101 (number) - Definition and Overview

101 is the natural number following 100 and preceding 102.

In mathematics

101 is the 26th prime number and a palindromic number (therefore also a palindromic prime). The next prime is 103, with which it comprises a twin prime. Because the period length of its reciprocal is unique among primes, 101 is a unique prime.

101 is the sum of five consecutive primes (13 + 17 + 19 + 23 + 29). Given 101, the Mertens function returns 0.

101 is a centered decagonal number.

For a 3-digit number in base 10, this number has a relatively simple divisibility test. The number is split into groups of four, starting with the rightmost four, and added up to produce a 4-digit number. If this 4-digit number is of the form 1000a + 100b + 10a + b (where a and b are integers from 0 to 9), such as 3232 or 9797, or of the form 100b + b, such as 707 and 808, then the number is divisible by 101. This might not be as simple as the divisibility tests for numbers like 3 and 5, and it might not be terribly practical, but it is simpler than the divisibility tests for other 3-digit numbers.

In other fields

101 is also:

• The atomic number of mendelevium, an actinide.
• The designation of US Highway 101, which runs from California to Washington.
• In universities, sometimes the course number of basic or entry-level courses. Also used in titles of books to indicate the book is meant for a beginner. At universities with four-digit course numbers, the equivalent course number is 1001 or 1010.
• In the title of the book The Hundred and One Dalmatians by Dodie Smith (and the various movie versions thereof).
• The number of keys on a standard PC alphanumeric keyboard, including 12 or so function keys, cursor keys, and a numeric keypads and various other additions to the QWERTY typewriter keyboard.
• According to Books in Print, more books are now published with a title that begins with '101' than '100'. They usually describe or discuss a list of items, such as 101 ways to ... or 101 questions and answers about .... This marketing tool is used to imply that the customer is given a little extra information beyond books that include only 100 items. Some books have taken this marketing scheme even further with titles that begin with '102', '103', or '1001'.
• Room 101 in George Orwell's novel Nineteen Eighty-Four
• The year AD 101 or 101 BC.

• See also 101st km