/sci/ - Science & Math

That's just the sieve of Eratosthenes. Look at when they eliminate all numbers divisible by 3. There are two kinds of numbers divisible by 3, the odd and the even, and the pattern that repeats throughout all numbers is
a, (divisible by 3, odd), b, c, (divisible by 3, even), d
The numbers a, b, and "divisible by 3, even" are even, so they can't be prime numbers. The first number divisible by 3 also can't be a prime.
Primes can only be c and d in this notation. The even number divisible by 3 is also divisible by 6, so it can be expressed as 6*k. Therefore, c and d are 6*k +/- 1, and so are all primes.

>>9275437
If I understand it correctly, the book is talking about the case where you're using the sieve of Eratosthenes to get the list of prime numbers up to and including n. I think the part you quoted is there to explain that you don't have to cross out multiples of m = 11, 13, etc, when you're only trying to find the primes up to n = 100, this is why it talks in the context of n and not m.
The reason you don't get it may be that you don't get the difference between a run of the mill prime finding algorithm and a sieve.

>>7422386
1 being prime means you need to make an exception for it with the sieve of Eratosthenes, and you might consider that sieve to be what's really "going on" rather than the almost equivalent divisor definition.

Sieve of Eratosthenes

Definition: A natural number (i.e. 1, 2, 3, 4, 5, 6, etc.) is called a prime or a prime number if it has exactly two positive divisors, 1 and the number itself.

The number 2 is prime but the number 1 is excluded to uphold the fundamental theorem of arithmetic.

en.wikipedia.org/wiki/Prime_number

>>6042774

this

>>5621316

Is every number that is not evenly divisible by 2, 3, 5, or 7 prime?