Computational number theory, also
known as algorithmic number theory, is the study of algorithms for performing
number theoretic computations. The best known problem in the field is the integer factorization, the great common divisor or the least common multiple.The largest known primes, which are usually Mersenne primes, and they were
usually found by GIMPS, the Great Internet Mersenne Prime Search.
But in my opinion, the concepts of
computational number theory could be more comprehensive, covering a wide range,including all the study of number theory by computers. For me, computers are so
important for number theorists, just like telescopes for astronomers.
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