Why is 57 not a prime number

In different versions it is said to have happened during or after a Grothendieck's talk. Did anybody hear this story from somebody present at Grothendieck's talk?

Edit: Just for the sake of completeness, here is what Georges Elencwajg had to say about this issue extracted from my conversation with him in comments to an answer to this math. The story is not made up: Grothendieck did make that silly blunder, in an exchange after a talk, after being asked to be more concrete by a member of the audience. Of course this doesn't change anything to the fact that Grothendieck was one of the most profound arithmeticians of the 20th century.

And indeed 57 looks a bit prime for some psychological reason Conversely many mathematicians think I'm pulling their leg when I tell them that is prime! I've heard this story a long time ago. I think it is true but I can't prove it since, alas, most of the protagonists are dead. Anyway, this is just an amusing but quite meaningless anecdote: a genius made a lapsus linguae. So what? On the other hand I'm quite sure that Allyn Jackson can't disprove what he strangely calls a legend While it certainly does not confirm nor refutes Grothendieck's episode, the fact that Hermann Weyl did commit this mistake might add some 'substance' to it.

The notion of prime number is of course as old and as primitive as that of the multiplication of natural numbers. Hence it is most surprising to find the distribution of primes among all natural numbers is of such a highly irregular and almost mysterious character. While on the whole the prime numbers thin out the further one gets in the sequence of numbers, wide gaps are always followed again by clusters.

An old conjecture of Goldbach's maintains that there even come along again and again pairs of primes of the smallest possible difference 2, like 57 and A half-century of mathematics. The American mathematical monthly, 58 8 , Factors of 1, 3, 19, 57 Since 57 has more than 2 factors, we can say that 57 is not a prime number. Problem Statements: Is 57 a Prime Number? No Is 57 a Composite Number? Yes Is 57 an Even Number? No Multiples of 57 57, , , , , , , , , Cube Root of 57 3.

No Is 57 a Perfect Square? How do you find the prime factorization of 20? How do you find prime factorization of a number? What is the prime factorization of 44?

See all questions in Prime Factorization. Impact of this question views around the world. You can reuse this answer Creative Commons License. The smallest multiples of 57 are:. To determine the primality of a number, several algorithms can be used. The most naive technique is to test all divisors strictly smaller to the number of which we want to determine the primality here First, we can eliminate all even numbers greater than 2 and hence 4 , 6 , 8 …. Then, we can stop this check when we reach the square root of the number of which we want to determine the primality here the square root is about 7.

Historically, the sieve of Eratosthenes dating from the Greek mathematics implements this technique in a relatively efficient manner.