Multiply together all the prime numbers from 2 up thru n, then add 1 to the result. Show that the final total is never a perfect square.
No doubt lots of you know how easy that one is. So, what’s a better example of a problem that stumps people in spite of being easy?
If you’re not already acquainted with the above example, being told that it’s easy helps you solve it. Can you find a problem where hearing that it’s easy doesn’t help?
This isn’t true. For example for N=4, we have 2 times 3 times 4 plus 1 is 25, which is a perfect square. It isn’t a perfect square of any integer up to N, which may be the proof you were thinking of
ETA: Erroneous answer now spoiler protected, so I don’t confuse other people.
Primes up to N. For N=4, we have 2*3+1 = 7, which is not a perfect square
D’oh. My apologies. I misread the OP and now must slink off in shame.
This one is plainly easy, as long as you’re 75+ years old. How easy is it for younger people? (Pencil and paper allowed, nothing else.)
How many digits in 5 to the 300th power?
A converse is Goldbachs’s conjecture. Every even number can be expressed as the sum ot two primes.
Easy to state and just about anyone can understand it. But still not proved.