2 is the only even prime.

But the total number of primes is infinite.

Therefore the probability that a given prime number is even is 1 over infinity, or zero.

Hence it’s impossible for a prime number to be even — and 2 does not exist.

2 is the only even prime.

But the total number of primes is infinite.

Therefore the probability that a given prime number is even is 1 over infinity, or zero.

Hence it’s impossible for a prime number to be even — and 2 does not exist.

5^{5} + 4^{5} + 7^{5} + 4^{5} + 8^{5} = 54748

Let’s say that the densest human head of hair contains 200,000 strands, and that the human population is 6 billion. That means there’s a group of at least 30,000 people today who have precisely the same number of hairs on their heads.

Do you see why?

Suppose the earth were a perfect sphere and you fitted a belt around its equator.

The belt would be 40 million meters long. If you now increased its length by a mere 5 meters, how high would it ride above the earth’s surface?

The answer, surprisingly, is 0.8 meters — well above the current limbo record.

1634 = 1^{4} + 6^{4} + 3^{4} + 4^{4}

A pangram is a sentence that uses each letter of the alphabet exactly once:

CWM FJORD BANK GLYPHS VEXT QUIZ.

“Carved symbols in a mountain hollow and on the bank of a fjord irritated an eccentric person.” They’re a bit awkward in English, so here’s the same idea using numbers. Each of these (valid) equations uses the digits 1-9 exactly once:

42 × 138 = 5796

27 × 198 = 5346

39 × 186 = 7254

48 × 159 = 7632

28 × 157 = 4396

4 × 1738 = 6952

4 × 1963 = 7852

Even better: The numbers 3 and 51249876, between them, use all 9 digits — and so does their product, 153749628.

Imagine a large sheet of rice paper one-thousandth of an inch thick. Tear it in half and stack the pieces, then tear the stack in half and stack those, and so on. If you could do this 50 times in succession, how tall would the final stack be?

A. 0.6 inches

B. 22.84 feet

C. 17 million miles

Surprisingly, the answer is 17 million miles:

2^{50} ply × 0.001 inches/ply

= 1.12589991 × 10^{12} inches

= 17,769,884.9 miles