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Change AUTO_INCREMENT PRIMARY KEY to partition

I need to split a MySQL table among temporary data (the field starts in the following table).

CREATE TABLE `table1` (
  `id` bigint(20) NOT NULL AUTO_INCREMENT, 
  `fk_id` bigint(20) NOT NULL,  
  `begin` bigint(20) NOT NULL,     
  PRIMARY KEY (`id`),
  KEY `FK1E57078DB20EC268` (`fk_id`)
) ENGINE=MyISAM AUTO_INCREMENT=10443288 DEFAULT CHARSET=latin1

When I try to break as follows:

alter table table1 partition by range (begin) (
PARTITION until_2010_07 VALUES LESS THAN (1280620800000),
PARTITION 2010_08 VALUES LESS THAN (1283299200000),
PARTITION 2010_09 VALUES LESS THAN (1285891200000),
PARTITION 2010_10 VALUES LESS THAN (1288569600000),
PARTITION 2010_11 VALUES LESS THAN (1291161600000),
PARTITION 2010_12 VALUES LESS THAN (1293840000000),
PARTITION from_2011 VALUES LESS THAN MAXVALUE
);

I get a MySQL error: ERROR 1503 (HY000): A PRIMARY KEY must include all columns in the table partitioning function

As I understand from the mysql document, the partition column should belong to the primary key. The problem for me is that I want to change PRIMARY_KEY as compound, i.e. PRIMARY KEY ('id','fk_id','begin')without changing existing identifier columns (because this is the field used in the application to generate bookmarks, so renumbering identifiers is not an option)

How can I change PRIMARY_KEY so that I can perform partitioning?

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//drop auto_increment capability
alter table table1 change column id id BIGINT NOT NULL;
//in one line, drop primary key and rebuild one
alter table table1 drop primary key, add primary key(id,fk_id,begin);
//re add the auto_increment capability, last value is remembered
alter table table1 change column id id BIGINT NOT NULL AUTO_INCREMENT;
//build the partition
alter table table1 partition by range (begin) ( 
    PARTITION until_2010_07 VALUES LESS THAN (1280620800000), 
    PARTITION 2010_08 VALUES LESS THAN (1283299200000), 
    PARTITION 2010_09 VALUES LESS THAN (1285891200000), 
    PARTITION 2010_10 VALUES LESS THAN (1288569600000), 
    PARTITION 2010_11 VALUES LESS THAN (1291161600000), 
    PARTITION 2010_12 VALUES LESS THAN (1293840000000), 
    PARTITION from_2011 VALUES LESS THAN MAXVALUE 
);

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