Sam Ruben Abraham

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Sincerely, Ad Orientem (talk) 05:35, 8 July 2020 (UTC)   (Leave me a message)

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Ad Orientem (talk) 05:35, 8 July 2020 (UTC)

The Six-Series Prime Number Sieve

This is an idea for a prime number sieve which I came across this week. I'm not sure about its authenticity, but here's how it goes:

1. 1. Write 2, 3 on top.
2. 2. Write 5 ( = 2 + 3) and 7 ( = 2² + 3) below 2 and 3 respectively.
3. 3. With 5 as beginning term and common difference 6, write an AP of the form 5 + (k - 1)×6 in a column below 5.
4. 4. Do step 3 below 7 with 7 as the beginning term.
5. 5. Starting with 5 in the first column, remove all numbers of the form 5 + (k - 1)×5×6 [except 5 (k = 1)]
6. 6. Do the same with the other numbers coming under 5 (let the number be 'n') , by removing numbers of the form n + (k - 1)×6×n [except the numbers at k = 1]
7. 7. Execute steps 5 & 6 under the column of 7, starting with 7 as the first number used.

I tried this algorithm and found that only prime numbers appeared to be coming out of the sieve. What I want to know are the following:

• Has this algorithm ever been discovered before ?
• If not, how efficient is this algorithm ?
• How efficient will this be once translated into a computer program ?

--Sam Ruben Abraham (talk) 05:52, 8 July 2020 (UTC)