The number R₄₉₀₈₁ = (10⁴⁹⁰⁸¹ - 1)/9 = 111...111 (written with 49081 1's) is probably prime. Harvey Dubner announced this in the April 2002 issue of Mathematics of Computation.

It had been previously shown that the repunits R₂, R₁₉, R₂₃, R₃₁₇, and R₁₀₃₁ are primes. It is conjectured that there are infinitely many prime repunits.

The claim that R₄₉₀₈₁ is probably prime is substantiated by the fact that it passes the following "pseudo-primality" test.

Fermat's Little Theorem (not to be confused with Fermat's Last Theorem recently proven by Wiles) states that if p is prime, then p divides a^p - a. Equivalently if p does not divide a^p - a, then p cannot be prime. Given a number p that does not divide 2^p - 2, 3^p - 3, 5^p - 5, etc. for a large number of values, we can be fairly certain that it is prime. However, this does not constitute a proof that p is prime.

One method to actually prove that R₄₉₀₈₁ is prime involves knowing a large number of the prime factors of R₄₉₀₈₀. Dubner gives the current status of that number's factorization, but states that knowing enough factors to determine the primality of R₄₉₀₈₁ will probably require significant breakthroughs in theory and/or computer technology.