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PDF-inlowestterms,weclaimthat(1)logq(x)~(x)logxwhere~(x)=(x)(Cx1=5:5 PDF document

e C0xlogx6c qx 6j2zxj1 xwhichgivesx1InotherwordsbetweenCx155andxifxislargeenoughthereisatleastoneprimeItisclearthatthisimpliesthestatedboundObviouslythisproofisquiteridicu

e C0~(x)logx6c q(x) 6j(2)z(x)j1 xwhichgives~(x)1:Inotherwords betweenCx1=5:5andx ifxislargeenough thereisatleastoneprime.Itisclearthatthisimpliesthestatedbound.Obviouslythis\proof"isquiteridicu

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