Discoveries / number-theory

The Banks-Martin Conjecture on Primitive Sets

Banks and Martin conjectured in 2013 that for a primitive set $A$ and any set $Q$ of primes, the Erdos sum of the members of $A$ composed only of primes in $Q$ is at most the corresponding sum over $Q$ itself. The unrestricted form turned out to be false once $Q$ is allowed to contain $2$; Lichtman proposed a revised form restricted to odd primes. That revised conjecture, long viewed as a unifying master theorem for the area, is proved here.