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We show that using character sum estimates due to H. Iwaniec leads to animprovement of recent results about the distribution and finding RSA moduli$M=pl$, where $p$ and $l$ are primes, with prescribed bit patterns. We are nowable to specify about $n$ bits instead of about $n/2$ bits as in the previouswork. We also show that the same result of H. Iwaniec can be used to obtain anunconditional version of a combinatorial result of W. de Launey and D. Gordonthat was originally derived under the Extended Riemann Hypothesis.

On RSA Moduli with Almost Half of the Bits Prescribed