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https://github.com/trizen/julia-scripts/blob/master/Math/elliptic-curve_factorization_method.jl and https://github.com/trizen/julia-scripts/blob/master/Math/continued_fraction_factorization_method.jl are two possible significant algorithmic improvements mentioned in https://github.com/JuliaMath/Primes.jl/issues/49. The elliptic curve method in particular looks like a good compromise of speed and performance. It is (according to wikipedia) the best algorithm for numbers up to around 60 digits and is only around 70 lines of code.
https://github.com/trizen/julia-scripts/blob/master/Math/elliptic-curve_factorization_method.jl and https://github.com/trizen/julia-scripts/blob/master/Math/continued_fraction_factorization_method.jl are two possible significant algorithmic improvements mentioned in https://github.com/JuliaMath/Primes.jl/issues/49. The elliptic curve method in particular looks like a good compromise of speed and performance. It is (according to wikipedia) the best algorithm for numbers up to around 60 digits and is only around 70 lines of code.