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t(1)=2 t(2)=3 t(3)=t(1)*t(2)+1 t(4)=t(1)*t(2)*t(3)+1 . . . t(n)=t(1)*t(2)*t(3)*...*t(n-1)+1 PROVE or DISPROVE that t(n) will surely be PRIME

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This sounds like a very hard problem.
Maybe not....
I dont know..... But I think it will not be surely prime.

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Other answers:

If not, we just need a counterexample.
I doubt it is all primes as well.
remainder is gonna be one
Looks like an Euclid proof of the infinite number of prime numbers.
Euclid never said there was an infinity of primes (didn't believe in infinity)
t(5)=2*3*7*43+1=1807 1807/13=139
Euclid said that you could always construct another one out of a supposedly complete list.
that dosent make sense
There are infinitely many primes, as demonstrated by Euclid around 300 BC.
True but he never said anything about infinity (Greeks weren't too keen on that idea)
You deepened into the history. But I spoke about the method.
The method, I agree, is very like the question.....
P_n = p1p2p3....+1
The "infinitely many" part got added later.....
Personally, I like "you can always get another one" better....
"Construct another one"
do you mean induction
No, it is an explicit construction...
You give me a list of primes and say "That's all there are" And I give you another one not in the list...

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