This is not a duplicate question, so here is a solution that might work for you:
$productId = {PRODUCT_ID};
$orders = array();
$collection = Mage::getResourceModel('sales/order_item_collection')
->addAttributeToFilter('product_id', array('eq' => $productId))
->load();
foreach($collection as $orderItem) {
$orders[$orderItem->getOrder()->getIncrementId()] = $orderItem->getOrder();
}
You’ll end up with an array of orders that contains the orderitem for this {PRODUCT_ID}.
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