R49081 is the natural number consisting of 49081 “1” digits in decimal base, or (10^49081 - 1)/9. This number has now been proven to be a prime number, using some number-crunching algorithm. Somebody else will have to ELI5 that algorithm.
This would be totally inexplicable to 5 year olds, except the odd genius. But we took it as intended i.e. "can someone explain this in a simpler way, defining terms like "R""
Idk, I'd try something like "you know how the number one is a single 1 digit, and eleven is two 1 digits? If you have 49081 one digits, that number is really big! We don't even have a word for it, so we call it R49081. Some very smart people worked really hard and found out that number is prime!", after explaining what "prime" is (which I think would be a lot easier).
I like that you've tried, however I have an 8yo (Y3 in UK, so 2nd grade US) and I don't think she would get it yet. She has just started simple devision while doing times tables. She hasn't covered the concept of remainders from devision, and has no concept of fractions. I could probably just about explain the concept of a Prime to her, but it's using concepts she hasn't learnt. She is also generally towards the top of her class for maths.
My 4.5yo will have no chance, more interested in sharks, trains or even better shark trains!
Don't forget that 5 year olds generally haven't learned addition or subtraction yet, let alone division (which is generally taught at 7 years AFAIK). Explaining what "prime" is will be difficult.
Okay, so let us try to explain the concept of looking for large primes by analogy so we don't have to explain all the mathy stuff.
If you tried to convey this to an actual five year old you would probably have to speak more in questions to keep them engaged and interact more and use even simpler language but all that is hard to convey in written text in a language that I never spoke to a five year old. But I digress, so here we go:
You know how some things are red and some are not? There are probably multiple red things in the same room as you are right now. Most people can easily tell if something is red or not by simply looking at it.
But what about places we cannot see? Even though we have never been there, it is a save bet that there are red things in let's say New York. And if we wanted to make sure, we could book a flight and go check. But is there something red in every village in the world? My guess would be yes, but we do not know for sure and it will be hard to visit every place because there are so many.
At this point you might have explained some things, but if you have not lost them yet you could take this further.
There are places even further away than every village. We know that Mars is red because it is so big and people have sent a robot there to be absolutely sure. But what about other planets? It is hard to tell because planets can be very far away and red things can be very small. And going there is no option because even the fastest rocket would not get there any time soon.
What this post mentions is the equivalent of someone building a very precise telescope fixed at a very specific place very far away and they saw something red there.
Here the analogy breaks because there are other more conceptual problems with building such a telescope. Otherwise, I am surprised how many similarities there are actually :)
Brain development I would guess too. We are talking 5 year olds. If a 5 year old can read and write well that is pretty advanced. Mathematics comes later. They might
count on fingers, know some immediate additions, and vaguely understand the concept of multiplication.
I knew nothing about Repunit numbers until a few minutes ago. So far, the most interesting bit for me was that:
> As of March 2022, the largest known prime number 282,589,933 − 1, the largest probable prime R8177207 and the largest elliptic curve primality prime R49081 are all repunits.
