## sauravshakya 3 years ago 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

1. TuringTest

This sounds like a very hard problem.

2. estudier

Maybe not....

3. sauravshakya

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

4. estudier

If not, we just need a counterexample.

5. TuringTest

I doubt it is all primes as well.

6. UnkleRhaukus

remainder is gonna be one

7. klimenkov

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

8. estudier

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

9. swissgirl

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

10. estudier

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

11. UnkleRhaukus

that dosent make sense

12. klimenkov

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

13. estudier

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

14. klimenkov

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

15. estudier

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

16. estudier

P_n = p1p2p3....+1

17. UnkleRhaukus

18. estudier

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

19. estudier

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

20. estudier

"Construct another one"

21. UnkleRhaukus

do you mean induction

22. estudier

No, it is an explicit construction...

23. estudier

You give me a list of primes and say "That's all there are" And I give you another one not in the list...