# 101 number

101 (one hundred [and] one) is the natural number following 100 and preceding 102.

 Template:Numbers 100s Cardinal one hundred [and] one Ordinal 101st (one hundred [and] first) Factorization prime Roman numeral CI Binary 1100101 Hexadecimal 65 Hebrew קא (Qof Alef)

## 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 (making 101 a Chen prime). Because the period length of its reciprocal is unique among primes, 101 is a unique prime. 101 is an Eisenstein prime with no imaginary part and real part of the form ${\displaystyle 3n-1}$.

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.

101 is also: