Find my number

Number Theory Level 2

My number:

  1. Is a 3-digit number.
  2. All its digits are prime digits.
  3. A number formed by its 1st 2 digits is prime.
  4. So is the number formed by its last 2 digits.
  5. It is the smallest number satisfying the above conditions.

Find it.

Rem: The digits in my number do not have to be distinct


The answer is 237.

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Danish Ahmed by Danish Ahmed , 24, India

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2 solutions

Danish Ahmed
Jan 15, 2015

a) Prime digits are 2,3,5,7

b) 2 is the smallest of these.

c) 23 is the smallest two digit prime using these digits that starts with 2. So, problem is solved if I can just form a two digit prime starting with 3 and one of those digits.

d) Oh yes, I can, it is 37. (32, 33 and 35 are not prime)

So final answer is 237.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Brock Brown
Jan 15, 2015 
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from math import sqrt
def is_prime(x):
    if x < 2:
        return False
    i = 2
    while i <= sqrt(x):
        if x % i == 0:
            return False
        i+=1
    return True
for n in xrange(100,1000):
    solved = True
    s = str(n)
    for digit in s:
        if not is_prime(int(digit)):
            solved = False
            break
    if not is_prime(int(s[:2])):
        solved = False
    if not is_prime(int(s[1:3])):
        solved = False
    if solved:
        print "Answer:", n
        break

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