A prime time traveler

Question

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?

Answer 1

There are 25 primes below 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

So the question is whether we can gather 24 variants plus yourself in one room with all these ages.

Here is one method for doing so.
Exclude $67$ from the list of primes, and call the remaining $24$ primes $p_0$ to $p_{23}$ (so $p_0=2$, $p_{23}=97$).
You could do $24$ pickups with exactly one year between pickups, which takes a period of $23$ years. After the $n$-th year (where $n$ ranges from $0$ to $23$) you can pick up a version with age $p_{23-n}-(23-n)$.
After the $24$th pickup, the variants you picked up will have aged to become $p_0$ to $p_{23}$ years old.
You will have aged by $23$ years during these actions, but you want to be $67$ at the end of it to fill out the complete set of primes, so you should wait $4$ years before doing your first pickup of the variant with age $p_{23}-23=74$.

Note that $p_{23-n}-(23-n)$ is always positive. There is however the minor issue that $p_0-0 = p_1-1 = 2$, so you are picking up a $2$-year old variant twice. This does not seem to be against the rules, though you may need to shift one pickup by a day or so in the variant's timeline so the two pickups don't interfere with each other. If it is against the rules, you can swap the primes $3$ and $5$ so that $p_1=5$ and $p_2=3$, and then also swap the primes $7$ and $11$ to avoid picking up a $4$-year old twice.