# 100

This number is a composite.

The first 3 primes add to 10 and the first 3^{2} primes add to 10^{2} = 100. [Moody]

The first century (xx00 to xx99) with no prime is 1671800 to 1671899. [Howell]

2^{100} * 100^{2} + 1 is prime. [Kulsha]

The sum of the fourth powers of all the primes less than 100 is prime. [Patterson]

100*2^213 - 1 is prime. Note that 213*2^100 - 1 is also prime. This is the smallest pair of three-digit numbers with such property. [Opao]

(*n*th prime)!/*n*! + 1 is prime, where *n* = 100. [Firoozbakht]

100 is the smallest perfect square whose summation of the differences between itself and each of its digits, where each difference is raised to the power of the corresponding digit, is equal to a prime number, i.e., (100-1)^1 + (100-0)^0 + (100-0)^0 is prime. [Opao]

100! plus the 101st prime is prime. [Mojdeh]

The smallest perfect square that is the sum of first primes. [Silva]

The number of primes with distinct digits in ascending order. [Capelle]

τ(100*10^{7}) = 100. [Wesolowski]

The largest natural number n equal to the sum of primes smaller or equal to π(n). [Capelle]

The smallest number whose common logarithm is a prime number. [Gudipati]

Sum of two consecutive emirprimes. [Silva]

The number of steps to reach 1 from 100 in the Collatz trajectory equals the number of primes less than or equal to 100, or π(100). The sequence of these numbers begin 1, 2, 4, 81, 98, 99, 100, ... . What's the largest example you can find? [Honaker]

(100-1)*100^100+1 is prime. [Aggarwal]

There are twenty-five primes less than 100. Note that 100 is also the sum of all prime numbers less than twenty-five. [Luen]

π(100) = sum of all odd digits. [Honaker]