**From New Scientist #2387, 22nd March 2003** [link]

Here is a list of properties which a number may or may not have.

1. Several numbers divide into it exactly, but only one of them is prime.

2. It can be written as the sum of two or more consecutive positive integers.

3. It has more than two digits.

4. It is prime.

5. It is over 10000.

6. It is a perfect square.

You can choose any number and write down (in order) the numbers of the statements which are true. For example for the number 135 you would get statements 2 and 3 only, which written as one number gives 23.

There is just one number for which the list of true statements gives the number itself.

Which number?

[enigma1231]

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Recently I added the

prime_factor()routine toenigma.py, which generates the (prime,exponent) pairs in the prime factorisation of a positive integer. This puzzle provides a good opportunity to use it.This Python code runs in 32ms.

Solution:The number is 16.