QRA is pleased to announce that one of its core development team, Douglas Staple, has set the world record for computing the prime counting function. The prime counting function is usually denoted by π(x), and counts the number of primes less-than or equal to x. Previously, the largest x for which π(x) was known was x = 1025: Dr. Staple calculated π(x) for x = 1026.
Dr. Staple performed the calculation using an enhanced version of the combinatorial method originally due to Meissel. Starting from the version of the algorithm published by T. Oliveira e Silva, he incorporated modifications permitting shared- and distributed-memory parallelism, as well as numerous improvements resulting in constant- factor reductions in time and space.
Calculations were performed on the Guillimin, Briarée, and Colosse supercomputers from McGill University, Université de Montréal, and Laval Université, managed by Calcul Québec and Compute Canada.
When asked why Dr. Staple sought this achievement, he said although the results have applications within number theory, his drive came from helping develop the underlying algorithm, and refining his skills in number theory and computer science.
Dr. Staple extends his gratitude to Prof. Karl Dilcher for guiding his education in number theory, and for his comments and suggestions regarding this calculation. We at QRA are proud to have Doug as part of our team and would like to once again congratulate him on his achievement.
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