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- W1873609844 abstract "The probability of finding a prime multiplet, i.e., a sequence of primes $p$ and $p+a_i$, $i=1... m$, being all primes where $p$ is some prime less than the integer $n$ is naively $1/log(n)^{m+1}$. It is shown that, in reality, it is proportional to this probability by a constant factor which depends on $a_i$ and $m$ but not on $n$, for large $n$. These constants are appellated as PDF (prime distribution factors). Moreover, it is argued that the PDF depend on the $a_i$ in a week way, only on the prime factors of the differences $a_i-a_j$ and not on their exponents. For example $p$ and $p+2^s$ will have the exact same probability for all integer $s>0$. The exact formulae for the PDF ratios are given. Moreover, the actual 'basic' PDF's are calculated exactly and are shown to be bigger than 1, which indicates that primes 'repel' each other. An exact asymptotic formula for the number of basic multiplets is given." @default.
- W1873609844 created "2016-06-24" @default.
- W1873609844 creator A5058057746 @default.
- W1873609844 date "2003-04-29" @default.
- W1873609844 modified "2023-09-27" @default.
- W1873609844 title "On the distribution of prime multiplets" @default.
- W1873609844 hasPublicationYear "2003" @default.
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