Hide and seek with Spiderman(The previous answer was wrong)

Number Theory Level 3

There are 500 windows in a building and Spiderman knows that behind one window, there is a villain. Spiderman labelled each window from 1-500 and using his Spider Senses, received hints to which window the villain is hiding behind. The following are the hints he received:

  • The number comprises three digits.

  • The number is a prime number in a prime position.

  • The number has a digital sum of 11.

  • The square of the number has six distinct digits.

From these hints, find out which window is the villain hiding behind

Explanation

  • A prime number in a prime position is where you label each prime in their order. For example :

1st - 2

2nd - 3

3rd - 5

4th - 7

If the number is in a prime position(e.g. 2nd, 3rd, llth), it is a prime in a prime position. The first prime in a prime position is therefore 3.

  • A digital sum of a number is the sum of all its digits. For example, the digital sum of 532 is 5+3+2 = 10.


The answer is 353.

Charlton Teo by Charlton Teo , 21, Singapore

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1 solution

Bill Bell
Jul 30, 2014

Using the Python sympy library:

>>> from sympy import *

>>> for w in range(101,499):

... if isprime(w) :

... if isprime (sieve.search(w)[0]):

... if sum([int(c) for c in str(w)]) == 11:

... if len(list(set([c for c in str(w*w)])))==6 :

... print w

...

353

sieve provides a list of primes that is extended as required. Its search function returns the position of a prime number within it as a pair of identical integers. The [0] thingy simply selects the first of them.

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