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- W80030342 abstract "We introduce a fundamental theorem of prime sieving (FTPS) and show how it illuminates structure on numbers co-prime to a random product of unique prime numbers. This theorem operates on the transition between the set of numbers coprime to any product of unique prime numbers and the new set when another prime number is introduced in the product. We use this to develop tools which exactly count certain gap n-tuples in sets modulo a unique product of prime numbers. 1 Notation Let Pm be the m th prime with the usual ordering Pm < Pm+1. Though 1 is not prime it is co-prime to every number and we include it as P0, the zeroth prime. We count primes strictly by their index so the usual counting works in the sense that 1 is ignored. We begin with collections of random primes which we denote as {P}m having m unique prime numbers chosen at random and ordered by size. By insisting on local ordering we induce a local index count, that is we have if Pa ∈ {P}m and Pb ∈ {P}m and Pa < Pb than a < b. Define their random product as" @default.
- W80030342 created "2016-06-24" @default.
- W80030342 creator A5008245944 @default.
- W80030342 date "2014-07-01" @default.
- W80030342 modified "2023-09-26" @default.
- W80030342 title "A Fundamental Therorem Of Prime Sieving" @default.
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- W80030342 hasPublicationYear "2014" @default.
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