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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.

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

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...