100000000001

100000000001 is the integer equal to ten to the eleventh power plus one, written in decimal as 100,000,000,001. It equals 10^11 + 1 and lies between 100,000,000,000 and 100,000,000,002. The number has twelve digits and is odd.

The number is composite. A basic divisibility observation comes from the algebraic identity: for any odd exponent n, a^n + 1 is divisible by a + 1. With a = 10 and n = 11, 10^11 + 1 is divisible by 11, and indeed 100000000001 = 11 × 9090909091. The quotient 9,090,909,091 may have additional factors, but the explicit factorization shows the number is not prime.

In terms of simple properties, 100000000001 is not divisible by 2 or 5 (it ends in 1), and it is congruent to 1 modulo 10. As a member of the family of numbers of the form 10^n + 1 with odd n, it provides a straightforward example of how certain algebraic patterns yield small prime factors, even though the overall number itself is not prime.

Applications and relevance: such numbers are commonly cited in discussions of divisibility, factorization, and testing of algorithms for primality and big-integer arithmetic. They illustrate how the structure a^n + 1 with odd n guarantees a nontrivial factor (a + 1), which is a basic tool in elementary number theory.