It is the year 2140 and you have just turned 40. After years of research, you have finally invented the time machine! It is a small device that fits in your pocket and allows you to travel in time. You can travel backwards or forwards in time to any given year, but once you traveled you must wait at least one year before traveling again (the device needs to recharge). You can also take any number of people who are in the same room with you.
You want to use the time machine to meet versions of yourself at a different age. The following conditions apply:
- Once you enter time travel, a version of yourself is created who continues to live in the timeline that you left.
- Time travel is instantaneous, so you don't age while traveling.
- You and your versions will all live to 100 years.
- You can wait in any timeline as many years as you want (until your death).
What is the most number of versions of yourself you can gather in one room where everyone has a different age and they are all prime numbers?