Resolution criteria

For the purposes of this prediction, the date of factoring is the date of discovery shown for the first-discovered factor on https://www.mersenne.ca/exponent/1277. "Factored" does not necessarily mean "fully factored."

Background

2^1277-1 is the smallest Mersenne number with no known factors. Attempts to find relatively small factors with the Elliptic Curve Method (ECM) and other algorithms have so far failed, and according to mersenne.ca it is likely that there are no factors with 70 digits or less. ECM still has a small chance to produce a factor, but only one factor with more than 80 digits has ever been found with ECM as of August 2026. If the factors of 2^1277 - 1 are much larger than 80 digits, as is quite likely, it is not feasible to find them with ECM; the factors will most likely have to be found by the Special Number Field Sieve.