suppose my frend picks a # 1,2 or 3. If i can only ask 1 question to find out his #, what question do i ask? where the question can only be a yes,no,idk question. assume my frend is a math genius

Gonna go with....

"If you divide your number by the next lowest integer, is the new number an integer?"

1/0 -> idk ?
2/1 -> yes
3/2 -> no

Only way to get this right is to ask a question where one of them is a for sure idk, another is a for sure yes, and the other is a for sure no.

This post was edited by Dontrunaway on Dec 3 2014 07:40pm

i had a similar answer to urs. "if u divide ur number by the previous number, is the result a fraction?"
only problem is that i think for 1/0 the answer should be no cuz its not defined. not a integer or fraction :/

If N is the picked number, ask him if :

N + ( (10^(N-1))^(10^N) )^(10^N)

is a prime number.

(notice that the answer is obviously "no" when N = 2, because it's a multiple of 3)

i see if N is equal to 1 the answer is yes but what about for N=3?

For N = 3, the answer is "I don't know". Even if your friend is a math genius.

An easier formula with the same question could be :

N + 2 + (N-1)*(N-2)*K

with K either an incredible large number, making things impossible to compute, or simply an unknown integer (but still defined).

Example of unknown numbers :

- the last world-record of 100 m race (express it in 100th seconds, to get an integer),
Since the sequence of world-records is decreasing and bounded down by zero, it must have a limit (ie : a last record, that will never be beaten).
- the number of atoms of gold (Au) in the whole universe, at a given time,
- the first number that will appear in the next national lottery (or any kind of public betting game),

etc

You can't ask binary questions. You need an idk and "is this prime" is litmus. There is no idk.

You don't seem to know that, for many large numbers, it's impossible to know if they are prime or not.

Many things in the field of mathematics are beyond human knowledge - that's why we have researchers.

There is no number which is indeterminate as to whether or not it is prime. With enough time and a brute force program, it is quite easy to determine if a number is prime or not.

Sun will collapse in the next 5 billion years. We can expect humanity to disappear before that.
"enough time" may exceed that delay. In this case, noone will ever know if some given number is prime or not.

By the way, do you know that most of encrypted systems, nowadays, are based on the fact that a large number is impossible to "break" into 2 smaller primes ?