UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                           WASHINGTON, D.C.  20549


                                 SCHEDULE 13D


                  UNDER THE SECURITIES EXCHANGE ACT OF 1934
                             (AMENDMENT NO. 3)*



                           PrimeEnergy Corporation
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                               (Name of Issuer)


                        Common Stock, $.10 par value
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                        (Title of Class of Securities)

                                  74158E104
                     -----------------------------------
                                (CUSIP Number)

                                James F. Gilbert

           4015 Holland #101, Dallas, TX 75291  (214) 526-2030
--------------------------------------------------------------------------------
                 (Name, Address and Telephone Number of Person
               Authorized to Receive Notices and Communications)


                             September 25, 2006
                     -----------------------------------
           (Date of Event which Requires Filing of this Statement)


If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(b)(3) or (4), check the following box / /.

Check the following box if a fee is being paid with the statement /X/. (A fee
is not required only if the reporting person: (1) has a previous statement on
file reporting beneficial ownership of more than five percent of the class of
securities described in Item 1; and (2) has filed no amendment subsequent
thereto reporting beneficial ownership of five percent or less of such class.)
(See Rule 13d-7.)

NOTE: Six copies of this statement, including all exhibits, should be filed
with the Commission. See Rule 13d-1(a) for other parties to whom copies are to
be sent.

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities,
and for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be
deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise subject to the liabilities of that section of
the Act but shall be subject to all other provisions of the Act (however, see
the Notes).


                             Page 1 of 5 Pages

                                 SCHEDULE 13D

CUSIP NO.  74158E104                                           PAGE 2 OF 5 PAGES



--------------------------------------------------------------------------------
 1    NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

           Matthias Eckenstein

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 2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) /  /
                                                                        (b) /  /

--------------------------------------------------------------------------------
 3    SEC USE ONLY



--------------------------------------------------------------------------------
 4    SOURCE OF FUNDS*

           PF (See Item 3. herein)

--------------------------------------------------------------------------------
 5    CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO
      ITEMS 2(d) or 2(e)                                                    /  /



--------------------------------------------------------------------------------
 6    CITIZENSHIP OR PLACE OF ORGANIZATION

          Switzerland

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                               7     SOLE VOTING POWER

          NUMBER OF                       225,829 See Item 5.

           SHARES              -------------------------------------------------
                               8     SHARED VOTING POWER
        BENEFICIALLY
                                          -0-
          OWNED BY
                               ------------------------------------------------
            EACH               9     SOLE DISPOSITIVE POWER

          REPORTING                       1,829 See Item 5.

           PERSON              ------------------------------------------------
                               10    SHARED DISPOSITIVE POWER
            WITH
                                          -0-

-------------------------------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

           225,829 See Item 5.

--------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
                                                                            /  /



--------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

           6.9

--------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON*

           IN

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                     *SEE INSTRUCTION BEFORE FILLING OUT!
        INCLUDED BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
       (INCLUDING EXHIBITS) OF THE SCHEDULE, AND SIGNATURE ATTESTATION.





                                                               Page 3 of 5 pages

Item 1. Security and Issuer.

        This Amendment No. 3 to Schedule 13D relates to the Common Stock, $.10
par value, (the "Common Stock") of PrimeEnergy Corporation, a Delaware
corporation ("PrimeEnergy"). The principal executive office of PrimeEnergy is
located at One Landmark Square, Stamford, Connecticut 06901.

Item 2. Identity and Background.

        This Amendment No. 3 to Schedule 13D is being filed on behalf of Mr.
Matthias Eckenstein. Mr. Eckenstein, who is a citizen of Switzerland, is an
investor, architect and developer. His business address is Solothurner Strasse
94, 4008 Basel, Switzerland. Mr. Eckenstein is at present a Director of
PrimeEnergy, the issuer of the securities to which this Schedule relates and has
held that position since August, 1989.

        Mr. Eckenstein has not, during the past five years, (a) been convicted
in a criminal proceeding (excluding traffic violations or similar
misdemeanors), or (b) been a party to a civil proceeding of a judicial or
administrative body of competent jurisdiction and as a result of such
proceeding was or is subject to a judgment, decree or final order enjoining
further violations of, or prohibiting or mandating activities subject to,
federal or state securities laws or finding any violation with respect to such
laws.

Item 3. Source and Amount of Funds or Other Consideration.

