## Monday, October 27, 2008

### 1969

1969 = 11 x 179.

1969 is a composite number not ending in zero that yields a prime number when turned upside down: 6961 is prime.

1969
is the only known counterexample to a conjecture about modular Ackermann functions.

Now useful in computer science, the
Ackermann function was first studied by David Hilbert and Wilhelm Ackermann about 90 years ago. It grows faster than an exponential function or even a multiple exponential function.

The Ackermann function
A(x, y) is defined for integer x and y in the following way:
A(x, y) is y + 1 if x = 0; A(x – 1, 1) if y = 0; A(x – 1), A(x, y – 1) otherwise.

We can also restrict the range of the Ackermann function to a finite set, defining the mod-
n Ackermann function. For a given n, the numbers initially bounce around wildly as x increases, but nearly always stabilize to a certain value or an alternating pair of values.

According to Jerrold W. Grossman of Oakland University, the only value of
n less than 4,000,000 for which the standard mod-n Ackermann function does not stabilize is n = 1969. Why this is so remains a mystery.

Neil Armstrong became the first man to step onto the moon's surface on July 20,
1969.

Source: Jon Froemke and Jerrold W. Grossman. 1993. A mod-n Ackermann function, or what’s so special about 1969? American Mathematical Monthly 100(February):180-183.

#### 1 comment:

Rod Ball said...

There's a slight error (typo) in the definition of Ackermann function:

3rd part should be:
"A(x-1,A(x,y-1)) otherwise"
and not:
"A(x-1),A(x,y-1) otherwise"