  We present evidence that it is unlikely that the streaming instability (SI)
can form planetesimals from mm grains inside axisymmetric pressure bumps. We
conducted the largest simulation of the SI so far (7 million CPU hours),
consisting of a large slice of the disk with mm grains, a solar-like
dust-to-gas ratio ($Z = 0.01$), and the largest pressure bump that does not
cause gravitational instability (GI) in the particle layer. We used a high
resolution of $1000/H$ to resolve as many SI unstable modes as possible. The
simulation produced a long-lived particle over-density far exceeding the SI
criteria (i.e., a critical solid abundance to headwind parameter ratio $Z/\Pi$)
where strong clumping would occur if these conditions were present over an
extended region of the disk; yet we observed none. The likely reason is that
the time it takes particles to cross the high-$Z/\Pi$ region ($t_{\rm cross}$)
is shorter than the growth timescale of the SI ($t_{\rm grow}$). We propose an
added criterion for planetesimal formation by the SI -- that $t_{\rm cross} >
t_{\rm grow}$. We show that any bump larger than the one in this run would form
planetesimals by the GI instead of the SI. Our results significantly restrict
the pathways to planet formation: Either protoplanetary disks regularly form
grains larger than 1~mm, or planetesimals do not form by the SI in axisymmetric
pressure bumps. Since bumps large enough to induce the GI are likely
Rossby-wave unstable, we propose that mm grains may only form planetesimals in
vortices.
