# Exponential speedup of prime sieving

It is surprisingly easy to show that when n equals a primorial (product of successive primes) the inner spacing between co-prime members of Z_n forms a palindrome whose length is one less than the size of the set. Since you can construct the set for the next primorial boundary from your current boundary by expanding the residuals you can double the speed of each new set's construction by taking advantage of this internal symmetry. Meaning at each step you only need to identify half of each new sets co-prime members, the rest is solved by taking advantage of the palindrome.

Please read the paper in the link, I have a lot more equally cool and surprising proofs.

Please read the paper in the link, I have a lot more equally cool and surprising proofs.

## All Answers (3)

Piotr Sawuk· University of Viennabtw, as a rule of thumb: every proof related to primes which is making use of probability and statistical methods, most likely is implicitely using RH or similar, because you need such hypothesis to prove that primes behave randomly and obey laws of statistics (not that I have seen such proof). so when I read a paper about primes, as soon as the author mentions randomness and statistics I stop reading, especially when the paper claims to prove some hypothesis.

Russell Letkeman· University of ManitobaThere is no implicit use of RH

Patrick Solé· Institut Mines-TélécomCan you help by adding an answer?