1111111111111

1111111111111 is the 13-digit repunit in base 10, a number consisting entirely of the digit 1. It can be written as (10^13 − 1)/9 and equals 1,111,111,111,111. In decimal notation it is the repunit R13, the thirteenth member of the sequence of numbers formed by repeating the digit 1.

The number is composite. It factors as 53 × 79 × 265,371,653, with 53 and 79 being prime. The remaining factor, 265,371,653, is itself an odd integer. The divisors 53 and 79 arise because 10^13 ≡ 1 mod p for p = 53 and p = 79, a consequence of the multiplicative order of 10 modulo those primes.

As a repunit, 1111111111111 is part of a broader family of numbers known as repunits: integers of the form (10^n − 1)/9 for a positive integer n. A general property is that if n is composite, Rn is composite; if Rn is prime, n must be prime. For base 10 repunits, only certain values of n yield prime Rn; these prime-length repunits are rare.

In practical terms, numbers like 1111111111111 occasionally appear in mathematical examples, testing, and recreational problems involving digit patterns, divisibility, and factorization. There is no notable historical event specifically tied to this particular repunit.