Every odd perfect number has a prime factor which exceeds 10⁶

Abstract

It is proved here that every odd perfect number is divisible by a prime greater than <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="10 Superscript 6"> <mml:semantics> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> <mml:annotation encoding="application/x-tex">10^{6}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.