Memtest86+ is thorough, stand alone memory test for Intel/AMD x86 architecture systems.  BIOS based memory tests are only a quick check and often miss failures that are detected by Memtest86+.

For updates go to the Memtest86+ web page:

        http://www.memtest.org

Installation (Linux Only)

============================
Memtest86+ is a stand alone program and can be loaded from either a disk
partition or from a floppy disk.

To build Memtest86+:
   1) Review the Makefile and adjust options as needed.
   2) Type "make"

This creates a file named "memtest.bin" which is a bootable image.  This
image file may be copied to a floppy disk or lilo may be used to boot this
image from a hard disk partition.

To create a Memtest86+ bootdisk
   1) Insert a blank write enabled floppy disk.
   2) As root, Type "make install"

To boot from a disk partition via lilo
   1) Copy the image file to a permanent location (ie. /memtest).
   2) Add an entry in the lilo config file (usually /etc/lilo.conf) to boot
      Memtest86+.  Only the image and label fields need to be specified.
      The following is a sample lilo entry for booting Memtest86+:

        image = /memtest
        label = memtest

   3) As root,  type "lilo"

      At the lilo prompt enter memtest to boot Memtest86+.

If you encounter build problems a binary image has been included (precomp.bin).
To create a boot-disk with this pre-built image do the following:
   1) Insert a blank write enabled floppy disk.
   2) Type "make install-precomp"

Red Hat Enterprise Linux ships a memory test tool called memtest86+. It is a bootable utility that tests physical memory by writing various patterns to it and reading them back. Since memtest86+ runs directly off the hardware it does not require any operating system support for execution.

    This tool is available as an RPM package from Red Hat Network (RHN) as well as a boot option from the Red Hat Enterprise Linux rescue disk.

    To boot memtest86+ from the rescue disk, you will need to boot your system from CD 1 of the Red Hat Enterprise Linux installation media, and type the following at the boot prompt (before the Linux kernel is started):

boot: memtest86

    If you would rather install memtest86+ on the system, here is an example of how to do it on a Red Hat Enterprise Linux 5 machine registered to RHN:

# yum install memtest86+

    For the Red Hat Enterprise Linux version 4, perform the following command to install memtest86+. Make sure current system has been registered to RHN:

# up2date -i memtest86+

    Then you will have to configure it to run on next reboot:

# memtest-setup

    After reboot, the GRUB menu will list memtest. Select this item and it will start testing the memory.
        Please note that once memtest86+ is running it will never stop unless you interrupt it by pressing the Esc key. It is usually a good idea to let it run for a few hours so it has time to test each block of memory several times.

https://access.redhat.com/site/solutions/15693

memtester

       At some condition, memory is the one of the suspcious part, or you just want have a quick test. memtester  is an effective userspace tester for stress-testing the memory subsystem.  It is very effective at finding intermittent and non-deterministic faults.

Example: note: on 32 bit machine, there might be a 4GB memory limit

NOTE
       memtester must be run with root privileges to mlock(3) its pages.  Testing memory without locking the pages in place is mostly  pointless and slow.

EXIT CODE
       memtester’s exit code is 0 when everything works properly.  Otherwise, it is the logical OR of the following values:

       x01    error allocating or locking memory, or invocation error

       x02    error during stuck address test

       x04    error during one of the other tests

Other way:

I found this solution on nixCraft, I think it makes sense and quicker.

First find out memory site using free command.


It shows that this server has 32GB memory,

free reports by k and use 1050 is to make sure file memtest is bigger than physical memory.  To get better performance, use proper bs size, for example 2048 or 4096, depends on your local disk i/o,  the rule is to make bs * count > 32 GB.
run
If you see md5sum mismatch in different run, you have faulty memory guaranteed.
The theory is simple, the file /home/memtest will cache data in memory by filling up all available memory during read operation. Using md5sum command you are reading same data from memory.