We prove that there exists a universal constant c such that any finite primitive permutation group of degree n with a non-trivial point stabilizer is a product of no more than class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316303453&_mathId=si1.gif&_user=111111111&_pii=S0021869316303453&_rdoc=1&_issn=00218693&md5=34923039bf178b4af3b9c8c40d458459" title="Click to view the MathML source">clognclass="mathContainer hidden">class="mathCode"> point stabilizers.