| 单词 | prime |
| 释义 | prime It is known that there are infinitely many primes. Euclid's proof argues by contradiction as follows. Suppose that there are finitely many primes p1, p2,…,pn. Consider the number p1p2×… ×pn + 1. This is not divisible by any of p1, p2,…, pn—division by each leaves a remainder of 1—so it is either another prime itself or is divisible by primes not among the pi. It follows that the number of primes is not finite. The notion of a prime number generalizes to that of a prime element in the theory of rings. At any time, the largest known prime is usually the largest known Mersenne prime. There are many deep results in number theory relating to prime numbers, such as Fermat's Two Square Theorem, Bertrand's postulate, and the Green-Tao theorem, and many important open problems, such as Goldbach's conjecture, Legendre's conjecture, Riemann hypothesis, and Twin prime conjecture. See also Fundamental Theorem of Arithmetic, prime number theorem. |
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