I'm not talking about prime factors, although I suppose if you could get all the composite factors, you could get the prime factorization. I'm almost completely ignorant to how encryption works, I know it involves primes and have never given it more thought... I'm probably like most people, which is why it works I suppose. So you are saying that an formula to list out the factors of a number 𝑁 doesn't exist, and using a "cheat list" was the best way to solve this?

I'm not talking about prime factors, although I suppose if you could get all the composite factors, you could get the prime factorization. I'm almost completely ignorant to how encryption works, I know it involves primes and have never given it more thought... I'm probably like most people, which is why it works I suppose. So you are saying that an formula ...[text shortened]... ut the factors of a number 𝑁 doesn't exist, and using a "cheat list" was the best way to solve this?

All factors are either prime factors or compounds of prime factors. That's what the fundamental theorem of arithmetic means. If you can easily factor a number, you can easily find primes - and vice versa.

And yes, the only known way of doing so is doing the divisions and the divisions of the divisions. Which is easy for small numbers, but increasingly hard for large numbers; and that means that products of massive prime numbers play a role in cryptography. I know enough to know that, and I know just about enough to know that to explain it properly, I'd better refer you to Numberphile and Computerphile. If I tried to explain it myself, I'd get into an almighty muddle.

@shallow-bluesaid All factors are either prime factors or compounds of prime factors. That's what the fundamental theorem of arithmetic means. If you can easily factor a number, you can easily find primes - and vice versa.

And yes, the only known way of doing so is doing the divisions and the divisions of the divisions. Which is easy for small numbers, but increasingly hard for large ...[text shortened]... to Numberphile and Computerphile. If I tried to explain it myself, I'd get into an almighty muddle.

I looked at public key cryptography once in relation to sending messages and as you say it's all to do with prime numbers.

I don't have a lot of time for the forums at the moment,but I'll post this weeks newspaper puzzle for your amusement.It looks quite simple.I think it's just Venn diagrams:-
The Butchers ,Bakers and Candlestick makers union have merged into 1 union.The new union has (guess what!!)700 members.The butchers'union had 400 members.The Bakers' had 250 and the candlestick makers' 150.However there were 48 Butcher-Bakers,28 Butcher-Candlestick makers and 25 Baker-Candlestick makers.How can this all add up?

@vendasaid I don't have a lot of time for the forums at the moment,but I'll post this weeks newspaper puzzle for your amusement.It looks quite simple.I think it's just Venn diagrams:-
The Butchers ,Bakers and Candlestick makers union have merged into 1 union.The new union has (guess what!!)700 members.The butchers'union had 400 members.The Bakers' had 250 and the candlestick makers' 150. ...[text shortened]... akers,28 Butcher-Candlestick makers and 25 Baker-Candlestick makers.How can this all add up?

Its not entirely clear what they are asking for, but

I typed this out and as I was typing ,realised how easy it was but having gone to the trouble of typing it I thought I might as well leave it.
The queen threw all her regular six sided dice,added up the total and asked a citizen to roll that many dice and total their rolls.She then repeated this process for every citizen and the royal counter calculated that the average total thrown by the citizens was 7,007. what is the most likely number of dice in the Queens collection?