A method of factoring and the factorization of 𝐹₇

Abstract

The continued fraction method for factoring integers, which was introduced by D. H. Lehmer and R. E. Powers, is discussed along with its computer implementation. The power of the method is demonstrated by the factorization of the seventh Fermat number <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F 7"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>7</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{F_7}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and other large numbers of interest.