Quantum random number generators (QRNGs) are an increasingly popular method to obtain information-theoretically provable random keys for cryptographic applications. Here, we experimentally demonstrate a probable prime generation protocol using a vacuum-based QRNG and compare its output with the one yielded by an electronic noise source. The quantum source significantly outperformed the classical scheme for lengths smaller than 128 bits, with increases of up to 837.1% in the number of unique primes being reported. By mapping the input noise to a uniform distribution, this figure was additionally increased by up to 844.3% and the output statistical distribution for small primes significantly improved.