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There is an updated kernel for CentOS-3.1

https://rhn.redhat.com/errata/RHSA-2004-255.html refers.

Updated files are :-

all in updates/i386/RPMS/

kernel-2.4.21-15.0.3.EL.c0.athlon.rpm kernel-2.4.21-15.0.3.EL.c0.i686.rpm kernel-BOOT-2.4.21-15.0.3.EL.c0.i386.rpm kernel-doc-2.4.21-15.0.3.EL.c0.i386.rpm kernel-hugemem-2.4.21-15.0.3.EL.c0.i686.rpm kernel-hugemem-unsupported-2.4.21-15.0.3.EL.c0.i686.rpm kernel-smp-2.4.21-15.0.3.EL.c0.athlon.rpm kernel-smp-2.4.21-15.0.3.EL.c0.i686.rpm kernel-smp-unsupported-2.4.21-15.0.3.EL.c0.athlon.rpm kernel-smp-unsupported-2.4.21-15.0.3.EL.c0.i686.rpm kernel-source-2.4.21-15.0.3.EL.c0.i386.rpm kernel-unsupported-2.4.21-15.0.3.EL.c0.athlon.rpm kernel-unsupported-2.4.21-15.0.3.EL.c0.i686.rpm

These are available at http://mirror.centos.org/3.1/ and should be on all mirrors within a few hours.

To update to the latest version 'yum update kernel' should be sufficient.