Magento: Category Details On Product Page

On product page, generally its located in
app/design/frontend/{designPackageName}/{themeName}/template/catalog/product/view.phtml

put the following code on view.phtml file:

<?php
$_helper = $this->helper('catalog/output');
    $_category_detail=Mage::registry('current_category');
    echo  $_category_detail->getName(); //gives current  category name
    echo $_category_detail->getId(); //gives current category id
?>