        The shares of the Common Stock beneficially held by Mr. Eckenstein were
acquired utilizing personal funds of Mr. Eckenstein.

        No borrowed funds were used in connection with the purchase or
acquisition of the shares of the Common stock beneficially owned by Mr.
Eckenstein.

                                                               Page 4 of 5 pages

Item 4. Purpose of Transaction.

        See Item 5. herein with respect to transactions in the Common Stock by
Mr. Eckenstein in the sixty day period prior to the date of this Amendment No.
3.

        The shares of the Common Stock beneficially held by Mr. Eckenstein were
acquired as an investment. As noted, Mr. Eckenstein is a Director of
PrimeEnergy. Although Mr. Eckenstein may develop other plans or proposals in the
future, at present he has no plans or proposals which relate to or would result
in:

        (a)  The acquisition by any person of additional securities of the
issuer, or the disposition of securities of the issuer; (b) an extraordinary
corporate transaction, such as a merger, reorganization or liquidation,
involving the issuer or any of its subsidiaries; (c) a sale or transfer of a
material amount of assets of the issuer or of any of its subsidiaries; (d) any
change in the present Board of Directors or management of the issuer, including
any plans or proposals to change the number or term of Directors or to fill any
existing vacancies on the Board; (e) any material change in the present
capitalization or dividend policy of the issuer; (f) any other material change
in the issuer's business or corporate structure, including but not limited to,
if the issuer is a closed-end investment company, any plans or proposals to make
any changes in its investment policy for which a vote is required by Section 13
of the Investment Company Act of 1940; (g) changes in the issuer's charter,
bylaws or instruments corresponding thereto or other actions which may impede
the acquisition of control of the issuer by any person; (h) causing a class of
securities of the issuer to be delisted from a national securities exchange or
to cease to be authorized to be quoted in an inter-dealer quotation system of
a registered national securities association; (i) a class of equity securities
of the issuer becoming eligible for termination of registration pursuant to
Section 12(g)(4) of the Act; or (j) any action similar to any of those
enumerated above.

Item 5. Interest in Securities of the Issuer.

        Mr. Eckenstein is the beneficial owner of an aggregate of 225,829 shares
of the Common Stock, of which 1,829 shares are held of record and beneficially,
and as to which he has sole voting and dispositive power. As to 224,000 shares,
which are held of record as to 112,000 shares by each of his two adult
children, Mr. Eckenstein has sole voting power, pursuant to Voting Agreements
each dated September 25, 2006, between Mr. Eckenstein and each of his two adult
children, Corinne Eckenstein and Gabriel Eckenstein. Mr. Eckenstein has no
dispositive power as to such 224,000 shares and no pecuniary interest in such
shares.

        On August 11, 2006, Mr. Eckenstein sold 15,000 shares of the Common
Stock to PrimeEnergy for $70.00 per share. On September 25, 2006, Mr.
Eckenstein transferred by gift 112,000 shares of the Common Stock to each of
his two adult children. There have been no other transactions in the Common
Stock by Mr. Eckenstein in the past sixty days.

        In its Form 10-Q for the quarter ended June 30, 2006, filed with the
Commission, PrimeEnergy reported 3,257,977 shares of Common Stock outstanding.
Based on that filing, Mr. Eckenstein may be deemed the beneficial owner of 6.9%
of the Common Stock.

                                                               Page 5 of 5 pages

Item 6. Contracts, Arrangements, Understandings or Relationships with Respect
to Securities of the Issuer.

        There are no contracts, arrangements or understandings of any kind,
legal or otherwise, between Mr. Eckenstein and any person with respect to any
securities of the issuer except the Voting Agreements between Mr. Eckenstein and
his adult children described in Item 5. herein. As noted, Mr. Eckenstein is a
Director of PrimeEnergy.

Item 7. Material Required to be Filed as Exhibits.

        The following exhibits are filed herewith:

        Exhibit 3.1  Voting Agreement dated September 25, 2006, between Corinne
                     Eckenstein and Matthias Eckenstein

        Exhibit 3.2  Voting Agreement dated September 25, 2006, between Gabriel
                     Eckenstein and Matthias Eckenstein

                                   Signature

        After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

Dated:  October 3, 2006



                                         /s/ Matthias Eckenstein
                                         --------------------------------------
                                         Matthias Eckenstein