Nucor (NUE)

Exhibit 32

Nucor Corporation

Certification of Principal Executive Officer

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

(18 U.S.C. 1350)

In connection with the Annual Report of Nucor Corporation (the “Registrant”), on Form 10-K for the year ended December 31, 2004, as filed with the Securities and Exchange Commission (the “Report”), I, Daniel R. DiMicco, Vice Chairman, President and Chief Executive Officer (principal executive officer) of the Registrant, certify, pursuant to § 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. § 1350), that to the best of my knowledge:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Registrant.

A signed original of this written statement required by Section 906, or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to the Company and will be retained by the Company and furnished to the Securities and Exchange Commission or its staff upon request.

The foregoing certification is being furnished to the Securities and Exchange Commission as an exhibit to the Form 10-K and shall not be considered filed as part of the Form 10-K.