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.
God may not play dice with the universe, but something strange is going on with the prime numbers.
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.
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. 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.
The obvious mathematical breakthrough would be development of an easy way to factor large prime numbers.
Twin primes: pairs of prime numbers that are close to each other, almost neighbors, but between them there is always an even number that prevents them from truly touching. If you go on counting, you discover that these pairs gradually become rarer, lost in that silent, measured space made only of ciphers. You develop a distressing presentiment that the pairs encountered up until that point were accidental, that solitude is the true destiny. Then, just when you’re about to surrender, you come across another pair of twins, clutching each other tightly.
Although the prime numbers are rigidly determined, they somehow feel like experimental data.
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.
My work on prime gaps lead to lots of media coverage, some good, some bad, some ugly, and some merely ridiculous. For example, a reporter of our university newspaper, who admitted that he is still learning English, wrote that "Prof. Goldston solved one of the most controversial problems in the prime number theory last month with support from his Turkish partner."
The largest known prime number is 2^32582657-1. I am proud to say that I memorized all its digits-in binary.
Number theorists say that number theory is too complicated, so let's pretend that there is only one prime number, and then let's combine all these results. Surprisingly, sometimes it works.
It never happens that, when we go home and open the refrigerator, we see all infinitely many prime numbers there.
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.
Quadratic reciprocity is the song of love in the land of prime numbers.
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.
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.
The brain is the only kind of object capable of understanding that the cosmos is even there, or why there are infinitely many prime numbers, or that apples fall because of the curvature of space-time, or that obeying its own inborn instincts can be morally wrong, or that it itself exists.
A prime number is one (which is) measured by a unit alone.
or simply:
