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Thread: Primes Ordering Themselves

  1. #1 Primes Ordering Themselves 
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    I have found something about primes directly from the numbers.

    Except for 2 and 3 there are just six types of other primes. The idea is to let the primes order themselves into subsets as follows.

    1) Compute the recursive sum of digits, then the 6 types are those with matching recursive sum of digits. See the following list:

    primes: 5 7 11 13 17 19
    SigmaR: 5 7 2 4 8 1
    Kind: 5 7 11 13 17 19

    2) List the primes in their order together with their kind. Then patterns can be computed from every series of increasing primes (according to the kind). The list starts:

    Primes: 23, 29, 31, 37 | 41, 43, 47, 53 |
    Kind:___5 11 13 19__| 5 7 11 17____|
    Pattern: []*[][]*[]____| [][][]*[]*_____|

    where the pattern essentially compares the kind with 5, 7, 11, 13, 17, 19 with symbol [] if the kind occurs in the string and * if not. Matching patterns defines subsets satisfying item 3.

    3) Patterns that match (not singletons like *[]****) have difference of their first members being divisable by 6.

    The first matching pattern with [][][]*[]* is:

    Primes: 347, 349, 353, 359
    Kind: 5 7 11 17

    and 347 - 41 = 306 and is divisable by 6. Item 3 was tested untill 1733.


    It also matters what isn't there - Tao Te Ching interpreted.
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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Just out of curiosity, but you do know that the easy way to compute the recursive sum of digits is just to take the number mod 9?


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  4. #3  
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    Didn't know. So it is remainder after dividing by 9?
    It also matters what isn't there - Tao Te Ching interpreted.
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  5. #4  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Yeah, with the caveat that if you would get a 0, the answer is really 9 (unless the original number was 0).
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  6. #5  
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    The problem is to prove item 3 for all primes. I can't see a starting point.
    It also matters what isn't there - Tao Te Ching interpreted.
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