EXHIBIT 23.1 CONSENT OF INDEPENDENT ACCOUNTANTS We hereby consent to the incorporation by reference in the Registration Statements on Form S-3 (No. 333-107595) and Form S-8 (Nos. 33-18966-99, 33-46724-99, 33-50270-99, 33-57675-99, 33-62394-99, 333-17407-99, 333-25857-99, 333-53912-99, 333-80511-99, 333-107450, and 333-107451) of Noble Corporation of our report dated January 29, 2004 relating to the consolidated financial statements, which appears in this Form 10-K. PricewaterhouseCoopers LLP Houston, Texas March 1, 2004