Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.
Prime numbers are what is left when you have taken all the patterns away. I think prime numbers are like life. They are very logical but you could never work out the rules, even if you spent all your time thinking about them.
The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
Why add prime numbers? Prime numbers are made to be multiplied, not added.
3 is a prime, 5 is a prime, and 7 is a prime. Why bother with non-prime numbers when the primes can do everything?
Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.
Mathematicians deal with large numbers sometimes, but never in their income.
The prime ideal is a princess of the world of ideals. Her father is the prince 'Point' in the world of geometry. Her mother is the princess 'Prime Numbers' in the world of numbers. She inherits the purity from her parents.
The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic. It has engaged the industry and wisdom of ancient and modern geometers to such an extent that it would be superfluous to discuss the problem at length. ... Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.
It never happens that, when we go home and open the refrigerator, we see all infinitely many prime numbers there.
After decades of faithful study, ecologists have begun to fathom hidden likenesses among many interwoven systems. ...a canon of nature's laws, strategies, and principles...
Nature runs on sunlight.
Nature uses only the energy it needs.
Nature fits form to function.
Nature recycles everything.
Nature rewards cooperation.
Nature banks on diversity.
Nature demands local expertise.
Nature curbs excesses from within.
Nature taps the power of limits.
Relations between pure and applied mathematicians are based on trust and understanding.
Namely, pure mathematicians do not trust applied mathematicians, and applied mathematicians do not understand pure mathematicians.
If all sentient beings in the universe disappeared, there would remain a sense in which mathematical objects and theorems would continue to exist even though there would be no one around to write or talk about them. Huge prime numbers would continue to be prime, even if no one had proved them prime.
What is natural does not have to be a representation of something. I'm now working on a thing that is a reconstruction of a starry sky, and yet I'm making it without a given from nature. Someone who says he uses a theme from nature can be right, but also someone who says he uses nothing at all.
I, Galileo, son of the late Vicenzo Galilei, swear that I never said that the prime numbers are useless. What I said was that you cannot count lunar craters by counting 2, 3, 5, 7.
3 is prime, 5 is prime, 7 is prime. According to some ancient manuscripts 9 is not a prime number, but beyond the distant horizon of the oceans, in the New World that I am going to discover, there are surely lots of them.