How to pass BigInteger from java to Postgres?

Support for BigInteger was added in JDBC 4.1 (Java 7), somehow I had missed that when I originally wrote this answer.

Specifically section 3.1 Overview of changes of the JDBC 4.1 specification states:

• Additional Mappings to Table B-4, Mapping from Java Object to JDBC Types
  [..]
  Support was also added to map java.lang.BigInteger[sic] to JDBC BIGINT.
• Additional Mappings to Table B-5, Performed by setObject and setNull between Java Object Types and Target JDBC Types
  [..]
  Allow conversion of java.lang.BigInteger[sic] to CHAR, VARCHAR, LONGVARCHAR, and BIGINT.

I'm not sure how well this is supported across drivers.

Original answer

The JDBC specification does not include support for BigInteger; you either need to use a different datatype (eg BigDecimal with scale 0), or find out if the PostgreSQL driver offers some implementation specific way to set a BigInteger value.