# Puzzle for 25 Jun 2009

Discussion in '\$1 Daily Competition' started by shabbir, Jun 25, 2009.

1. ### shabbirAdministratorStaff Member

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Find a three digit prime number which

• Has all prime digits
• Forms primes with its first two digits.
• Forms primes with its last two digits.

2. ### nimeshNew Member

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I say 373

Has all prime digits - All are Prime 3, 7
Forms primes with its first two digits - Forms Prime with first 2 digits 37
Forms primes with its and last two digits. - Forms Prime with Last two - 73

The last condition looks incomplete.
There was no condition of uniqueness of digits
There was no condition like least 3 digit prime

3. ### MridulaNew Member

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179 - 3 unique digit prime no.

17 is a prime no.
79 is prime no.

4. ### nimeshNew Member

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But 1 is not a prime no :lol:
Sorry Mridula for Yesterday

5. ### shabbirAdministratorStaff Member

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Like.
Dont confuse with yesterdays problem and its a fresh one with not any condition.

I would like to also see a reason as to how you landed to the number you have as answer.

6. ### nimeshNew Member

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"The last condition looks incomplete."
I mean the sentence formation is incorrect. Which you have corrected now...haha

What reason would you like? [btw, you didn't asked earlier to specify the reason]
I just looked at the list of prime numbers and checked with the conditions you gave.

Other numbers that I thought were:
113, 131, 137, 173, 197, 311, 313, 317 - But 1 is not a prime number
So the first number that I got was 373

7. ### xpi0t0sMentor

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All possible results are
237
373
537
737

Code:
```int is_prime(int n)
{
if (n==2) return 1;
if (n<3) return 0;
if (!(n%2)) return 0;
for (int i=3; i*i<=n; i+=2)
{
if (!(n%i))
return 0;
}
return 1;
}

int _tmain(int argc, _TCHAR* argv[])
{
for (int i=100; i<1000; i++)
{
int digits[3];
int temp=i;
digits[2]=temp%10; temp/=10;
digits[1]=temp%10; temp/=10;
digits[0]=temp%10;
temp=i;
int ms100,ls100;
ms100=digits[0]*10+digits[1];
ls100=digits[1]*10+digits[2];
if (is_prime(digits[0]) && is_prime(digits[1]) && is_prime(digits[2]))
{
if (is_prime(ms100) && is_prime(ls100))
{
printf("%d\n",i);
}
}
}
return 0;
}
```

8. ### SaswatPadhi~ Б0ЯИ Τ0 С0δЭ ~

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LOL @ xpi0t0s, you brute-forced the solution for such a simple question !!
I mean, shabbir didn't even mention the word "smallest". So, that was really easy to figure out a 3-digit number.

Congrats nimesh.

@ shabbir:
So, you changed the posting time today (by almost -12 hours) !!
I'll have to wait till 2morrow.

Last edited: Jun 25, 2009
9. ### nimeshNew Member

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xpi0t0s - 237 is not a prime number (237 = 3 * 79) List of Prime Numbers

Thanks Saswat, but the winner is not yet confirmed by Shabbir

10. ### xpi0t0sMentor

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Whoops, you're right, neither are 537 and 737 so the only result is 373. Adding
Code:
```if (is_prime(i))
```
fixed the problem.

11. ### xpi0t0sMentor

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Yes Saswat I brute forced it. I'm obviously not up to your standards.

12. ### shabbirAdministratorStaff Member

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Yes. It was not conditional error but a typo.

Just curious. Nothing to with the competition

So its not predictable.

Logic is also there. 2,3,5,7 are the digits which needs to be filled in the 3 slots.

• 2 and 5 cannot come in the last slot other wise number would not be prime, so it has to be 3 and 7.
• With the above logic 2 and 5 also cannot come in the second slot as the number with those should also be prime.
• Any combination of 5,3,7 or 2,3,7 is divisible by 3
• 7 and 3 cannot be at consecutive places as we need primes by both the numbers.
• so the option left is 373 and 737
• 737 is not prime
Winner is Nimesh and I did not mention smallest largest anything because I knew it has unique solution

nimesh likes this.
13. ### nimeshNew Member

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Cool...
Nice explanation Shabbir. I like it.:2thumbsup

14. ### SaswatPadhi~ Б0ЯИ Τ0 С0δЭ ~

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So, you have implemented a manual version of my random posting time idea

15. ### shabbirAdministratorStaff Member

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To an extent.