Frank and Tank, who are twin brothers, have invited 5 men to play a new game they have created. Andy, Bob, Charlie, Dave, and Eddy have agreed to play after hearing Frank explain the following:

In a small room, behind closed doors, a very large sum of money will be randomly placed into one of 5 [...]

John provided the following problem on a comment on the “Black or White” page:

There are a number of cards in a hat, 20% of which are white on both sides, 50% of which are black on one side and white on the other and 30% of which are black on both sides.

One card is drawn [...]

Find three different prime numbers between 10 and 99, where the average of any two is a prime and the average of all three is a prime.

Obviously no computers and minimal trial and errror only.

What is the smallest factor of 123456! + 1?

That number is approximately 2.6 * 10574964