I never get a prime number when I multiply two prime numbers together. But if someone else does the multiplying and the two primes are large enough I don't have any hope of factorising the product.
If you're only looking at positive integers, then yes, of course, the product of two positive primes has only 1
, the two primes and itself as divisors.
Call σ0
the function that tells you how many positive divisors a positive number n has. Then, if p and q are primes, then σ0(pq)=4 and those four divisors are 1,p,q,pq. Example: 65=5×13. The only positive divisors are 1,5,13,65.
When you are dealing with incredibly large numbers it's impossible to work this stuff out manually even using "classical computers" -- of course Quantum computing puts another whole issue at stake.
However with some of the nonsense some Banks now make when you try and access YOUR OWN MONEY e.g Tesco Bank in the UK - with ENDLESS text messages to enter a texted security code -- then you get another message "Your password had changed" - and then another whole thing again - and even then "Password" incorrect or whatever -- when just trying to check your balance -- or need 3 different devices --logon to phone app, fix password by logging on to website app etc etc. Just to CHECK YOUR OWN MONEY !! your balance or whether a €30 /£27.50 payment was made !!!! - while hackers seem tio be able to access people's banls with impunity. !!
Cheers
I HATE MODERN BANKS !!!
jimbo
