Brain Teasers
Once Prime, Always Prime
What is the smallest prime number with 3 distinct digits that remains prime no matter which one of its digits is removed?
Answer
137.When you remove a number you get 13, 17, or 37.
When you remove 2 numbers you get 1, 3, or 7. All prime.
Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
I thought 1 isn't prime?
zat is not ze question !!!! what happens when you remove three ? kapoot ! Zero !
Before corrections the answer read, "When you remove 2 numbers you get 1, 3, or 7. All prime." The claim that "1" is a prime number is INCORRECT.
1 and 0 aren't prime.
1 is not prime, as a prime number has exactly two factors: 1 and itself. 1 has only 2 factor, and is therefore a cardinal number.
0 is not a prime number because it can have no factors, else it would have infinite factors, for anything multiplied by 0 is 0.
However, with regard to the question, it does ask "What is the smallest prime number with 3 distinct digits that remains prime no matter which one of its digits is removed?" (with emphasis on the "one of its digits"). The explanation afterwards is slightly confusing for it also shows what happens if two of its digits are removed. I do not think that the question is incorrect, but there certainly is a lack of consistency betweeen the question and the explanation, which is probably the reason for confusion.
0 is not a prime number because it can have no factors, else it would have infinite factors, for anything multiplied by 0 is 0.
However, with regard to the question, it does ask "What is the smallest prime number with 3 distinct digits that remains prime no matter which one of its digits is removed?" (with emphasis on the "one of its digits"). The explanation afterwards is slightly confusing for it also shows what happens if two of its digits are removed. I do not think that the question is incorrect, but there certainly is a lack of consistency betweeen the question and the explanation, which is probably the reason for confusion.
I had 173... D'Oh. Didn't think long enough to switch the 3 and 7!
The body has been corrected, but the answer is still wrong (includes one as prime).
It says "no matter which ONE of its digits are removed"... you cannot get 1 by removing a single digit. Good teaser.
Fun facts!
If we agree that 1 is not a prime number, and we can remove one or two numbers, then we do not have an answer.
There are 4 one-digit prime numbers:2,3,5, and 7.
We can remove sets with doubles, which will be divisable by 11. 2 and seven, as well as 5 and 7, will be divisible by 3 with 2 digits left. That means that there is no 7. Therefore, the only set could be 2,3,5. If the five is last, it will be divisible by 5, and if the 2 is last, it will be divisable by 2. Thus, 3 must be last. However, on the two digit number not including the 3, 52 and 25 are both composite, proving that there is no answer to this question!
There are 4 one-digit prime numbers:2,3,5, and 7.
We can remove sets with doubles, which will be divisable by 11. 2 and seven, as well as 5 and 7, will be divisible by 3 with 2 digits left. That means that there is no 7. Therefore, the only set could be 2,3,5. If the five is last, it will be divisible by 5, and if the 2 is last, it will be divisable by 2. Thus, 3 must be last. However, on the two digit number not including the 3, 52 and 25 are both composite, proving that there is no answer to this question!
Of course there is an answer, what is wrong with 137?
Just because you are unable to find a mathematical solution, you cannot poo-poo the answer given when there is clearly no flaw.
Just because you are unable to find a mathematical solution, you cannot poo-poo the answer given when there is clearly no flaw.
i thot the q was about just ONE digit so i got 113..
it could be 11 13 or 13...i think you should make the question clearer....
it could be 11 13 or 13...i think you should make the question clearer....
It asks for 3 distinct digits - distinct meaning different.
Technically, 1 is not formally identified as prime. In that case, there is no answer. That being the case, I tried to consider 1 as a prime and got 137 as the answer too.
But still 1 is not a prime number. So the question is a bit problematic
But still 1 is not a prime number. So the question is a bit problematic
To post a comment, please create an account and sign in.
Follow Braingle!