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.

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

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.

"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

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; }

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.

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

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

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