Question

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

Answer 1

This sounds like a very hard problem.

Answer 2

Maybe not....

Answer 3

I dont know..... But I think it will not be surely prime.

Answer 4

If not, we just need a counterexample.

Answer 5

I doubt it is all primes as well.

Answer 6

remainder is gonna be one

Answer 7

Looks like an Euclid proof of the infinite number of prime numbers.

Answer 8

Euclid never said there was an infinity of primes (didn't believe in infinity)

Answer 9

t(5)=2*3*7*43+1=1807
1807/13=139

Answer 10

Euclid said that you could always construct another one out of a supposedly complete list.

Answer 11

that dosent make sense

Answer 12

There are infinitely many primes, as demonstrated by Euclid around 300 BC.
http://en.wikipedia.org/wiki/Prime_number

Answer 13

True but he never said anything about infinity (Greeks weren't too keen on that idea)

Answer 14

You deepened into the history. But I spoke about the method.

Answer 15

The method, I agree, is very like the question.....

Answer 16

P_n = p1p2p3....+1

Answer 17

The "infinitely many" part got added later.....

Answer 18

Personally, I like "you can always get another one" better....

Answer 19

"Construct another one"

Answer 20

do you mean induction

Answer 21

No, it is an explicit construction...

Answer 22

You give me a list of primes and say "That's all there are"

And I give you another one not in the list...