**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.

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

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:

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"

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