## Tuesday, June 23, 2015

### Special properties of number 23 (Today’s Date)

1. According to the birthday paradox, in a group of 23 (or more) randomly chosen people, the probability is more than 50% that some pair of them will have the same birthday. For 60 or more people, the probability is greater than 99 per cent!
2. 23 is the smallest prime number with consecutive digits.
3. 23! is 23 digits long.
4. Twenty-three is the sum of three other, consecutive, prime numbers; 5, 7 and 11. It is the first prime number showing this characteristic.
5. The sum of the first 23 primes is 874, which is divisible by 23, a property shared by few other numbers.
6. Repeat the digit 1, 23 times like this: 11,111,111,111,111,111,111,111 and you obtain a prime number.
7. Every positive whole number can be written as the sum of eight cubes (including 0^3 when necessary) except 23 (and 239). Those two numbers require 9 cubes.
8. Nobel Prize-winning economist John Forbes Nash, the inspiration for the film A Beautiful Mind, was obsessed with the number 23 and it featured prominently in his nervous breakdown. He claimed that Pope John XXIII was in fact himself, the evidence being that 23 was his favorite number. Nash also published only 23 scientific articles.
9. The axis of the planet Earth is 23.5 degrees to the vertical. The tropics of Cancer
and Capricorn are at 23.5˚ north and south respectively.
10. The Chemical Element Vanadium has an atomic number of 23.
11. Normal human sex cells have 23 chromosomes. Each parent contributes 23 chromosomes to the start of human life. The nuclei of cells in human bodies have 46 chromosomes made out of 23 pairs.

#### 1 comment:

1. This site is designed to investigate non-negative integer solutions to the equation

n = x2 + y2 + z3 +w3

I conjecture that n = 23 is the only non-negative integer which does not have non-negative integer solutions to this equation.

I have run a Visual Basic 6.0 program against the first 2,000,000,000,000 integer values of n , and for each of these except n=23 there exist non-negative integers x, y, z, w such that this equation has a solution.

### NUMBER OF TRAILING ZEROES IN A PRODUCT (PART -2)

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