abilityolz.blogg.se - A list of prime numbers from 1 to 100

Since we know that i + j + 2ij = n, this can easily be calculated as u = (n-i)/(1+2*i) J) The inner loop index j should start from i and run up to the point it can go with the current i value.

We can easily solve the positive value for i by using the quadratic formula and that is the line with t = (Math.sqrt(4+8*n)-2)/4, I) So we have to find the the max value i and j can take when they are equal. As we need i and j values to calculate the numbers to cross out, i + j + 2ij up to n let's see how we can approach. Sieve of Sundaram is only fast if the loop indices start and end limits are correctly selected such that there shall be no (or minimal) redundant (multiple) elimination of the non-primes. It's proof is beautifully explained here.

The final stage is in fact the auto discounting of the even numbers. Once we cross out every i + j + 2ij, the remaining numbers are doubled and oddified (2n+1) to reveal a list of prime numbers. To select which integers to cross out the rule is i + j + 2ij ≤ n where i and j are two indices and n is the number of the total elements. Just like the Sieve of Erasthotenes, the Sieve of Sundaram algorithm also crosses out some selected integers from the list. The fundamental theorem of arithmetic says that any number can be expressed by a unique product of prime numbers.For(var j = i j <= u j++) a = true įor(var i = 0 i<= n i++) !a & r.push(i*2+1)

Here is a interesting sequence of prime numbers in which all of the digits have circles in them:.

It also looks like the word Google if you type it into a calculator and look at it upside down!

The Greek mathematician Euclid studied prime numbers in 300BC.

The largest prime number known has around 13 million digits!.

The number 1 used to be considered a prime number, but it generally isn't anymore.

Prime numbers are often used in cryptography or security for technology and the internet.

There are an infinite number of prime numbers.

All even numbers greater than 2 are not prime numbers.

The number 1 is not considered a prime number.

(hint: we promise the answer is "no" and they are, therefore, prime numbers). Take a look at a few of them and see if you can figure out any other number that they can be divided by other than the number itself or the number 1. Ah, but it can be divided by 5, so it is not a prime number. The number 4 is not a prime number because it can be divided evenly by 4, 2, and 1. The number 5 is a prime number because it cannot be divided evenly by any other numbers except for 5 and 1. Okay, maybe that's a bit hard to understand. A prime number is a whole number with exactly two factors, itself and 1.