Number of Prime Numbers
There are infinitely many prime numbers. Another way of saying this is that the sequence
- 2, 3, 5, 7, 11, 13, ...
of prime numbers never ends. This statement is referred to as Euclid's theorem in honor of the ancient Greek mathematician Euclid, since the first known proof for this statement is attributed to him. Many more proofs of the infinitude of primes are known, including an analytical proof by Euler, Goldbach's proof based on Fermat numbers, Fürstenberg's proof using general topology, and Kummer's elegant proof.
Read more about this topic: Prime Number
Famous quotes containing the words number of, number, prime and/or numbers:
“Can a woman become a genius of the first class? Nobody can know unless women in general shall have equal opportunity with men in education, in vocational choice, and in social welcome of their best intellectual work for a number of generations.”
—Anna Garlin Spencer (1851–1931)
“To finish the moment, to find the journey’s end in every step of the road, to live the greatest number of good hours, is wisdom. It is not the part of men, but of fanatics, or of mathematicians, if you will, to say, that, the shortness of life considered, it is not worth caring whether for so short a duration we were sprawling in want, or sitting high. Since our office is with moments, let us husband them.”
—Ralph Waldo Emerson (1803–1882)
“If Montaigne is a man in the prime of life sitting in his study on a warm morning and putting down the sum of his experience in his rich, sinewy prose, then Pascal is that same man lying awake in the small hours of the night when death seems very close and every thought is heightened by the apprehension that it may be his last.”
—Cyril Connolly (1903–1974)
“The only phenomenon with which writing has always been concomitant is the creation of cities and empires, that is the integration of large numbers of individuals into a political system, and their grading into castes or classes.... It seems to have favored the exploitation of human beings rather than their enlightenment.”
—Claude Lévi-Strauss (b. 1908)