3,139,971,973,786,634,711,391,448,651,577,269,485,891,759,419,122,938,744,591,877,656,925,789,747,974,914,319,422,889,611,373,939,731 produces reversible primes in each row, column and diagonal when distributed in a 10×10 square.

Diagram by HT Jens Kruse Andersen.

## Repunit Primes

Write the digit “1” exactly 317 times, and you get a palindromic prime number. Moreover, 317 itself is a prime number!

## “Magic” Factorials

There are many fun facts regarding the factorials. For instance:

- 0! = 1 by convention. As weird as it may sound, this is a fact that we must remember.

- The number of zeroes at the end of
*n*! is roughly*n*/4. - 70! is the smallest factorial larger than a
.*googol* - The sum of the reciprocals of all factorials is
.*e* - Factorials can be extended to fractions, negative numbers and complex numbers by the
.*Gamma function*

It is possible to “peel” each layer off of a factorial and create a different factorial, as shown in the neat number pattern below. A prime pattern can be found when adding and subtracting factorials. Alternating adding and subtracting factorials, as shown in the picture, yields primes numbers until you get to 9! Continue reading ““Magic” Factorials”

## Prime Fractions

Did you know? You can write the number 1 as a sum of 48 different fractions, where every numerator is 1 and every denominator is a product of exactly two primes.

This problem is related to the Egyptian fractions.