My code looks like this for now - and it works fine....

What I would like to do is:

EITHER restrict the query to items where Primary_Contacts_Umantis_ID__c and Umantis_NUM_ID__c are equal (both a formula fields of type TEXT.

OR remove any items from the variable SCOPE where Primary_Contacts_Umantis_ID__c and Umantis_NUM_ID__c are NOT equal...

hope this is clear?

global class MassUpdateParentsProject implements Database.Batchable<sObject>{
	
	global final string query; 
	
	global MassUpdateParentsProject ()
	{
	   query = 'SELECT id, Umantis_Account_ID__c, Ultimate_Parent_Account__c, Ultimate_Parent_Id__c, Related_Contact__c, Umantis_NUM_ID__c, Primary_Contacts_Umantis_ID__c FROM Opportunity WHERE Project_Code__c !=\'Budget\' ';
	}
	
	global Database.QueryLocator start(Database.BatchableContext BC){
	
	   return Database.getQueryLocator(query);
	}
	
	global void execute(Database.BatchableContext BC, List<Opportunity> scope){
	
	  for(Opportunity o : scope){
	  	Integer i;
	  	if(o.Umantis_Account_ID__c !=null){
	  		i = Integer.valueOf(o.Umantis_Account_ID__c);
	  	}
	  	else{
	  		i=0;
	  	}
	  		if(i >= 600 && o.Related_Contact__c!=null){
	  			o.Ultimate_Parent_Account__c = o.Ultimate_Parent_Id__c;
	  		}
	  }
	  update scope;
	}
	
	
	global void finish(Database.BatchableContext BC){
	  // Get the ID of the AsyncApexJob representing this batch job  
	  // from Database.BatchableContext.    
	  // Query the AsyncApexJob object to retrieve the current job's information.  
	
	 AsyncApexJob a = [Select Id, Status, NumberOfErrors, JobItemsProcessed,
	   TotalJobItems, CreatedBy.Email
	   from AsyncApexJob where Id =:BC.getJobId()];
	
	  // Send an email to the Apex job's submitter notifying of job completion.  
	  Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
	  String[] toAddresses = new String[] {a.CreatedBy.Email};
	  mail.setToAddresses(toAddresses);
	  mail.setSubject('Apex Sharing Recalculation ' + a.Status);
	  mail.setPlainTextBody('The batch Apex job processed ' + a.TotalJobItems +
	    ' batches with '+ a.NumberOfErrors + ' failures.');
	
	  Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });
	}	
}