Two existing algorithms that count representations as sums of consecutive primes are analyzed, giving O(x log x) time with sublinear memory, and run to 10^14, producing the first integer with 14 representations and heuristic yes-answers to Moser's four questions.
Algorithmic number theory
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Analysis of Algorithms for Moser's Problems on Sums of Consecutive Primes
Two existing algorithms that count representations as sums of consecutive primes are analyzed, giving O(x log x) time with sublinear memory, and run to 10^14, producing the first integer with 14 representations and heuristic yes-answers to Moser's four questions.