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FORM 4                                                     OMB APPROVAL
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[ ] CHECK THIS BOX IF NO                            OMB Number:      3235-0287
    LONGER SUBJECT TO                               Expires: December 31, 2001
    SECTION 16. FORM 4                              Estimated average burden
    OR FORM 5 OBLIGATIONS                           hours per response.... 0.5
    MAY CONTINUE. SEE                               --------------------------
    INSTRUCTION 1(b).

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

                 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP

   Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934,
       Section 17(a) of the Public Utility Holding Company Act of 1935
            or Section 30(f) of the Investment Company Act of 1940


                                                                                                       
(Print or Type Responses)
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 1. Name and Address of Reporting Person*      2. Issuer Name and Ticker or Trading Symbol   6. Relationship of Reporting Person(s)
Slade             Jarvis              J.       PrimeEnergy Corporation PNRG                     to Issuer (Check all applicable)
---------------------------------------------  ----------------------------------------------    X  Director         10% Owner
  (Last)          (First)          (Middle)    3. IRS Identification      4. Statement for      ----              ---
                                                  Number of Reporting        Month/Year             Officer (give    Other (Specify
275 Madison Avenue  Suite 1511                    Person, if an entity    May 2001              ----        title ---       below)
---------------------------------------------     (voluntary)             -------------------               below)
                 (Street)                                                 5. If Amendment,
New York             NY         10016-1101                                   Date of Original
---------------------------------------------     --------------------       (Month/Year)         --------------------------------
  (City)           (State)           (Zip)                                       N/A         7. Individual or Joint/Group Filing
                                                                             -------------      (Check Applicable Line)
                                                                                                  X Form filed by One Reporting
                                                                                                 ---   Person
                                                                                                    Form filed by More than One
                                                                                                 ---   Reporting Person

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                                               TABLE I -- NON-DERIVATIVE SECURITIES ACQUIRED, DISPOSED OF, OR BENEFICIALLY OWNED
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 1. Title of Security         2. Trans-   3. Transac-  4. Securities Acquired (A)  5.  Amount of Se-    6. Owner-      7. Nature
  (Instr. 3)                     action      tion         or Disposed of (D)           curities Benefi-    ship           of In-
                                 Date        Code         (Instr. 3, 4 and 5)          cially Owned at     Form:          direct
                                             (Instr. 8)                                End of Month        Direct         Benefi-
                                (Month/                                                (Instr. 3 and 4)    (D) or         cial
                                 Day/        ------------------------------------                          Indirect       Owner-
                                 Year)       Code    V     Amount  (A) or   Price                          (I)            ship
                                                                   (D)                                     (Instr. 4)     (Instr. 4)
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Common Stock, $.10 par value     5/21/01      S             750    (D)      $15.30
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Common Stock, $.10 par value     5/21/01      S             500    (D)      $16.00
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Common Stock, $.10 par value     5/21/01      S           1,000    (D)      $15.35
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Common Stock, $.10 par value     5/21/01      S           1,000    (D)      $15.25         8,240             (D)
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Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.                   (Over)
* If the form is filed by more than one reporting person, see Instruction 4(b)(v).                                   SEC 1474 (3-99)

                                                        POTENTIAL PERSONS WHO ARE TO RESPOND TO THE COLLECTIONS OF INFORMATION
                                                        CONTAINED IN THIS FORM ARE NOT REQUIRED TO RESPOND UNLESS THE FORM DISPLAYS
                                                        A CURRENTLY VALID OMB CONTROL NUMBER.

   2


FORM 4 (CONTINUED)        TABLE II -- DERIVATIVE SECURITIES ACQUIRED, DISPOSED OF, OR BENEFICIALLY OWNED
                                  (e.g., PUTS, CALLS, WARRANTS, OPTIONS, CONVERTIBLE SECURITIES)

                                                                                                
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1. Title of Derivative    2. Conver-   3. Trans-  4. Trans-   5. Number of     6. Date Exer-   7. Title and Amount   8. Price
   Security                  sion or      action     action      Derivative       cisable and     of Underlying         of
   (Instr. 3)                Exercise     Date       Code        Securities Ac-   Expiration      Securities            Deriv-
                             Price of     (Month/    (Instr. 8)  quired (A) or    Date            (Instr. 3 and 4)      ative
                             Deriv-       Day/                   Disposed of (D)  (Month/Day/                           Secur-
                             ative        Year)                  (Instr. 3, 4,    Year)                                 ity
                             Security                            and 5)                                                 (Instr. 5)
                                                                               -----------------------------------
                                                                               Date    Expira-            Amount or
                                                    -------------------------- Exer-   tion       Title   Number of
                                                    Code  V     (A)     (D)    cisable Date               Shares
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9. Number of           10. Ownership               11. Nature of
   Derivative              Form of                     Indirect
   Securities              Derivative                  Beneficial
   Beneficially            Security:                   Ownership
   Owned at End            Direct (D)                  (Instr. 4)
   of Month                or Indirect (I)
   (Instr. 4)              (Instr. 4)

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Explanation of Responses:


                                                                                           /s/ JARVIS J. SLADE               6/4/01
**Intentional misstatements or omissions of facts constitute Federal Criminal Violations. -----------------------------   ----------
  See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).                                               **Signature of Reporting Person    Date
                                                                                          Jarvis J. Slade

Note: File three copies of this Form, one of which must be manually signed.                                                  Page 2
      If space is insufficient, see Instruction 6 for procedure.                                                     SEC 1474 (3-99)

Potential persons who are to respond to the collection of information contained
in this form are not required to respond unless the form displays a currently
valid OMB number.