Sieve of Sundaram

In mathematics, the sieve of Sundaram is a simple deterministic algorithm for finding all prime numbers up to a specified integer. It was discovered by Indian mathematician S. P. Sundaram in 1934.

Start with a list of the integers from 1 to n. From this list, remove all numbers of the form i + j + 2ij where:

The remaining numbers are doubled and incremented by one, giving a list of the odd prime numbers (i.e., all primes except 2) below 2n + 2.

The sieve of Sundaram sieves out the composite numbers just as sieve of Eratosthenes does, but even numbers are not considered; the work of "crossing out" the multiples of 2 is done by the final double-and-increment step. Whenever Eratosthenes' method would cross out k different multiples of a prime ${\displaystyle 2i+1}$, Sundaram's method crosses out ${\displaystyle i+j(2i+1)}$ for ${\displaystyle 1\leq j\leq \lfloor k/2\rfloor }$.

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