<?xml version="1.0"?><ownershipDocument>
    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType><periodOfReport>2003-12-18</periodOfReport><notSubjectToSection16>0</notSubjectToSection16>
    <issuer>
        <issuerCik>0000318107</issuerCik>
        <issuerName>PRIMA ENERGY CORP</issuerName>
        <issuerTradingSymbol>PENG</issuerTradingSymbol></issuer><reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001228516</rptOwnerCik>
            <rptOwnerName>GUION DOUGLAS J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1099 18TH STREET</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 400</rptOwnerStreet2>
            <rptOwnerCity>DENVER</rptOwnerCity>
            <rptOwnerState>CO</rptOwnerState>
            <rptOwnerZipCode>80202-1908</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
            <reportingOwnerRelationship>
<isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common stock</value></securityTitle><transactionDate><value>2003-12-18</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>18900.0000</value></transactionShares><transactionPricePerShare><value>6.6700</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>29621.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common stock</value></securityTitle><transactionDate><value>2003-12-18</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>18900.0000</value></transactionShares><transactionPricePerShare><value>34.3100</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>10721.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeTransaction><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>6.6700</value></conversionOrExercisePrice><transactionDate><value>2003-12-18</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>18900.0000</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2008-09-17</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>18900.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>0</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>9.8300</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2009-09-17</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>5625.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>5625.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>32.3300</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2010-09-17</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>5625.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>5625.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>23.5600</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2011-09-17</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>5625.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>5625.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>20.7800</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2012-09-17</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>5625.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>5625.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding><derivativeHolding><securityTitle><value>Stock options</value></securityTitle><conversionOrExercisePrice><value>25.8300</value></conversionOrExercisePrice><exerciseDate><footnoteId id="F1" /></exerciseDate><expirationDate><value>2013-09-17</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>5625.0000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>5625.0000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeHolding></derivativeTable><footnotes><footnote id="F1">Stock options vest 20% per year over five years.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>Sandra J. Irlando as Attorney-in-Fact for
Douglas J. Guion</signatureName><signatureDate>2003-12-19</signatureDate></ownerSignature></ownershipDocument>

