"Prime numbers must of necessity be regarded as beautiful."
"The distribution of prime numbers is one of the biggest mysteries in all of math."
"Infinity is pretty big. If we counted each prime number, 2, 3, 5, 7, it would go on forever."
"The function always increases by 1 at each prime number."
"There are infinitely many prime numbers."
"Primes are faster lenses. With primes, I'm able to get faster lenses that let in more light."
"...if it is composite one of its factors must be less than ten point nine and the only primes less than that are two, three, five, and seven..."
"Prime numbers... integers that are only divisible by themselves and one."
"Just like the ordinary primes, Gaussian primes go on forever. And what I showed is that the Gaussian primes contain constellations of any shape."
"He showed that no matter how far you go down the number line, there will be these primes that get clumped bizarrely close together."
"No matter how far you go along, there's always going to be some bigger primes and in fact infinitely many bigger primes that differ by just exactly two."
"They can provide witness for your good character - or more specifically they provide a witness for if a number is prime or not. And there's nothing we enjoy more in mathematics than working out if a number is prime or not."
"But if a single witness says not prime, not prime. That's it, the number is kicked out of the court or whatever this the prime test place, they are turfed out they are not a prime number the moment of witness says no."
"The primes are the building blocks from which all other whole numbers are constructed."
"There are an infinite number of primes."
"All sufficiently large even numbers are the sum of a prime and the product of at most two primes."
"Primes grow like weeds, seeming to obey no other law than that of chance. Nobody can predict where the next one will sprout."
"Primes are important and that's because this definition is actually precisely the right definition and it's incredibly useful for mathematicians."
"Primes are the fundamental building blocks of numbers comparable to atoms that are the building blocks of nature."
"It is not at all difficult to understand why zeta secretly captures information about primes."
"One standard question that turns out to be a very interesting question that one asks in the field of algebraic number theory is given such a polynomial p of x, for which primes P."
"Primes, oh my God! What would have been done with these things?"
"The primes are like the atomic elements of integer multiplication."
"The primes have weird patterns that we don't fully understand."
"The primes are this sort of fascinating combination of three things."
"So, Vinogradov's theorem tells you that if n is big enough, every odd number is the sum of three primes."
"The primes are separable into some pseudo-random set and some nice looking set. What does the nice looking part look like? It's sort of a weighted version of that."
"Primes are the fundamental building blocks of all numbers."
"For any prime, there will always be a bigger prime."
"Every prime squared is one bigger than a multiple of 24."
"All natural numbers are either prime numbers or they can be expressed as a product of prime numbers."
"Euclid proved that anyone who tried to write down the primes in some great big table would be writing forever because he proved that there are infinitely many primes."
"The primes never run out; there are infinitely many of these indivisible numbers."
"The Riemann hypothesis, if it's true, there's this pattern in the primes... it will explain to us why there aren't any patterns in the primes."
"Nature gave us these numbers which didn't seem to have any pattern to them at all, just noisy numbers, but by changing our perspective, looking at things in a new way, we suddenly found where the real pattern is."
"The symbols are the language of the primes."
"There are infinitely many primes."
"Every even number greater than 2 is the sum of two primes."
"N can be written as a sum of squares if and only if every prime of the form 4k plus 3 in the factorization of n occurs with an even exponent."
"Every positive whole number can be decomposed, can be expressed in a unique way as products of prime numbers."
"The lowest common multiple of all the prime numbers between one and six is thirty."
"Every odd number greater than five can be written as the sum of three primes."
"There are infinitely many primes that are congruent to one mod four."
"There are infinitely many such primes."
"Primes feel random for at least two reasons: first, they don't appear as much in our lives... second, we don't have a formula for primes."
"Prove that there are infinitely many prime numbers."
"Prime factorization is writing the number as a product of its primes."
"The Riemann hypothesis has strong implications on the distribution of prime numbers and on the growth of many other important functions."
"If you add any two different prime numbers, the answer will never be a square number."