1201

1201 is a prime number.

1201 has a representation as a sum of two squares: 1201 = 24² + 25².

1201 is the hypotenuse of a primitive Pythagorean triple: 1201² = 49² + 1200².

1201 is a centered square number.

1201 has a square that is formed by inserted three 4s into it: 1201² = 1442401.

The Apollo Guidance Computer showed a 1201 alarm (Executive overflow--no vacant areas) during Apollo 11's descent to the lunar surface.

Source: What's Special About This Number?