NUMBERS

Million and billion

A million seconds is 12 days. A billion seconds is 32 years.

Percentages

Percentages are reversible. 8% of 25 is the same as 25% of 8.

3435

3435 has the property that the sum of its digits to their powers is 3435.

27 (3 cubed) + 256 (4 power 4) + 27 (3 cubed) + 3125 (5 power 5) = 3435.

142857

142857, the six repeating digits of 1/7, 0.142857, is a cyclic number.

• 1 × 142,857 = 142,857
• 2 × 142,857 = 285,714
• 3 × 142,857 = 428,571
• 4 × 142,857 = 571,428
• 5 × 142,857 = 714,285
• 6 × 142,857 = 857,142

7 × 142,857 = 999,999 (= 142,857 + 857,142)

333333331

• 31 (prime number)
• 331 (prime number)
• 3331 (prime number)
• 33331 (prime number)
• 333331 (prime number)
• 3333331 (prime number)
• 33333331 (prime number)

333333331 (not a prime number)

1000000000000066600000000000001

Belphegor's Prime, a prime number that is also a palindrome, contains two sets of 13 zeros with 666 in the centre, and is 13 backwards digits long. It is named after Belphegor, one of the seven princes of Hell, who tempts people with the gift of discovery and invention.

Shakespeare

William Shakespeare was born on 23 April 1564 and died on 23 April 1616. 23 + 23 = 46. Shakespeare was 46 when the King James Bible was completed, and 'William Shakespeare' is an anagram of 'Here was I, like a psalm'. So let's look at Psalm 46. The 46th word is 'shake' and the 46th word from the end is 'spear'.