PrimeEnergy Resources Corporation Description of Securities Registered Pursuant to Section 12 of the Securities Exchange Act of 1934

Exhibit 4.1

PRIMEENERGY RESOURCES CORPORATION

DESCRIPTION OF SECURITIES REGISTERED

PURSUANT TO SECTION 12 OF THE

SECURITIES EXCHANGE ACT OF 1934

The common stock of PrimeEnergy Resources Corporation (“we,” “us” and “our”) is listed and principally traded on the Nasdaq Stock Market (“Nasdaq”) under the ticker symbol “PNRG.” Our authorized capital stock consists of 2,810,000 shares of common stock, par value $0.10 per share.

The following summary of the material terms of our capital stock, Restated Certificate of Incorporation (the “certificate of incorporation”) and Amended and Restated Bylaws (the “bylaws”) does not purport to be complete and is qualified in its entirety by reference to the provisions of applicable law and to our certificate of incorporation and bylaws.

Common Stock

Each share of common stock entitles the holder to one vote on all matters on which holders are permitted to vote, including the election of directors. There are no cumulative voting rights. Accordingly, holders of a plurality of the total votes entitled to vote in an election of directors will be able to elect all of the directors standing for election. The holders of the common stock will share equally on a per share basis any dividends when, as and if declared by the board of directors out of funds legally available for that purpose. If we are liquidated, dissolved or wound up, the holders of our common stock will be entitled to a ratable share of any distribution to stockholders, after satisfaction of all of our liabilities. Our common stock has no preemptive or conversion rights or other subscription rights. There are no redemption or sinking fund provisions applicable to our common stock. All outstanding shares of our common stock are fully paid and nonassessable.

Election and Removal of Directors

Our board of directors must consist of not less than three nor more than fifteen members. The exact number of directors is fixed from time to time by resolution of the board. Each director shall be elected by a plurality of the votes cast at each annual meeting of stockholders and each director so elected shall hold office until the next annual meeting of stockholders and until such director’s successor is duly elected and qualified, or until such director’s earlier death, resignation or removal. In addition, any director or the entire Board of Directors may be removed from office at any time, with or without cause, by the affirmative vote of the holders of at least a majority in voting power of our issued and outstanding capital stock. Any vacancy occurring on the board of directors or any committee thereof may be filled only by a majority of the directors then in office, though less than a quorum, or by a sole remaining director.

Stockholder Meetings

Our bylaws provide that special meetings of our stockholders may be called by either the chairman of our board of directors, if there be one, or by our president or secretary, and shall be called by any such officer at the request in writing of our board of directors, a committee of our board of directors that has been duly designated by the board of directors and whose powers and authority include the power to call such meetings, or stockholders owning a majority of our capital stock issued and outstanding and entitled to vote on the matter for which such special meeting of stockholders is called.

Stockholder Action by Written Consent

Our certificate of incorporation provides that any action required or permitted to be taken at any annual or special meeting of the stockholders by the stockholders of our company may be taken without a meeting, without prior notice and without a vote, if a consent or consents in writing, setting forth the action so taken, shall be executed by the holders of outstanding stock having not less than the minimum number of votes that would be necessary to authorize or take such action at a meeting at which all shares entitled to vote thereon were present and voted.

Amendment of Bylaws

Our bylaws may generally be altered, amended or repealed, in whole or in part, and new bylaws may be adopted, by approval of either the holders of a majority of the outstanding capital stock entitled to vote thereon or by a majority of our board of directors then in office.

Advance Notice Requirements for Stockholder Proposals and Director Nominations

Our Bylaws provide that stockholders seeking to bring business before an annual meeting of stockholders, or to nominate candidates for election as directors at an annual or special meeting of stockholders, must provide timely notice to us thereof in writing within the time periods specified in our Bylaws. Our Bylaws also specify requirements as to the form and content of a stockholder’s notice.

Limitation on Liability of Directors

No person serving as a director of our board of directors shall have any personal liability to us or our stockholders for monetary damages for breach of fiduciary duty as a director, provided that, such restriction on personal liability shall not eliminate or limit the liability of a director (i) for any breach of the director’s duty of loyalty to us or our stockholders, (ii) for acts or omissions not in good faith or which involve intentional misconduct or a knowing violation of law, (iii) for unlawful payment of any dividend or unlawful stock purchase or redemption under Section 174 of the Delaware General Corporation Law (“DGCL”); or (iv) for any transaction from which the director derived an improper personal benefit.

Our bylaws provide that, to the fullest extent permitted by law, we will indemnify any officer or director of our company against all damages, claims and liabilities arising out of the fact that the person is or was our director or officer, or served another corporation, partnership, joint venture, trust or other enterprise at our request as a director, officer, employee or agent.

Expenses, including attorneys’ fees, incurred by our directors or officers in defending any civil, criminal, administrative or investigative action, suit or proceeding shall be paid by us in advance of the final disposition of such action, suit or proceeding upon receipt of an undertaking by or on behalf of such director or officer to repay such amount if it shall ultimately be determined that such person is not entitled to be indemnified by us. Such expenses, including attorneys’ fees, incurred by our former directors and officers or other employees and agents or by persons serving at our request as directors, officers, employees or agents of another corporation, partnership, joint venture, trust or other enterprise may be so paid upon such terms and conditions, if any, as we deem appropriate.

Anti-Takeover Effects of Delaware Law

We are a Delaware corporation and are subject to Section 203 of the DGCL. Section 203 provides that we may not engage in a broad range of “business combinations” with any “interested stockholder” for a three-year period following the time that the person became an interested stockholder unless:

Generally, a business combination includes a merger, consolidation, asset or stock sale or other transaction resulting in a financial benefit to the interested stockholder. Subject to certain exceptions, an interested stockholder is a person who, together with that person’s affiliates and associates, owns, or within the previous three years owned, 15% or more of our voting stock. Under Section 203, the restrictions described above also do not apply to specific business combinations proposed by an interested stockholder following the announcement or notification of designated extraordinary transactions involving the corporation and a person who had not been an interested stockholder during the previous three years or who became an interested stockholder with the approval of a majority of the corporation’s directors, if such extraordinary transaction is approved or not opposed by a majority of the directors who were directors prior to any person becoming an interested stockholder during the previous three years or were recommended for election or elected to succeed such directors by a majority of such directors.

Section 203 could prohibit or delay mergers or other takeover or change in control attempts with respect to us and, accordingly, may discourage attempts to acquire us.

Transfer Agent and Registrar

We may from time to time maintain one or more transfer offices or agencies and registry offices or agencies at such place or places as may be determined from time to time by the board of directors, subject to the rules and regulations of any securities exchange or quotation system on which our securities are listed or quoted for trading.