Math Is Fun Forum

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

The Pattern Of The Primes.

I have posted this on other topics, but I wanted to make sure everybody has got it!

My theory is simple, Primes have a pattern and I shall tell you what it is.

The pattern is based on primes multiplied together. 2, 6, 30, 210, 2310, 30030.
Then just multiply by the next prime in the series to get, 30030*17=510510 the next number in the series.
From now on you will regard 1 as a prime number as it behaves in much the same way as the primes, but from now on if you see a 1 just remember that it is indeed not a prime.
Okay, let's start with 2.
Write down 2 cross it out, then put a 1 before it. Now just add 2 up to 6........1 3 5. Now times 3 by all no.'s below 2 = 3. Cross it out.
Now let's start with 6. Now add 6 up to 30.............1 5 7 11 13 17 19 23 25 29. Now times 5 by all no.'s below 6 = 5,25. Cross it out.
Now 210. Now add 30 up to 210...........1 7 11 13 17 19 23 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 131 133 137 139 143 149 151 157 161 163 167 169 173 179 181 187 191 193 197 199 203 209. Now times 7 by all no.'s below 30 = 7,49,77,91,119,133,161,203. Cross them out.
Keep doing this and you will generate all the primes.
Note: In using 210 I have used the primes 2,3,5 and 7. The next prime is 11, so I have only generated the primes up to

and so on............................................................................2310 up to

etc.

Last edited by Primenumbers (2015-10-26 14:41:30)

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"Time not important. Only life important." - The Fifth Element 1997

hemiboso

Member

Registered: 2014-10-23

Posts: 4

Re: The Pattern Of The Primes.

Your method is generating the set of natural numbers not divisible by 2, 3 or 5 (aka numbers congruent to {1, 7, 11, 13, 17, 19, 23, 29} modulo 30), which I explore in great depth employing the Prime Spiral Sieve (a spiraling 8-dimensional modulo 30 wheel factorization algorithm that accounts for all prime numbers >5 and their multiplicative multiples, starting with 7^2 -- which is why 49 is the first composite number in the string you've created, followed by 7 x 11=77 ... the 2nd composite number in your sequence, etc.). The algorithm in question (usually called the "Croft Spiral") has been written in several programming languages and is widely used for efficient deterministic (non-probabilistic) prime factorization. Check it out at http://www.primesdemystified.com.

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Re: The Pattern Of The Primes.

Thanks for the post. I have checked out the website. Very interesting!

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"Time not important. Only life important." - The Fifth Element 1997