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\section{Abstract}  I investigate the use of the notation $d;n$, meaning repeat the digit $d$, $n$ times. The convergence of rational expressions and the primality of larger sequences are explored. A way of ruling some non-trivial numbers out in $\mathrm{log}_10(digits)$ $\mathrm{log}_{10}(digits)$  is found for prime searches. The relationship of numbers written in such notation and thier prime decompositions is investigated.