mathematician and physicist John von Neumann draft-authored a highly influential document titled "First Draft of a Report on the EDVAC". In this paper, he formulated the design for a general-purpose electronic computer where program instructions and data are stored together in the same memory space. This design is widely known today as the Von Neumann architecture (or the stored-program computer model).

Before this innovation, early digital computers like the ENIAC had to be physically rewired or programmed manually using external plugboards and switches to perform different calculations. Storing instructions in memory alongside data enabled the computer to easily switch between tasks by simply executing a different program loaded in its memory, laying the groundwork for modern software-driven computing.

In this architecture, data and instructions continuously move between the central processing unit (which processes the instructions) and the memory unit (which stores them), a fundamental operational concept that remains the basis of almost all modern desktop computers, laptops, and smartphones.