Updated Java packages are available for CentOS 5, 6, and 7:

[CentOS-announce] CESA-2016:1776 Important CentOS 5 java-1.6.0-openjdk Security Update
[CentOS-announce] CESA-2016:1776 Important CentOS 6 java-1.6.0-openjdk Security Update
[CentOS-announce] CESA-2016:1776 Important CentOS 7 java-1.6.0-openjdk Security Update

CESA-2016:1776 Important CentOS 5 java-1.6.0-openjdk Security Update

CentOS Errata and Security Advisory 2016:1776 Important

Upstream details at : https://rhn.redhat.com/errata/RHSA-2016-1776.html

The following updated files have been uploaded and are currently
syncing to the mirrors: ( sha256sum Filename )

i386:
d6d0f386a6f9d22a393a247f7cd7c58b1239c6ae7b313828b87fcdfa65a68b1e java-1.6.0-openjdk-1.6.0.40-1.13.12.4.el5_11.i386.rpm
003823d694e9316c0f58b2cef8ec2f1c5a785a0548a5ae82b9c8c00ed42a5e3a java-1.6.0-openjdk-demo-1.6.0.40-1.13.12.4.el5_11.i386.rpm
a901afc3d0ab6313a4b1f95e7af4a6d452925643899807365453285232c320db java-1.6.0-openjdk-devel-1.6.0.40-1.13.12.4.el5_11.i386.rpm
daf59f8a6ba2bb995a58c9bf836130882508d4cd0df923078e11ba7b622437cd java-1.6.0-openjdk-javadoc-1.6.0.40-1.13.12.4.el5_11.i386.rpm
26112915bd3ce6e56f376abe8d6c7c7c3ec34bd291ab024171941082191c5ab2 java-1.6.0-openjdk-src-1.6.0.40-1.13.12.4.el5_11.i386.rpm

x86_64:
7facd58d760041b41707cbc04fea6404e5760aa89a64b09a63d0f642453e601c java-1.6.0-openjdk-1.6.0.40-1.13.12.4.el5_11.x86_64.rpm
acdd1a149a650802bab713348efed3cea94c3fa1e4a3eedef0b14dc530f63e11 java-1.6.0-openjdk-demo-1.6.0.40-1.13.12.4.el5_11.x86_64.rpm
faa0bb044816096b5c322ed889500fab4226b773add9da74ac3785533a06233b java-1.6.0-openjdk-devel-1.6.0.40-1.13.12.4.el5_11.x86_64.rpm
9098ab7a6fa89b673952660495ff0fe4814ba653bcb36e58d3b40514398fd057 java-1.6.0-openjdk-javadoc-1.6.0.40-1.13.12.4.el5_11.x86_64.rpm
ac196f3ec06eb8008d9104d9bb8b27ca9142e2bdaff848053c7ad25f9765656b java-1.6.0-openjdk-src-1.6.0.40-1.13.12.4.el5_11.x86_64.rpm

Source:
dfc80c864a12dd91aa6b026969da5dfceeafbce0c3ee8862ee8ec892943ddae6 java-1.6.0-openjdk-1.6.0.40-1.13.12.4.el5_11.src.rpm

CESA-2016:1776 Important CentOS 6 java-1.6.0-openjdk Security Update

CentOS Errata and Security Advisory 2016:1776 Important

Upstream details at : https://rhn.redhat.com/errata/RHSA-2016-1776.html

The following updated files have been uploaded and are currently
syncing to the mirrors: ( sha256sum Filename )

i386:
85a42b9dc7548e3f8b86cacd1609fc14bc8e8e519a4ce4858e15d320d09d6c9d java-1.6.0-openjdk-1.6.0.40-1.13.12.6.el6_8.i686.rpm
a44a315add63888bdb90fd5c6dec550396d8c6a3ac3daa0dba40f07520927d6c java-1.6.0-openjdk-demo-1.6.0.40-1.13.12.6.el6_8.i686.rpm
358bda472da2634563588274cd6f8f8095dd7af95fc6ecc1b28c6eabcde63a1b java-1.6.0-openjdk-devel-1.6.0.40-1.13.12.6.el6_8.i686.rpm
4365bf6681d15abcb1967eb66c365ea867ed39e9272a6b2babfadbf9dc5faf70 java-1.6.0-openjdk-javadoc-1.6.0.40-1.13.12.6.el6_8.i686.rpm
64b7542290a9531ee58d69027f060fabb9d87bd0a3c1c56856e4993a0b69048c java-1.6.0-openjdk-src-1.6.0.40-1.13.12.6.el6_8.i686.rpm

x86_64:
867d64c8e0b0a7ab80aa705b96f64ea8c2a8637374dca25707180cb9fe3a55a8 java-1.6.0-openjdk-1.6.0.40-1.13.12.6.el6_8.x86_64.rpm
3ec19d952f64d6a3b5cdbb5d0012117d842128474f880f621a77f67381e66149 java-1.6.0-openjdk-demo-1.6.0.40-1.13.12.6.el6_8.x86_64.rpm
ec5818e8e2670df9b68140febdbcccb1cab99cf016b7fc1f57442bbe03579ac1 java-1.6.0-openjdk-devel-1.6.0.40-1.13.12.6.el6_8.x86_64.rpm
e582a9589e7f51391dbb900eb0b9e6d7872e1382a1ab23aa9f41fb64254c5109 java-1.6.0-openjdk-javadoc-1.6.0.40-1.13.12.6.el6_8.x86_64.rpm
05cca14dd0a3ba8fa4e8c794ac83610766104ce9215141148da92730754db124 java-1.6.0-openjdk-src-1.6.0.40-1.13.12.6.el6_8.x86_64.rpm

Source:
2ca712c6daf3a2597d52228823cf01e58a77613f07bd201ae1739a32d32090db java-1.6.0-openjdk-1.6.0.40-1.13.12.6.el6_8.src.rpm

CESA-2016:1776 Important CentOS 7 java-1.6.0-openjdk Security Update

CentOS Errata and Security Advisory 2016:1776 Important

Upstream details at : https://rhn.redhat.com/errata/RHSA-2016-1776.html

The following updated files have been uploaded and are currently
syncing to the mirrors: ( sha256sum Filename )

x86_64:
f2a27f7b6061bed7fc189feb3b25b63319d8b41f6d0c67c3feebcc297aa7487f java-1.6.0-openjdk-1.6.0.40-1.13.12.5.el7_2.x86_64.rpm
b685ba29ba96991483b3120219338e90919708d21b2ac4a4b68100ad022ce381 java-1.6.0-openjdk-demo-1.6.0.40-1.13.12.5.el7_2.x86_64.rpm
0a136da5d7ed5a505effabe1218ff47245c84c4cbb2fa59cfbe5d248dceb4310 java-1.6.0-openjdk-devel-1.6.0.40-1.13.12.5.el7_2.x86_64.rpm
3ec9d367a743952bf34c36152e087e9b071f1d07fa7cac3fc7bed03a2748e559 java-1.6.0-openjdk-javadoc-1.6.0.40-1.13.12.5.el7_2.x86_64.rpm
2eeabee30ab8056b61e4b2f258b973586edc47eb9d23aed27c972f12022bef40 java-1.6.0-openjdk-src-1.6.0.40-1.13.12.5.el7_2.x86_64.rpm

Source:
e9a9b3b63cdfd7cec648b4893ba5f09c1c3ee68a9e3e9079ad5c67d7aafac10f java-1.6.0-openjdk-1.6.0.40-1.13.12.5.el7_2.src.rpm