  We use the spectrum tmf to obtain new nonimmersion results for many real
projective spaces RP^n for n as small as 113. The only new ingredient is some
new calculations of tmf-cohomology groups. We present an expanded table of
nonimmersion results. Our new theorem is new for 17% of the values of n between
2^i and 2^i + 2^14 for i > 14.
